# LaTeX2HTML 2002-2-1 (1.71)
# Associate images original text with physical files.


$key = q/{displaymath}P={calE},I=(0.020),(1)=0.020,{{rm{W}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1024.png"
 ALT="\begin{displaymath}
P = {\cal E} I = (0.020) (1) = 0.020 {\rm W}.
\end{displaymath}">|; 

$key = q/V_0slashV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img512.png"
 ALT="$V_0/V$">|; 

$key = q/E=c,B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1278.png"
 ALT="$E=c B$">|; 

$key = q/24^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1339.png"
 ALT="$24^\circ$">|; 

$key = q/I_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img641.png"
 ALT="$I_0$">|; 

$key = q/10^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1264.png"
 ALT="$10^{-1}$">|; 

$key = q/{{bf{a}times{{bf{b}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="${\bf a}\times{\bf b} = {\bf0}$">|; 

$key = q/q_b=+4.0,mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img276.png"
 ALT="$q_b=+4.0 \mu{\rm C}$">|; 

$key = q/{displaymath}V=(10),(1.0times10^{-3})=1.0times10^{-2},{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img689.png"
 ALT="\begin{displaymath}
V = (10)  (1.0\times 10^{-3}) = 1.0\times 10^{-2}  {\rm V}.
\end{displaymath}">|; 

$key = q/sin(2pi,f,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img955.png"
 ALT="$\sin(2\pi  f  t)$">|; 

$key = q/{{bf{f}_{ca};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="${\bf f}_{ca}$">|; 

$key = q/displaystylef_{ac,y}+f_{bc,y}=3.45times10^{-3},{{rm{N}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img300.png"
 ALT="$\displaystyle f_{ac y} + f_{bc y} = 3.45 \times 10^{-3} {\rm N}.$">|; 

$key = q/{displaymath}V_c=V_a+V_b=1.20,times10^3,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img472.png"
 ALT="\begin{displaymath}
V_c = V_a + V_b =1.20 \times 10^3 {\rm V}.
\end{displaymath}">|; 

$key = q/{displaymath}E_b=-k_e,frac{q_b}{(cslash2)^2}=-(8.988times10^9),frac{(100times10^{-6})}{(0.5)^2}=-3.60times10^6,{{rm{N,C}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img315.png"
 ALT="\begin{displaymath}
E_b = -k_e \frac{q_b}{(c/2)^2} = -(8.988\times 10^9)  \fra...
...\times 10^{-6})}{(0.5)^2}
= -3.60\times 10^6 {\rm N C}^{-1}.
\end{displaymath}">|; 

$key = q/y(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img679.png"
 ALT="$y(x)$">|; 

$key = q/stackrel{displaystylerightarrow}{PR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="28" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\stackrel{\displaystyle \rightarrow}{PR}$">|; 

$key = q/V_B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img383.png"
 ALT="$V_B$">|; 

$key = q/{displaymath}frac{N_1}{N_2}=sqrt{frac{R'}{R}}=sqrt{frac{2times10^3}{5}}=20.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="56" BORDER="0"
 SRC="|."$dir".q|img1208.png"
 ALT="\begin{displaymath}
\frac{N_1}{N_2} = \sqrt{\frac{R'}{R} } = \sqrt{\frac{2\times 10^3}{5}}
= 20.
\end{displaymath}">|; 

$key = q/{{bf{a}equiv,stackrel{displaystylerightarrow}{PQ},equiv,stackrel{displaystylerightarrow}{SR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="${\bf a}\equiv  \stackrel{\displaystyle \rightarrow}{PQ} \equiv \stackrel{\displaystyle \rightarrow}{SR}$">|; 

$key = q/{{bf{a}times{{bf{a}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="${\bf a}\times{\bf a} = {\bf0}$">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{cyl.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="369" HEIGHT="399" BORDER="0"
 SRC="|."$dir".q|img334.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{cyl.eps}}
\end{figure}">|; 

$key = q/S,cosalpha_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$S \cos\alpha_y$">|; 

$key = q/{{bf{I}'=q,n,A,{{bf{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img763.png"
 ALT="${\bf I}' = q n A {\bf v}$">|; 

$key = q/{calE}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1002.png"
 ALT="${\cal E}_2$">|; 

$key = q/{displaymath}-I_3,R_3-{calE}_2-{calE}_1+I_2,R_2=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="239" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img717.png"
 ALT="\begin{displaymath}
-I_3 R_3 -{\cal E}_2 -{\cal E}_1 + I_2 R_2 = 0.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{solenoid.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="443" HEIGHT="349" BORDER="0"
 SRC="|."$dir".q|img809.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{solenoid.eps}}
\end{figure}">|; 

$key = q/{displaymath}{{bf{f}_{ba}=-{{bf{f}_{ab},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="\begin{displaymath}
{\bf f}_{ba} = - {\bf f}_{ab},
\end{displaymath}">|; 

$key = q/{{bf{b}=(1slashsqrt{2},,1slashsqrt{2},,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="${\bf b} = (1/\sqrt{2}, 
1/\sqrt{2},  0)$">|; 

$key = q/10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1263.png"
 ALT="$10^{-4}$">|; 

$key = q/{displaymath}frac{d}{dt}left({{bf{a}times{{bf{b}right)=frac{d{{bf{a}}{dt}times{{bf{b}+{{bf{a}timesfrac{d{{bf{b}}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="\begin{displaymath}
\frac{d}{dt}\left({\bf a}\times{\bf b}\right) = \frac{d{\bf a}}{dt}\times{\bf b} + {\bf a}\times
\frac{d{\bf b}}{dt}.
\end{displaymath}">|; 

$key = q/v_1=cslashn_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1309.png"
 ALT="$v_1=c/n_1$">|; 

$key = q/v_d,dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img623.png"
 ALT="$v_d dt$">|; 

$key = q/{displaymath}V_2=omega,(L_2,I_2+M,I_1).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1147.png"
 ALT="\begin{displaymath}
V_2 = \omega  (L_2 I_2 + M I_1).
\end{displaymath}">|; 

$key = q/{displaymath}V(x)=frac{q}{4piepsilon_0,x}+V_0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img430.png"
 ALT="\begin{displaymath}
V(x)= \frac{q}{4\pi\epsilon_0 x} + V_0,
\end{displaymath}">|; 

$key = q/{displaymath}i_2=I_2,sin(omega,t){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1140.png"
 ALT="\begin{displaymath}
i_2 = I_2 \sin (\omega  t)
\end{displaymath}">|; 

$key = q/{displaymath}E_0=c,B_0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1249.png"
 ALT="\begin{displaymath}
E_0= c B_0.
\end{displaymath}">|; 

$key = q/c,dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1273.png"
 ALT="$c dt$">|; 

$key = q/{displaymath}V=V_{{rm{max},sin(2pi,f,t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img963.png"
 ALT="\begin{displaymath}
V = V_{\rm max}  \sin (2\pi  f  t),
\end{displaymath}">|; 

$key = q/{displaymath}V+{calE}=i,R,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1096.png"
 ALT="\begin{displaymath}
V + {\cal E} = i R,
\end{displaymath}">|; 

$key = q/{displaymath}oint_{S}{{bf{v}cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="\begin{displaymath}
\oint_{S} {\bf v}\cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/w(r)=2pi,r,B(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img884.png"
 ALT="$w(r) = 2\pi  r B(r)$">|; 

$key = q/M_{12}=M_{21};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1050.png"
 ALT="$M_{12}= M_{21}$">|; 

$key = q/V_a=Q_aslash(4piepsilon_0,a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img488.png"
 ALT="$V_a = Q_a/(4\pi\epsilon_0 a)$">|; 

$key = q/I=VslashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img980.png"
 ALT="$I=V/R$">|; 

$key = q/displaystylea_x,b_x+a_y,b_y+a_z,b_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\displaystyle a_x  b_x + a_y  b_y + a_z  b_z.$">|; 

$key = q/alpha_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$\alpha_x$">|; 

$key = q/{displaymath}f=frac{q,q'}{4piepsilon_0,r^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="\begin{displaymath}
f = \frac{q q'}{4\pi\epsilon_0 r^2},
\end{displaymath}">|; 

$key = q/Q_{12}=Q_1+Q_2=10.3,mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img595.png"
 ALT="$Q_{12} = Q_1+Q_2 = 10.3 \mu{\rm C}$">|; 

$key = q/{displaymath}C=frac{epsilon,A}{d},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img516.png"
 ALT="\begin{displaymath}
C = \frac{\epsilon A}{d},
\end{displaymath}">|; 

$key = q/{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="${\bf S}$">|; 

$key = q/prightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1391.png"
 ALT="$p\rightarrow\infty$">|; 

$key = q/{displaymath}{mitDelta}V=E_x,d=(1.40times10^3),(5.00times10^{-2})=70.0,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img446.png"
 ALT="\begin{displaymath}
{\mit\Delta}V = E_x d = (1.40\times 10^3) (5.00\times 10^{-2})=70.0 {\rm V}.
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{(3.24times10^6)}{(3.6times10^6)}=0.9,{{rm{kWh}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img738.png"
 ALT="\begin{displaymath}
W = \frac{(3.24\times 10^6)}{(3.6\times 10^6)} = 0.9 {\rm kWh}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{rainbow2.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="483" HEIGHT="403" BORDER="0"
 SRC="|."$dir".q|img1346.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{rainbow2.eps}}
\end{figure}">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{critical.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="638" HEIGHT="402" BORDER="0"
 SRC="|."$dir".q|img1332.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{critical.eps}}
\end{figure}">|; 

$key = q/R_b<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1418.png"
 ALT="$R_b&lt;0$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{dc.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="673" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img962.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{dc.eps}}
\end{figure}">|; 

$key = q/P=-{calE},i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1083.png"
 ALT="$P=-{\cal E} i$">|; 

$key = q/{{bf{a}+{{bf{b}={{bf{b}+{{bf{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="${\bf a} + {\bf b} = {\bf b}+{\bf a}$">|; 

$key = q/{displaymath}{calE}_2=-M,frac{dI_1}{dt}=-(0.0188),frac{(10-0)}{(0.1)}=-1.88,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1176.png"
 ALT="\begin{displaymath}
{\cal E}_2 = - M \frac{dI_1}{d t}=
-(0.0188) \frac{(10-0)}{(0.1)} = -1.88  {\rm V}.
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{B^2}{2,mu_0},,l,A.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1087.png"
 ALT="\begin{displaymath}
W = \frac{B^2}{2 \mu_0}   l A.
\end{displaymath}">|; 

$key = q/V=10^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img869.png"
 ALT="$V=10^3$">|; 

$key = q/10^{-7};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1262.png"
 ALT="$10^{-7}$">|; 

$key = q/{displaymath}{mitDelta}P=-q_c,V_c=-(2times10^{-6}),(1.2times10^3)=-2.40times10^{-3},{{rm{J}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="470" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img474.png"
 ALT="\begin{displaymath}
{\mit\Delta}P = -q_c V_c = -(2\times 10^{-6}) (1.2\times 10^3)=-2.40\times 10^{-3} {\rm J}.
\end{displaymath}">|; 

$key = q/{displaymath}y_m'=frac{(m+1slash2),lambda,L}{d},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1508.png"
 ALT="\begin{displaymath}
y_m' = \frac{(m+1/2) \lambda L}{d},
\end{displaymath}">|; 

$key = q/90^circ-theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img290.png"
 ALT="$90^\circ-\theta$">|; 

$key = q/2times10^{-7};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img758.png"
 ALT="$2\times 10^{-7}$">|; 

$key = q/{{bf{c}equiv,stackrel{displaystylerightarrow}{PR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="28" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="${\bf c} \equiv
 \stackrel{\displaystyle \rightarrow}{PR}$">|; 

$key = q/{displaymath}W'=-{mitDelta}P.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img451.png"
 ALT="\begin{displaymath}
W' = - {\mit\Delta}P.
\end{displaymath}">|; 

$key = q/{displaymath}1,{{rm{A}equiv1,{{rm{C,s}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img605.png"
 ALT="\begin{displaymath}
1 {\rm A} \equiv 1 {\rm C  s}^{-1}.
\end{displaymath}">|; 

$key = q/B_2=5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img985.png"
 ALT="$B_2=5$">|; 

$key = q/{displaymath}I_1,V_1=omega,(L_1,I_1^{~2}+M,I_1,I_2)=omega,(L_2,I_2^{~2}+M,I_1,I_2)=I_2,V_2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="470" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1152.png"
 ALT="\begin{displaymath}
I_1 V_1 = \omega (L_1 I_1^{&nbsp;2} + M I_1 I_2)
= \omega  (L_2 I_2^{&nbsp;2} + M I_1 I_2) = I_2 V_2,
\end{displaymath}">|; 

$key = q/I_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img835.png"
 ALT="$I_{\rm max}$">|; 

$key = q/P;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$P$">|; 

$key = q/q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="$q$">|; 

$key = q/{{rm{J,C}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img385.png"
 ALT="${\rm J C}^{-1}$">|; 

$key = q/B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img362.png"
 ALT="$B$">|; 

$key = q/{displaymath}I_1=I_2+I_3=-1.2+1.2=0,{{rm{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img729.png"
 ALT="\begin{displaymath}
I_1 = I_2 + I_3 = -1.2+1.2 = 0 {\rm A}.
\end{displaymath}">|; 

$key = q/{calE}=N,B_parallel,A,omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img949.png"
 ALT="${\cal E} = N B_\parallel A \omega$">|; 

$key = q/V(q)=qslashC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img550.png"
 ALT="$V(q) = q/C$">|; 

$key = q/{displaymath}V(x)=V_0-E_x,x,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img408.png"
 ALT="\begin{displaymath}
V(x) = V_0 - E_x x,
\end{displaymath}">|; 

$key = q/d=0.60;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img563.png"
 ALT="$d=0.60$">|; 

$key = q/8.85times10^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img633.png"
 ALT="$8.85\times 10^{-8}$">|; 

$key = q/R_brightarrow-R_f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1416.png"
 ALT="$R_b \rightarrow -R_f$">|; 

$key = q/a_x=a,costheta_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$a_x=a \cos\theta_x$">|; 

$key = q/V_+-V_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img387.png"
 ALT="$V_+-V_-$">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img735.png"
 ALT="$t$">|; 

$key = q/{displaymath}f=F,l=(1.7times10^{-4}),(1.2)=2.04times10^{-4},{{rm{N}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img865.png"
 ALT="\begin{displaymath}
f = F l = (1.7\times 10^{-4}) (1.2) = 2.04\times 10^{-4} {\rm N}.
\end{displaymath}">|; 

$key = q/M=0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1457.png"
 ALT="$M=0.1$">|; 

$key = q/theta_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1327.png"
 ALT="$\theta_c$">|; 

$key = q/theta_1=30^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1360.png"
 ALT="$\theta_1=30^\circ$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{young1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="501" HEIGHT="340" BORDER="0"
 SRC="|."$dir".q|img1495.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{young1.eps}}
\end{figure}">|; 

$key = q/C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img502.png"
 ALT="$C$">|; 

$key = q/{displaymath}{{bf{F}={{bf{I}'times{{bf{B},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img745.png"
 ALT="\begin{displaymath}
{\bf F} = {\bf I}' \times{\bf B},
\end{displaymath}">|; 

$key = q/A_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1003.png"
 ALT="$A_1$">|; 

$key = q/l=0.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1014.png"
 ALT="$l=0.2$">|; 

$key = q/QslashV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img533.png"
 ALT="$Q/V$">|; 

$key = q/Q_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img500.png"
 ALT="$Q_0$">|; 

$key = q/R_S+R_G;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img852.png"
 ALT="$R_S+R_G$">|; 

$key = q/V_2=50;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1201.png"
 ALT="$V_2= 50$">|; 

$key = q/dislashdt=20,{{rm{A,s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1185.png"
 ALT="$d i/dt=20 {\rm A s}^{-1}$">|; 

$key = q/{displaymath}P=tau,omega={calE},I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img950.png"
 ALT="\begin{displaymath}
P= \tau \omega = {\cal E}  I.
\end{displaymath}">|; 

$key = q/N=15;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img982.png"
 ALT="$N=15$">|; 

$key = q/A(r)=4pi,r^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img354.png"
 ALT="$A(r) = 4\pi  r^2$">|; 

$key = q/{displaymath}lambda_2=frac{(2),(1.36),(250times10^{-9})}{(2)}=340,{{rm{nm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1531.png"
 ALT="\begin{displaymath}
\lambda_2 = \frac{(2) (1.36) (250\times 10^{-9})}{(2)} = 340 {\rm nm}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{q}{m}=frac{2,d,E}{l^2,B^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img777.png"
 ALT="\begin{displaymath}
\frac{q}{m} = \frac{2 d  E}{l^2  B^2}.
\end{displaymath}">|; 

$key = q/V_0=200;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img570.png"
 ALT="$V_0= 200$">|; 

$key = q/{displaymath}E_r(r)=left{array{{lcl}frac{Q}{4piepsilon_0,r^2}&mbox{hspace{1cm}}&ex]frac{Q,r}{4piepsilon_0,a^3}&&r<aarray{right..{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img358.png"
 ALT="\begin{displaymath}
E_r(r) =
\left\{\begin{array}{lcl}
\frac{Q}{4\pi\epsilon_0 ...
...5ex]
\frac{Q r}{4\pi\epsilon_0 a^3}&amp;&amp;r&lt;a
\end{array}\right..
\end{displaymath}">|; 

$key = q/V_b=Q_bslash(4piepsilon_0,b);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img489.png"
 ALT="$V_b = Q_b/(4\pi\epsilon_0 b)$">|; 

$key = q/t=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$t=0$">|; 

$key = q/{displaymath}{calE}_2=-frac{d{mitPhi}_{2}}{dt}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1056.png"
 ALT="\begin{displaymath}
{\cal E}_2 = - \frac{d{\mit\Phi}_{2}}{d t}
\end{displaymath}">|; 

$key = q/n_2>n_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1304.png"
 ALT="$n_2&gt;n_1$">|; 

$key = q/displaystyle-frac{d}{dt}int_{S'}{{bf{B}cdotd{{bf{S}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1237.png"
 ALT="$\displaystyle - \frac{d}{dt}\int_{S'}{\bf B}\cdot d{\bf S}',$">|; 

$key = q/tantheta=-h'slashq;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1380.png"
 ALT="$\tan\theta=-h'/q$">|; 

$key = q/{displaymath}{{bf{a}times{{bf{b}=left|array{{ccc}{{bf{e}_x&{{bf{e}_y&{{bf{e}_z[0.5ex]a_x&a_y&a_z[0.5ex]b_x&b_y&b_zarray{right|.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="84" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="\begin{displaymath}
{\bf a}\times {\bf b} = \left\vert\begin{array}{ccc}
{\bf e}...
...a_x&amp; a_y&amp; a_z\ [0.5ex]
b_x &amp; b_y &amp; b_z\end{array}\right\vert.
\end{displaymath}">|; 

$key = q/{displaymath}h'=M,h=-(6.67),(4)=-26.67,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="302" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1454.png"
 ALT="\begin{displaymath}
h' = M h = -(6.67) (4) = -26.67 {\rm cm}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{atomic.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="459" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img822.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{atomic.eps}}
\end{figure}">|; 

$key = q/displaystyle(10),(10times10^{-4}),(4pitimes10^{-7}),(400),frac{(50)}{(2)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1010.png"
 ALT="$\displaystyle (10) (10\times10^{-4}) (4\pi\times 10^{-7})  (400) \frac{(50)}{(2)}$">|; 

$key = q/{displaymath}K={mitDelta}K=-{mitDelta}P=2.40times10^{-3},{{rm{J}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img476.png"
 ALT="\begin{displaymath}
K = {\mit\Delta}K = -{\mit\Delta}P = 2.40\times 10^{-3} {\rm J}.
\end{displaymath}">|; 

$key = q/{{rm{e}^{-5}<0.01;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1109.png"
 ALT="${\rm e}^{-5}&lt; 0.01$">|; 

$key = q/{displaymath}oint_C{{bf{E}cdotd{{bf{r}=-frac{d{mitPhi}_B}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img902.png"
 ALT="\begin{displaymath}
\oint_C {\bf E} \cdot d{\bf r}= -\frac{d{\mit\Phi}_B}{dt}.
\end{displaymath}">|; 

$key = q/3,mu{{rm{F};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img586.png"
 ALT="$3 \mu{\rm F}$">|; 

$key = q/{displaymath}{{bf{a}=a_x,{{bf{e}_x+a_y,{{bf{e}_y+a_z,{{bf{e}_z.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="\begin{displaymath}
{\bf a} = a_x  {\bf e}_x + a_y  {\bf e}_y + a_z {\bf e}_z.
\end{displaymath}">|; 

$key = q/{displaymath}W={{bf{F}!cdot!{{bf{r}=-q,{{bf{E}!cdot!{{bf{r}=-q,E,r,costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img361.png"
 ALT="\begin{displaymath}
W = {\bf F} \!\cdot\! {\bf r} = -q {\bf E}\!\cdot\! {\bf r} = -q  E  r 
\cos\theta.
\end{displaymath}">|; 

$key = q/x_1=5.1,{{rm{cm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="$x_1=5.1 {\rm cm}$">|; 

$key = q/{displaymath}M_{12}=M_{21}=M,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1051.png"
 ALT="\begin{displaymath}
M_{12}= M_{21} = M,
\end{displaymath}">|; 

$key = q/h=7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1465.png"
 ALT="$h=7$">|; 

$key = q/displaystyle-a_xsintheta+a_ycostheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\displaystyle -a_x\sin\theta + a_y\cos\theta,$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{motor1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="494" HEIGHT="342" BORDER="0"
 SRC="|."$dir".q|img977.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{motor1.eps}}
\end{figure}">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{a}=|a|^2=a^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="\begin{displaymath}
{\bf a} \cdot {\bf a} = \vert a\vert^2 = a^2.
\end{displaymath}">|; 

$key = q/{displaymath}{calE}={calE}_{{rm{max},sin(2pi,f,t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img939.png"
 ALT="\begin{displaymath}
{\cal E} = {\cal E}_{\rm max} \sin (2\pi  f  t),
\end{displaymath}">|; 

$key = q/{{bf{f}_{ba};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="${\bf f}_{ba}$">|; 

$key = q/{displaymath}-R_2,I_2+R_3,I_3=-({calE}_1+{calE}_2).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img720.png"
 ALT="\begin{displaymath}
-R_2 I_2 +R_3 I_3 = -({\cal E}_1 +{\cal E}_2).
\end{displaymath}">|; 

$key = q/{displaymath}f_{ac}=k_e,frac{|q_a|,q_c}{c^2}=(8.988times10^9),frac{(6times10^{-6es10^{-6})}{(4^2+3^2)}=4.31times10^{-3},{{rm{N},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img282.png"
 ALT="\begin{displaymath}
f_{ac} = k_e \frac{\vert q_a\vert  q_c}{c^2}= (8.988\times...
...2\times 10^{-6})}
{(4^2+3^2)} = 4.31 \times 10^{-3}  {\rm N},
\end{displaymath}">|; 

$key = q/B_0=E_0slashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1294.png"
 ALT="$B_0=E_0/c$">|; 

$key = q/1.33;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1334.png"
 ALT="$1.33$">|; 

$key = q/K;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img453.png"
 ALT="$K$">|; 

$key = q/V=800,{{rm{V};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1190.png"
 ALT="$V = 800 {\rm V}$">|; 

$key = q/{displaymath}1,{{rm{J,C^{-1}}equiv1,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img386.png"
 ALT="\begin{displaymath}
1 {\rm J  C^{-1}} \equiv 1 {\rm V}.
\end{displaymath}">|; 

$key = q/RL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$RL$">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img518.png"
 ALT="$\epsilon$">|; 

$key = q/{displaymath}frac{P_1}{P_2}=frac{I_1^{~2},R}{I_2^{~2},R}=left(frac{2times10^6}{2times10^4}right)^2=10000,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1206.png"
 ALT="\begin{displaymath}
\frac{P_1}{P_2} = \frac{I_1^{&nbsp;2} R}{I_2^{&nbsp;2} R} = \left(\frac{2\times 10^6}
{2\times 10^4}\right)^2 = 10000,
\end{displaymath}">|; 

$key = q/d{{bf{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="$d{\bf r}$">|; 

$key = q/d{mitPhi}_B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img892.png"
 ALT="$d{\mit\Phi}_B$">|; 

$key = q/C=epsilon_0,Aslashd;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1224.png"
 ALT="$C=\epsilon_0  A/d$">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{b}=|a|,|b|,costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="\begin{displaymath}
{\bf a} \cdot {\bf b} = \vert a\vert  \vert b\vert  \cos\theta.
\end{displaymath}">|; 

$key = q/f_{13};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="$f_{13}$">|; 

$key = q/f_{13}=-41.69,{{rm{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="$f_{13} = - 41.69 {\rm N}$">|; 

$key = q/{displaymath}A=pi,r^2=pi,(0.1)^2=0.0314,{{rm{m}^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img988.png"
 ALT="\begin{displaymath}
A = \pi r^2 = \pi (0.1)^2 = 0.0314 {\rm m}^2.
\end{displaymath}">|; 

$key = q/{displaymath}q(r)=left{array{{lcl}Q&mbox{hspace{1cm}}&rgeqa[0.5ex]Q,(rslasha)^3&&r<aarray{right..{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="57" BORDER="0"
 SRC="|."$dir".q|img357.png"
 ALT="\begin{displaymath}
q(r) =
\left\{\begin{array}{lcl}
Q&amp;\mbox{\hspace{1cm}}&amp;r\geq a\ [0.5ex]
Q (r/a)^3&amp;&amp;r&lt;a
\end{array}\right..
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{anal1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="642" HEIGHT="342" BORDER="0"
 SRC="|."$dir".q|img1429.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{anal1.eps}}
\end{figure}">|; 

$key = q/{{bf{F};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="${\bf F}$">|; 

$key = q/displaystyleint_0^ar^3,drint_0^{pislash2}sintheta,costheta,dthetaint_0^{2pi}dphi=frac{pi,a^4}{4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="341" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="$\displaystyle \int_0^a r^3 dr \int_0^{\pi/2} \sin\theta  \cos\theta d\theta \int_0^{2\pi}
d\phi = \frac{\pi  a^4}{4},$">|; 

$key = q/{displaymath}rho=frac{2,m}{q^2,N,tau}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img626.png"
 ALT="\begin{displaymath}
\rho = \frac{2 m}{q^2 N \tau}.
\end{displaymath}">|; 

$key = q/gamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1258.png"
 ALT="$\gamma$">|; 

$key = q/{displaymath}lambda_m'=frac{2,n,t}{m+1slash2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1533.png"
 ALT="\begin{displaymath}
\lambda_m' = \frac{2 n t}{m+1/2},
\end{displaymath}">|; 

$key = q/{mitPhi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1070.png"
 ALT="${\mit\Phi}$">|; 

$key = q/{{bf{f}_{ac};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img281.png"
 ALT="${\bf f}_{ac}$">|; 

$key = q/I=5.0,{{rm{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1034.png"
 ALT="$I=5.0 {\rm A}$">|; 

$key = q/{displaymath}E=frac{q}{4piepsilon_0,r^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="\begin{displaymath}
E= \frac{q}{4\pi\epsilon_0 r^2},
\end{displaymath}">|; 

$key = q/{displaymath}R=frac{V}{I}=frac{(120)}{(1.25)}=96,Omega.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img734.png"
 ALT="\begin{displaymath}
R = \frac{V}{I} = \frac{(120)}{(1.25)} = 96  \Omega.
\end{displaymath}">|; 

$key = q/{displaymath}q=C,v=Q-i,R,C,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1122.png"
 ALT="\begin{displaymath}
q = C  v = Q -i R C,
\end{displaymath}">|; 

$key = q/{displaymath}omega,L_1,I_1^{~2}=omega,L_2,I_2^{~2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1153.png"
 ALT="\begin{displaymath}
\omega L_1 I_1^{&nbsp;2} = \omega  L_2 I_2^{&nbsp;2},
\end{displaymath}">|; 

$key = q/{displaymath}oint_S{{bf{E}cdotd{{bf{S}=frac{Q}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img326.png"
 ALT="\begin{displaymath}
\oint_S {\bf E}\cdot d{\bf S}=\frac{Q}{\epsilon_0},
\end{displaymath}">|; 

$key = q/I_{{rm{fsd},R_G;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img841.png"
 ALT="$I_{\rm fsd} R_G$">|; 

$key = q/{displaymath}1,{{rm{eV}equiv1.6times10^{-19},{{rm{J}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img393.png"
 ALT="\begin{displaymath}
1 {\rm eV} \equiv 1.6\times 10^{-19} {\rm J}.
\end{displaymath}">|; 

$key = q/Q=Q_a+Q_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img487.png"
 ALT="$Q = Q_a + Q_b$">|; 

$key = q/{displaymath}{mitPhi}_B=N_2,A_1,B.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1006.png"
 ALT="\begin{displaymath}
{\mit\Phi}_B = N_2 A_1 B.
\end{displaymath}">|; 

$key = q/S_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$S_x$">|; 

$key = q/10^{-11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1260.png"
 ALT="$10^{-11}$">|; 

$key = q/i=2.0,{{rm{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1184.png"
 ALT="$i=2.0 {\rm A}$">|; 

$key = q/{displaymath}oint_C{{bf{B}cdotd{{bf{r}=mu_0,I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img808.png"
 ALT="\begin{displaymath}
\oint_C {\bf B} \cdot d{\bf r} = \mu_0 I.
\end{displaymath}">|; 

$key = q/{{bf{f}_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img296.png"
 ALT="${\bf f}_c$">|; 

$key = q/{displaymath}W'=1.6times10^{-16},{{rm{J}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img452.png"
 ALT="\begin{displaymath}
W' = 1.6\times 10^{-16} {\rm J}.
\end{displaymath}">|; 

$key = q/{displaymath}tau=frac{{calE},I}{omega},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img948.png"
 ALT="\begin{displaymath}
\tau = \frac{{\cal E}  I}{\omega},
\end{displaymath}">|; 

$key = q/{displaymath}M_{12}=frac{{mitPhi}_{1}}{I_2}=frac{mu_0,N_1,N_2,A}{l}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1067.png"
 ALT="\begin{displaymath}
M_{12} = \frac{{\mit\Phi}_{1}}{I_2} = \frac{\mu_0 N_1 N_2 A}{l}.
\end{displaymath}">|; 

$key = q/{displaymath}sintheta_2=frac{(1.00)}{(1.52)},(0.5)=0.329,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1363.png"
 ALT="\begin{displaymath}
\sin\theta_2 =\frac{(1.00)}{(1.52)} (0.5)=0.329,
\end{displaymath}">|; 

$key = q/{displaymath}R_S=frac{1000}{1times10^{-5}}-40simeq10^8,Omega.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img857.png"
 ALT="\begin{displaymath}
R_S = \frac{1000}{1\times 10^{-5}} - 40 \simeq 10^8 \Omega.
\end{displaymath}">|; 

$key = q/2.0,{{rm{s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img998.png"
 ALT="$2.0 {\rm s}$">|; 

$key = q/{displaymath}theta_2=19.2^circ{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1364.png"
 ALT="\begin{displaymath}
\theta_2 = 19.2^\circ
\end{displaymath}">|; 

$key = q/V_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img539.png"
 ALT="$V_1$">|; 

$key = q/{displaymath}{calE}_{{rm{max}=2pi,N,B,A,f{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img940.png"
 ALT="\begin{displaymath}
{\cal E}_{\rm max}= 2\pi N B A f
\end{displaymath}">|; 

$key = q/R=0.020,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1017.png"
 ALT="$R=0.020 \Omega$">|; 

$key = q/100;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img848.png"
 ALT="$100$">|; 

$key = q/R_frightarrow-R_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1415.png"
 ALT="$R_f\rightarrow -R_b$">|; 

$key = q/{displaymath}2,y_4=12.6,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1526.png"
 ALT="\begin{displaymath}
2 y_4 = 12.6 {\rm cm}.
\end{displaymath}">|; 

$key = q/C_{{rm{eq}=QslashV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img542.png"
 ALT="$C_{\rm eq} = Q/V$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{qt.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="228" BORDER="0"
 SRC="|."$dir".q|img1132.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{qt.eps}}
\end{figure}">|; 

$key = q/{displaymath}f=frac{c}{lambda}=frac{(3times10^8)}{(0.3)}=1times10^9,{{rm{Hz}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1287.png"
 ALT="\begin{displaymath}
f = \frac{c}{\lambda} = \frac{(3\times 10^8)}{(0.3)} = 1\times 10^9 {\rm Hz}.
\end{displaymath}">|; 

$key = q/tanalpha=hslash(p-R);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1386.png"
 ALT="$\tan\alpha
=h/(p-R)$">|; 

$key = q/displaystylefrac{Q_a}{Q};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img491.png"
 ALT="$\displaystyle \frac{Q_a}{Q}$">|; 

$key = q/{displaymath}I_1=frac{V_{12}}{R_1}=frac{(0.857)}{(1)}=0.857,{{rm{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img703.png"
 ALT="\begin{displaymath}
I_1 = \frac{V_{12}}{R_1} = \frac{(0.857)}{(1)}= 0.857 {\rm A}.
\end{displaymath}">|; 

$key = q/{displaymath}I=frac{V}{R}=frac{(12)}{(5)}=2.4,{{rm{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1188.png"
 ALT="\begin{displaymath}
I= \frac{V}{R} = \frac{(12)}{(5)} = 2.4  {\rm A}.
\end{displaymath}">|; 

$key = q/{{bf{b}equiv(b_x,b_y,b_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="${\bf b} \equiv (b_x, b_y, b_z)$">|; 

$key = q/sintheta_2=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1330.png"
 ALT="$\sin\theta_2 = 1$">|; 

$key = q/{{bf{f}=q,{{bf{E}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img919.png"
 ALT="${\bf f} = q {\bf E}_0$">|; 

$key = q/{displaymath}K_B-K_A={mitDelta}K=-{mitDelta}P.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img458.png"
 ALT="\begin{displaymath}
K_B - K_A = {\mit\Delta} K = - {\mit\Delta}P.
\end{displaymath}">|; 

$key = q/displaystylefrac{b}{a+b}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img494.png"
 ALT="$\displaystyle \frac{b}{a+b}.$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{film.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="520" HEIGHT="341" BORDER="0"
 SRC="|."$dir".q|img1511.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{film.eps}}
\end{figure}">|; 

$key = q/dw;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img805.png"
 ALT="$dw$">|; 

$key = q/{displaymath}{calE}_{{rm{ext}=|{calE}|={calE}_{{rm{max},|sin(2pi,f,t)|.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img961.png"
 ALT="\begin{displaymath}
{\cal E}_{\rm ext} = \vert{\cal E}\vert = {\cal E}_{\rm max} \vert\sin (2\pi  f  t)\vert.
\end{displaymath}">|; 

$key = q/{displaymath}v=frac{E}{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img776.png"
 ALT="\begin{displaymath}
v = \frac{E}{B}.
\end{displaymath}">|; 

$key = q/R_G=40,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img846.png"
 ALT="$R_G = 40 \Omega$">|; 

$key = q/phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="$\phi$">|; 

$key = q/{displaymath}dV=-{{bf{E}!cdot!d{{bf{r}=-E,dr,costheta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img420.png"
 ALT="\begin{displaymath}
dV = -{\bf E}\!\cdot\! d{\bf r}= -E dr  \cos\theta,
\end{displaymath}">|; 

$key = q/{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img744.png"
 ALT="${\bf B}$">|; 

$key = q/d{{bf{r}=(dfslashdl,dgslashdl,dhslashdl),dl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$d{\bf r} = (df/dl, dg/dl, dh/dl) dl$">|; 

$key = q/q_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img466.png"
 ALT="$q_3$">|; 

$key = q/mu_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img748.png"
 ALT="$\mu_0$">|; 

$key = q/displaystylea_{x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\displaystyle a_{x'}$">|; 

$key = q/{{bf{a}cdot{{bf{b}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="${\bf a} \cdot {\bf b} =0$">|; 

$key = q/P_B-P_A=W;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img442.png"
 ALT="$P_B - P_A = W$">|; 

$key = q/{displaymath}v_1,sintheta_1=v_2,sintheta_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1488.png"
 ALT="\begin{displaymath}
v_1 \sin\theta_1 = v_2 \sin\theta_2.
\end{displaymath}">|; 

$key = q/-1.6times10^{-19};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img779.png"
 ALT="$-1.6\times 10^{-19}$">|; 

$key = q/+y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img291.png"
 ALT="$+y$">|; 

$key = q/{{bf{a}=(1,,0,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="${\bf a} = (1, 0, 0)$">|; 

$key = q/{displaymath}f=frac{c}{n_1,lambda_1}=frac{(3times10^8)}{(1.00),(589times10^{-9})}=5.09times10^{14},{{rm{Hz}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="406" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1366.png"
 ALT="\begin{displaymath}
f = \frac{c}{n_1 \lambda_1} = \frac{(3\times 10^8)}{(1.00) (589\times 10^{-9})}
=5.09\times 10^{14}  {\rm Hz}.
\end{displaymath}">|; 

$key = q/M_{21};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1046.png"
 ALT="$M_{21}$">|; 

$key = q/E_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img314.png"
 ALT="$E_b$">|; 

$key = q/(x',y',z');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$(x', y', z')$">|; 

$key = q/{displaymath}q=frac{1}{1slashf-1slashp}=frac{1}{(1slash20-1slash15)}=-60,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="350" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1444.png"
 ALT="\begin{displaymath}
q = \frac{1}{1/f - 1/p} = \frac{1}{(1/20-1/15)} = - 60 {\rm cm}.
\end{displaymath}">|; 

$key = q/tau=R,C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1131.png"
 ALT="$\tau=R C$">|; 

$key = q/10;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1173.png"
 ALT="$10$">|; 

$key = q/V_{12}=6-5.14=0.857,{{rm{V};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img702.png"
 ALT="$V_{12} = 6-5.14 = 0.857 {\rm V}$">|; 

$key = q/-sigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img507.png"
 ALT="$-\sigma$">|; 

$key = q/12,{{rm{V};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img644.png"
 ALT="$12 {\rm V}$">|; 

$key = q/0.636;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1476.png"
 ALT="$0.636$">|; 

$key = q/tau_{{rm{max}=({calE}_{{rm{max})^2slash(2pi,f,R);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img953.png"
 ALT="$\tau_{\rm max} = ({\cal E}_{\rm max})^2/(2\pi f R)$">|; 

$key = q/x=-a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img343.png"
 ALT="$x=-a$">|; 

$key = q/lambda,Lslashd;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1509.png"
 ALT="$\lambda L/d$">|; 

$key = q/{displaymath}(R_1R_2+R_2R_3+R_1R_3),I_2=(R_1+R_3),{calE}_1+R_1,{calE}_2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="405" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img726.png"
 ALT="\begin{displaymath}
(R_1 R_2 + R_2 R_3+ R_1 R_3) I_2 = (R_1+R_3) {\cal E}_1
+ R_1 {\cal E}_2,
\end{displaymath}">|; 

$key = q/V_a=V_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img490.png"
 ALT="$V_a = V_b$">|; 

$key = q/{displaymath}{calE}=-frac{d{mitPhi}}{dt}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1074.png"
 ALT="\begin{displaymath}
{\cal E} = - \frac{d{\mit\Phi}}{d t}
\end{displaymath}">|; 

$key = q/{displaymath}h'=M,h=(4),(4)=16,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1448.png"
 ALT="\begin{displaymath}
h' = M h = (4) (4) = 16 {\rm cm}.
\end{displaymath}">|; 

$key = q/L_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1142.png"
 ALT="$L_1$">|; 

$key = q/E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img316.png"
 ALT="$E$">|; 

$key = q/{displaymath}i'(t)=-I,{{rm{e}^{-R,tslashL}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1102.png"
 ALT="\begin{displaymath}
i'(t) = -I {\rm e}^{-R t/L}.
\end{displaymath}">|; 

$key = q/E=vslashd;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1218.png"
 ALT="$E= v/d$">|; 

$key = q/{displaymath}E=frac{sigma}{2,epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img348.png"
 ALT="\begin{displaymath}
E = \frac{\sigma}{2 \epsilon_0}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{rc.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="227" BORDER="0"
 SRC="|."$dir".q|img1120.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{rc.eps}}
\end{figure}">|; 

$key = q/A=w,l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img931.png"
 ALT="$A=w l$">|; 

$key = q/N_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1005.png"
 ALT="$N_2$">|; 

$key = q/2.0,{{rm{k}Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1207.png"
 ALT="$2.0 {\rm k}\Omega$">|; 

$key = q/y=g(l);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$y=g(l)$">|; 

$key = q/{displaymath}n_1,sintheta_1=n_2,sintheta_2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1299.png"
 ALT="\begin{displaymath}
n_1 \sin\theta_1 = n_2 \sin\theta_2,
\end{displaymath}">|; 

$key = q/{displaymath}frac{dsin(omega,t)}{dt}=omega,cos(omega,t).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1144.png"
 ALT="\begin{displaymath}
\frac{d\sin(\omega t)}{dt} = \omega \cos(\omega t).
\end{displaymath}">|; 

$key = q/{displaymath}{calE}=frac{d{mitPhi}_B}{dt}=B,l,v.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img910.png"
 ALT="\begin{displaymath}
{\cal E} = \frac{d{\mit\Phi}_B}{d t} = B l v.
\end{displaymath}">|; 

$key = q/R_1=100,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img707.png"
 ALT="$R_1= 100 \Omega$">|; 

$key = q/Q_a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img485.png"
 ALT="$Q_a$">|; 

$key = q/{displaymath}dW=V,dq.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img547.png"
 ALT="\begin{displaymath}
dW = V dq.
\end{displaymath}">|; 

$key = q/-x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="$-x$">|; 

$key = q/{{bf{a}cdot{{bf{a}times{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="${\bf a}\cdot {\bf a}\times{\bf b}$">|; 

$key = q/I>I_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img640.png"
 ALT="$I&gt;I_0$">|; 

$key = q/{displaymath}omega=frac{e,B}{m_e}=frac{(1.6times10^{-19}),(1.2)}{(9.11times10^{-31})}=2.11times10^{11},{{rm{rad.,s}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="427" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img877.png"
 ALT="\begin{displaymath}
\omega = \frac{e B}{m_e} = \frac{ (1.6\times 10^{-19}) (1....
....11\times 10^{-31})}
= 2.11\times 10^{11} {\rm rad. s}^{-1}.
\end{displaymath}">|; 

$key = q/sigma=QslashA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img508.png"
 ALT="$\sigma=Q/A$">|; 

$key = q/dW={{bf{F}cdotd{{bf{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="$dW={\bf F}\cdot d{\bf r}$">|; 

$key = q/displaystyleoint_S{{bf{E}cdotd{{bf{S},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1233.png"
 ALT="$\displaystyle \oint_S {\bf E}\cdot d{\bf S},$">|; 

$key = q/{displaymath}M_{21}=frac{{mitPhi}_{2}}{I_1}=frac{mu_0,N_1,N_2,A}{l}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1064.png"
 ALT="\begin{displaymath}
M_{21}= \frac{{\mit\Phi}_{2}}{I_1} = \frac{\mu_0 N_1 N_2 A}{l}.
\end{displaymath}">|; 

$key = q/tantheta=hslashp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1378.png"
 ALT="$\tan\theta=h/p$">|; 

$key = q/2.6times10^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img632.png"
 ALT="$2.6\times 10^{-8} $">|; 

$key = q/{displaymath}w=w_E+w_B=(18+40)=58,,{{rm{J,m}^{-3}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1181.png"
 ALT="\begin{displaymath}
w = w_E + w_B = (18 + 40) = 58  {\rm J m}^{-3}.
\end{displaymath}">|; 

$key = q/{{bf{f}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="${\bf f}({\bf r})$">|; 

$key = q/{displaymath}V_B-V_A=-E_x,c=-(1.40times10^3),(-3.50times10^{-2})=49.0,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="483" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img445.png"
 ALT="\begin{displaymath}
V_B - V_A = -E_x c= -(1.40\times 10^3) (-3.50\times 10^{-2})=49.0 {\rm V}.
\end{displaymath}">|; 

$key = q/-q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img760.png"
 ALT="$-q$">|; 

$key = q/y_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1506.png"
 ALT="$y_m$">|; 

$key = q/dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img413.png"
 ALT="$dz$">|; 

$key = q/{displaymath}P_2=I^2,R=(5.0)^2,(4.0)=100,{{rm{W}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="271" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1038.png"
 ALT="\begin{displaymath}
P_2 = I^2 R = (5.0)^2 (4.0) = 100 {\rm W}.
\end{displaymath}">|; 

$key = q/p=,90;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1473.png"
 ALT="$p= 90$">|; 

$key = q/{{bf{f}=q,{{bf{v}times{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img918.png"
 ALT="${\bf f} = q 
{\bf v}\times{\bf B}$">|; 

$key = q/{displaymath}frac{1}{R_{{rm{eq}}=frac{1}{R_1}+frac{1}{R_2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img659.png"
 ALT="\begin{displaymath}
\frac{1}{R_{\rm eq}} = \frac{1}{R_1} + \frac{1}{R_2}.
\end{displaymath}">|; 

$key = q/-y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img770.png"
 ALT="$-y$">|; 

$key = q/{{bf{e}_xequiv(1,0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="${\bf e}_x \equiv (1,0,0)$">|; 

$key = q/I_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img706.png"
 ALT="$I_3$">|; 

$key = q/{figure*}{epsfysize{=3in{centerline{epsffile{corner.eps}}{{figure*};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="340" BORDER="0"
 SRC="|."$dir".q|img1347.png"
 ALT="\begin{figure*}
\epsfysize =3in
\centerline{\epsffile{corner.eps}}
\end{figure*}">|; 

$key = q/f'<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img266.png"
 ALT="$f'&lt;0$">|; 

$key = q/{{bf{f};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img782.png"
 ALT="${\bf f}$">|; 

$key = q/rho,,,(Omega,{{rm{m});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img629.png"
 ALT="$\rho    (\Omega {\rm m})$">|; 

$key = q/q,E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img799.png"
 ALT="$q E$">|; 

$key = q/{displaymath}frac{1}{p}+frac{1}{q}=frac{2}{R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1390.png"
 ALT="\begin{displaymath}
\frac{1}{p}+\frac{1}{q} = \frac{2}{R}.
\end{displaymath}">|; 

$key = q/dz=lambda,f,dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1245.png"
 ALT="$d z = \lambda f d t$">|; 

$key = q/{displaymath}V=I,R,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img610.png"
 ALT="\begin{displaymath}
V = I R,
\end{displaymath}">|; 

$key = q/{mitPhi}_B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img887.png"
 ALT="${\mit\Phi}_B$">|; 

$key = q/x=f(l);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="$x=f(l)$">|; 

$key = q/LslashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$L/R$">|; 

$key = q/{displaymath}f=k_e,frac{q_1,q_3}{x_1^{~2}}=(8.988times10^9),frac{(6times10^{-6})es10^{-6})}{(5.1times10^{-2})^2}=+41.68,{{rm{N}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="508" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="\begin{displaymath}
f = k_e  \frac{q_1  q_3}{x_1^{&nbsp;2}} = (8.988\times 10^9) \...
...,(2\times
10^{-6})}{(5.1\times 10^{-2})^2} =
+41.68 {\rm N}.
\end{displaymath}">|; 

$key = q/16.8,{{rm{mm}^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img686.png"
 ALT="$16.8 {\rm mm}^2$">|; 

$key = q/{mitDelta}r_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img365.png"
 ALT="${\mit\Delta}r_i$">|; 

$key = q/theta=90^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img423.png"
 ALT="$\theta = 90^\circ$">|; 

$key = q/A,E_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1229.png"
 ALT="$A E_\perp$">|; 

$key = q/{displaymath}{{bf{E}=frac{{bf{f}{q'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="\begin{displaymath}
{\bf E} = \frac{\bf f}{q'}.
\end{displaymath}">|; 

$key = q/T=1slashf;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img942.png"
 ALT="$T= 1/f$">|; 

$key = q/{displaymath}Q=Q_0=8.8times10^{-10},{{rm{C}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img577.png"
 ALT="\begin{displaymath}
Q=Q_0 = 8.8\times 10^{-10}  {\rm C}.
\end{displaymath}">|; 

$key = q/v=(q,Eslashm),tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img619.png"
 ALT="$v = (q E/m) \tau$">|; 

$key = q/q=+1.20,mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img437.png"
 ALT="$q=+1.20 \mu{\rm C}$">|; 

$key = q/{displaymath}q,E=frac{q,V_H}{w}=q,v_d,B,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img800.png"
 ALT="\begin{displaymath}
q E = \frac{q V_H}{w} = q v_d B,
\end{displaymath}">|; 

$key = q/{displaymath}M=-frac{q}{p}=-frac{(57.27)}{(90)}=-0.636.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1475.png"
 ALT="\begin{displaymath}
M = -\frac{q}{p} = -\frac{(57.27)}{(90)} = -0.636.
\end{displaymath}">|; 

$key = q/{{bf{B}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img751.png"
 ALT="${\bf B}_1$">|; 

$key = q/{{bf{a}+({{bf{b}+{{bf{c})=({{bf{a}+{{bf{b})+{{bf{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="${\bf a} +
({\bf b} + {\bf c}) = ({\bf a} + {\bf b}) + {\bf c}$">|; 

$key = q/{displaymath}I_2=frac{(105),(12)+(100),(6)}{(1000+50+500)}=frac{(1860)}{(1550)}=1.2,{{rm{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="366" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img728.png"
 ALT="\begin{displaymath}
I_2 = \frac{ (105) (12) + (100) (6) }{ (1000+50 + 500)} = \frac{(1860)}{(1550)}
= 1.2 {\rm A}.
\end{displaymath}">|; 

$key = q/f=omegaslash2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img941.png"
 ALT="$f=\omega/2\pi$">|; 

$key = q/V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="$V$">|; 

$key = q/{displaymath}E=E_a+E_b=-1.8times10^6,{{rm{N,C}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img317.png"
 ALT="\begin{displaymath}
E = E_a + E_b = -1.8 \times 10^6 {\rm N C}^{-1}.
\end{displaymath}">|; 

$key = q/{displaymath}P_B-P_A=q,(V_B-V_A)=(-1.6times10^{-19}),(1000)=-1.6times10^{-16},{{rm{J},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="536" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img448.png"
 ALT="\begin{displaymath}
P_B- P_A = q (V_B - V_A)= (-1.6\times 10^{-19}) (1000) = -1.6\times 10^{-16} {\rm J},
\end{displaymath}">|; 

$key = q/R_2=0.050,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1001.png"
 ALT="$R_2=0.050 \Omega$">|; 

$key = q/{displaymath}frac{d}{dt}left({{bf{a}cdot{{bf{b}right)=frac{d{{bf{a}}{dt}cdot{{bf{b}+{{bf{a}cdotfrac{d{{bf{b}}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="\begin{displaymath}
\frac{d}{dt}\left({\bf a}\cdot{\bf b}\right) = \frac{d{\bf a}}{dt}\cdot {\bf b} +{\bf a}\cdot\frac{d{\bf b}}{dt}.
\end{displaymath}">|; 

$key = q/{{bf{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="${\bf r}$">|; 

$key = q/alpha_x=pislash2-alpha_y=alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$\alpha_x = \pi/2-\alpha_y=\alpha$">|; 

$key = q/{displaymath}V=frac{Q}{C}=frac{(8.8times10^{-10})}{(21times10^{-12})}=42,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="258" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img578.png"
 ALT="\begin{displaymath}
V = \frac{Q}{C} =\frac{(8.8\times 10^{-10})}{(21\times 10^{-12})} = 42  {\rm V}.
\end{displaymath}">|; 

$key = q/{displaymath}I_1,V_1=I_2,V_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1151.png"
 ALT="\begin{displaymath}
I_1 V_1 = I_2  V_2.
\end{displaymath}">|; 

$key = q/{figure*}{epsfysize{=2in{centerline{epsffile{fig1aa.eps}}{{figure*};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="228" BORDER="0"
 SRC="|."$dir".q|img468.png"
 ALT="\begin{figure*}
\epsfysize =2in
\centerline{\epsffile{fig1aa.eps}}
\end{figure*}">|; 

$key = q/-0.0667;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1482.png"
 ALT="$-0.0667$">|; 

$key = q/{displaymath}frac{sintheta_1}{sintheta_2}=frac{v_1}{v_2}=frac{n_2}{n_1},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1317.png"
 ALT="\begin{displaymath}
\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{n_2}{n_1},
\end{displaymath}">|; 

$key = q/({{bf{a}cdot{{bf{b})cdot{{bf{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$({\bf a}\cdot{\bf b}) \cdot{\bf c}$">|; 

$key = q/{displaymath}oint_C{{bf{B}cdotd{{bf{r}=mu_0int_{S'}{{bf{j}cdotd{{bf{S}',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1214.png"
 ALT="\begin{displaymath}
\oint_C {\bf B}\cdot d{\bf r} = \mu_0\int_{S'}{\bf j}\cdot d{\bf S}',
\end{displaymath}">|; 

$key = q/{displaymath}{calE}_{{rm{max}=2pi,N,B,A,f=(6.283),(10),(0.40),(0.12),(60)=181,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="484" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1030.png"
 ALT="\begin{displaymath}
{\cal E}_{\rm max} = 2\pi N B A f = (6.283) (10) (0.40) (0.12) (60) = 181  {\rm V}.
\end{displaymath}">|; 

$key = q/Q_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img530.png"
 ALT="$Q_1$">|; 

$key = q/{{bf{I}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img746.png"
 ALT="${\bf I}'$">|; 

$key = q/5.0times10^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img601.png"
 ALT="$5.0\times 10^{-8}$">|; 

$key = q/t=LslashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1116.png"
 ALT="$t=L/R$">|; 

$key = q/q,v_d,B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img796.png"
 ALT="$q v_d B$">|; 

$key = q/cd;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img812.png"
 ALT="$cd$">|; 

$key = q/{{bf{e}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="${\bf e}_z$">|; 

$key = q/{displaymath}R_S=frac{V_{{rm{max}}{I_{{rm{fsd}}-R_G.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img855.png"
 ALT="\begin{displaymath}
R_S = \frac{V_{\rm max}}{I_{\rm fsd}} - R_G.
\end{displaymath}">|; 

$key = q/l=0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1169.png"
 ALT="$l=0.1$">|; 

$key = q/l=1.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img862.png"
 ALT="$l=1.2$">|; 

$key = q/{displaymath}{calE}=oint_C{{bf{E}cdotd{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img901.png"
 ALT="\begin{displaymath}
{\cal E} = \oint_C {\bf E} \cdot d{\bf r}.
\end{displaymath}">|; 

$key = q/displaystylefrac{d{mitPhi}_B}{dt}=N_2,A_1,mu_0,n_1,frac{dI_1}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1009.png"
 ALT="$\displaystyle \frac{d{\mit\Phi}_B}{dt} =
N_2 A_1 \mu_0 n_1 \frac{dI_1}{dt}$">|; 

$key = q/+I,R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img663.png"
 ALT="$+I R$">|; 

$key = q/(R_1+R_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img721.png"
 ALT="$(R_1+R_2)$">|; 

$key = q/{displaymath}epsilon_0=8.854times10^{-12},,{{rm{N^{-1},m^{-2},C^2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="\begin{displaymath}
\epsilon_0 = 8.854\times 10^{-12}  {\rm N^{-1}  m^{-2} C^2}
\end{displaymath}">|; 

$key = q/B_parallel=B,sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img947.png"
 ALT="$B_\parallel=B \sin\theta$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{sin.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="737" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img943.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{sin.eps}}
\end{figure}">|; 

$key = q/n,L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img816.png"
 ALT="$n L$">|; 

$key = q/V=120,{{rm{V};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1033.png"
 ALT="$V=120 {\rm V}$">|; 

$key = q/p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1371.png"
 ALT="$p$">|; 

$key = q/M<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1452.png"
 ALT="$M&lt;0$">|; 

$key = q/{displaymath}{{bf{S}=sum_i{{bf{S}_i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="\begin{displaymath}
{\bf S} = \sum_i {\bf S}_i.
\end{displaymath}">|; 

$key = q/q_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="$q_c$">|; 

$key = q/y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$y$">|; 

$key = q/{displaymath}phi=tan^{-1}(f_{c,y}slashf_{c,x})=32.6^circ{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img302.png"
 ALT="\begin{displaymath}
\phi = \tan^{-1} (f_{c y}/f_{c x}) = 32.6^\circ
\end{displaymath}">|; 

$key = q/d{mitPhi}=L,dI;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1073.png"
 ALT="$d{\mit\Phi}
= L d I$">|; 

$key = q/{displaymath}R_{{rm{eq}=R_1+R_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img652.png"
 ALT="\begin{displaymath}
R_{\rm eq} = R_1 + R_2.
\end{displaymath}">|; 

$key = q/{displaymath}w(r)=2pi,r,B(r),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img879.png"
 ALT="\begin{displaymath}
w(r) = 2\pi  r B(r),
\end{displaymath}">|; 

$key = q/{displaymath}i(t=0)=I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1114.png"
 ALT="\begin{displaymath}
i(t=0)=I.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig3.6.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="415" HEIGHT="279" BORDER="0"
 SRC="|."$dir".q|img740.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig3.6.eps}}
\end{figure}">|; 

$key = q/{displaymath}v=frac{c}{n},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1307.png"
 ALT="\begin{displaymath}
v =\frac{c}{n},
\end{displaymath}">|; 

$key = q/R_{{rm{eq}'=0.667,{{rm{Omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img697.png"
 ALT="$R_{\rm eq}' = 0.667 {\rm\Omega}$">|; 

$key = q/225;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1462.png"
 ALT="$225$">|; 

$key = q/2.56,{{rm{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1523.png"
 ALT="$2.56 {\rm m}$">|; 

$key = q/m_e=9.11times10^{-31};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img871.png"
 ALT="$m_e
=9.11\times 10^{-31}$">|; 

$key = q/theta=omega,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img938.png"
 ALT="$\theta = \omega  t$">|; 

$key = q/{displaymath}R=frac{(1.7times10^{-8}),(1.0)}{(16.8times10^{-6})}=1.0times10^{-3},Omega.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img688.png"
 ALT="\begin{displaymath}
R = \frac{(1.7\times 10^{-8}) (1.0)}{(16.8\times 10^{-6})} = 1.0\times 10^{-3} 
\Omega.
\end{displaymath}">|; 

$key = q/R_f>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1417.png"
 ALT="$R_f&gt;0$">|; 

$key = q/R_b>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1420.png"
 ALT="$R_b&gt;0$">|; 

$key = q/{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="${\bf b}$">|; 

$key = q/{displaymath}1,{{rm{V,m^{-1}}equiv1,{{rm{N,C^{-1}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img407.png"
 ALT="\begin{displaymath}
1 {\rm V  m^{-1}} \equiv 1 {\rm N  C^{-1}}.
\end{displaymath}">|; 

$key = q/{displaymath}P=V,I=I^2,R=frac{V^2}{R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img668.png"
 ALT="\begin{displaymath}
P = V  I = I^2 R = \frac{V^2}{R}.
\end{displaymath}">|; 

$key = q/{displaymath}1,{{rm{kWh}=(1000),(60),(60)=3.6times10^6,{{rm{J}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="316" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img669.png"
 ALT="\begin{displaymath}
1 {\rm kWh} = (1000) (60) (60) = 3.6\times 10^6 {\rm J}.
\end{displaymath}">|; 

$key = q/A,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img967.png"
 ALT="$A,$">|; 

$key = q/{displaymath}M=-frac{q}{p}=1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1404.png"
 ALT="\begin{displaymath}
M = -\frac{q}{p} = 1.
\end{displaymath}">|; 

$key = q/60;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1445.png"
 ALT="$60$">|; 

$key = q/x>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img683.png"
 ALT="$x&gt;1$">|; 

$key = q/displaystylez';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$\displaystyle z'$">|; 

$key = q/{displaymath}i=frac{dq}{dt}=frac{dq'}{dt}=-frac{q'}{R,C}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1133.png"
 ALT="\begin{displaymath}
i = \frac{dq}{d t} = \frac{dq'}{dt}
= - \frac{q'}{R C}.
\end{displaymath}">|; 

$key = q/N_2=10;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img999.png"
 ALT="$N_2=10$">|; 

$key = q/{displaymath}I_D=epsilon_0,A,frac{dE_perp}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1228.png"
 ALT="\begin{displaymath}
I_D = \epsilon_0 A  \frac{dE_\perp}{dt}.
\end{displaymath}">|; 

$key = q/f=pmRslash2rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1400.png"
 ALT="$f=\pm R/2\rightarrow\infty$">|; 

$key = q/{displaymath}M=-frac{q}{p}=-frac{(100)}{(15)}=-6.67.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1451.png"
 ALT="\begin{displaymath}
M = -\frac{q}{p} = -\frac{(100)}{(15)} = -6.67.
\end{displaymath}">|; 

$key = q/{displaymath}C=K,C_0=(4.8),(4.4times10^{-12})=21,{{rm{pF}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img575.png"
 ALT="\begin{displaymath}
C= K C_0 = (4.8)  (4.4 \times 10^{-12}) = 21 {\rm pF}.
\end{displaymath}">|; 

$key = q/{{bf{E}times{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1248.png"
 ALT="${\bf E}\times{\bf B}$">|; 

$key = q/{displaymath}E_a=k_e,frac{q_a}{(cslash2)^2}=(8.988times10^9),frac{(50times10^{-6})}{(0.5)^2}=1.80times10^6,{{rm{N,C}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="515" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img313.png"
 ALT="\begin{displaymath}
E_a = k_e \frac{q_a}{(c/2)^2} = (8.988\times 10^9)  \frac{(50\times 10^{-6})}{(0.5)^2}
= 1.80\times 10^6 {\rm N C}^{-1}.
\end{displaymath}">|; 

$key = q/E_x(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img428.png"
 ALT="$E_x(x)$">|; 

$key = q/{displaymath}m,a_z=qleft(E-v,Bright),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img771.png"
 ALT="\begin{displaymath}
m  a_z = q\left(E - v  B\right),
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig2.3.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="219" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig2.3.eps}}
\end{figure}">|; 

$key = q/{displaymath}2,n,t=m,lambda,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1520.png"
 ALT="\begin{displaymath}
2 n t = m \lambda,
\end{displaymath}">|; 

$key = q/f=50;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img958.png"
 ALT="$f=50$">|; 

$key = q/-1.602times10^{-19};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="$-1.602\times 10^{-19}$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{slab.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="436" HEIGHT="342" BORDER="0"
 SRC="|."$dir".q|img1341.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{slab.eps}}
\end{figure}">|; 

$key = q/F=I,B,L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img825.png"
 ALT="$F= I B L$">|; 

$key = q/{displaymath}B=frac{mu_0,N,I}{l}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1076.png"
 ALT="\begin{displaymath}
B = \frac{\mu_0 N I}{l}
\end{displaymath}">|; 

$key = q/|f'|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img268.png"
 ALT="$\vert f'\vert$">|; 

$key = q/{{bf{A}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="${\bf A}({\bf r})$">|; 

$key = q/{displaymath}0+frac{1}{f}=frac{2}{R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1393.png"
 ALT="\begin{displaymath}
0 + \frac{1}{f} = \frac{2}{R}.
\end{displaymath}">|; 

$key = q/AP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1313.png"
 ALT="$AP$">|; 

$key = q/t=5,tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1107.png"
 ALT="$t=5 \tau$">|; 

$key = q/{displaymath}I=frac{calE}{R}=frac{(0.020)}{(0.020)}=1.0,{{rm{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1019.png"
 ALT="\begin{displaymath}
I = \frac{\cal E}{R} = \frac{(0.020)}{(0.020)} = 1.0 {\rm A}.
\end{displaymath}">|; 

$key = q/|a|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$\vert a\vert$">|; 

$key = q/theta_1=30.0^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1358.png"
 ALT="$\theta_1=
30.0^\circ$">|; 

$key = q/O;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$O$">|; 

$key = q/r^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img321.png"
 ALT="$r^2$">|; 

$key = q/theta_2>theta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1325.png"
 ALT="$\theta_2 &gt; \theta_1$">|; 

$key = q/{displaymath}I_1=frac{P}{V_1}=frac{(1times10^9)}{(500)}=2,{{rm{MA}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1204.png"
 ALT="\begin{displaymath}
I_1 = \frac{P}{V_1} = \frac{(1\times 10^9)}{(500)} = 2 {\rm MA}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{V_1}{V_2}=sqrt{frac{L_1}{L_2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img1155.png"
 ALT="\begin{displaymath}
\frac{V_1}{V_2} = \sqrt{\frac{L_1}{L_2}}.
\end{displaymath}">|; 

$key = q/{displaymath}P_1=i_1,v_1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1148.png"
 ALT="\begin{displaymath}
P_1 = i_1 v_1.
\end{displaymath}">|; 

$key = q/{displaymath}R'=frac{V_1}{I_1}=left(frac{N_1}{N_2}right)^2,frac{V_2}{I_2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1167.png"
 ALT="\begin{displaymath}
R' = \frac{V_1}{I_1} = \left(\frac{N_1}{N_2}\right)^2 \frac{V_2}{I_2},
\end{displaymath}">|; 

$key = q/4,{mu}{{rm{F};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img587.png"
 ALT="$4 {\mu}{\rm F}$">|; 

$key = q/I,V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img732.png"
 ALT="$I V$">|; 

$key = q/{displaymath}C_{{rm{eq}=frac{(12times10^{-6})}{(7)}=1.71,mu{{rm{F}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img589.png"
 ALT="\begin{displaymath}
C_{\rm eq} = \frac{(12\times 10^{-6})}{(7)} = 1.71 \mu{\rm F}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{N_2}{N_1}=frac{(5times10^4)}{(500)}=100.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1202.png"
 ALT="\begin{displaymath}
\frac{N_2}{N_1} = \frac{(5\times 10^4)}{(500)} = 100.
\end{displaymath}">|; 

$key = q/{displaymath}I_2=frac{(R_1+R_3),{calE}_1+R_1,{calE}_2}{R_1R_2+R_2R_3+R_1R_3},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img727.png"
 ALT="\begin{displaymath}
I_2 = \frac{ (R_1+R_3) {\cal E}_1
+ R_1 {\cal E}_2}{R_1 R_2 + R_2 R_3+ R_1 R_3},
\end{displaymath}">|; 

$key = q/c=dzslashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1246.png"
 ALT="$c = d z/d t$">|; 

$key = q/m=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1500.png"
 ALT="$m=0$">|; 

$key = q/g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$g$">|; 

$key = q/{displaymath}sintheta_1=frac{BQ}{AQ}=frac{v_1,{mitDelta}t}{AQ},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1315.png"
 ALT="\begin{displaymath}
\sin\theta_1 = \frac{BQ}{AQ} = \frac{v_1 {\mit\Delta} t}{AQ},
\end{displaymath}">|; 

$key = q/A=4pi,R^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img331.png"
 ALT="$A=4\pi  R^2$">|; 

$key = q/AC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img945.png"
 ALT="$AC$">|; 

$key = q/{{bf{a},{{rm{x},{{bf{b}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="${\bf a}  {\rm x}  {\bf b}= {\bf0}$">|; 

$key = q/theta=180^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img422.png"
 ALT="$\theta = 180^\circ$">|; 

$key = q/{displaymath}w=2pi,r,B=mu_0,I,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img807.png"
 ALT="\begin{displaymath}
w = 2\pi r B = \mu_0 I,
\end{displaymath}">|; 

$key = q/{displaymath}W=|F|,(|r|,costheta)={{bf{F}cdot{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="\begin{displaymath}
W = \vert F\vert  (\vert r\vert \cos\theta) = {\bf F}\cdot {\bf r}.
\end{displaymath}">|; 

$key = q/n_1simeq1.00;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1361.png"
 ALT="$n_1\simeq 1.00$">|; 

$key = q/V_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img471.png"
 ALT="$V_c$">|; 

$key = q/z=r,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$z= r \cos\theta$">|; 

$key = q/displaystyleB_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1242.png"
 ALT="$\displaystyle B_y$">|; 

$key = q/{displaymath}{{bf{f}=q,{{bf{E}+q,{{bf{v}times{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img767.png"
 ALT="\begin{displaymath}
{\bf f} = q {\bf E} + q {\bf v} \times{\bf B}.
\end{displaymath}">|; 

$key = q/wslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img925.png"
 ALT="$w/2$">|; 

$key = q/F_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1425.png"
 ALT="$F_i$">|; 

$key = q/30^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img983.png"
 ALT="$30^\circ$">|; 

$key = q/{displaymath}frac{d{{bf{a}}{dt}=left(frac{da_x}{dt},frac{da_y}{dt},frac{da_z}{dt}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="\begin{displaymath}
\frac{d {\bf a}}{dt} = \left(\frac{d a_x}{dt}, \frac{d a_y}{d t}, \frac{d a_z}{ d t}\right).
\end{displaymath}">|; 

$key = q/{displaymath}p=fleft(1-frac{1}{M}right)=-(45),(1-15)=630,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1483.png"
 ALT="\begin{displaymath}
p = f\left(1-\frac{1}{M}\right) = -(45) (1-15) = 630 {\rm cm}.
\end{displaymath}">|; 

$key = q/I_G;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img836.png"
 ALT="$I_G$">|; 

$key = q/E_{{rm{crit}sim10^6,,{{rm{V,m}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img480.png"
 ALT="$E_{\rm crit} \sim 10^6  {\rm V  m}^{-1}$">|; 

$key = q/q_a=-6.0,mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img275.png"
 ALT="$q_a=-6.0 \mu{\rm C}$">|; 

$key = q/n,({{bf{a}+{{bf{b})=n,{{bf{a}+n,{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$n ({\bf a} + {\bf b}) = n {\bf a} + n {\bf b}$">|; 

$key = q/22.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1464.png"
 ALT="$22.5$">|; 

$key = q/dI;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1072.png"
 ALT="$dI$">|; 

$key = q/lambda<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img340.png"
 ALT="$\lambda&lt;0$">|; 

$key = q/{displaymath}frac{lambda_2}{lambda_1}=frac{v_2slashf}{v_1slashf}=frac{v_2}{v_1}=frac{n_1}{n_2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1321.png"
 ALT="\begin{displaymath}
\frac{\lambda_2}{\lambda_1} = \frac{v_2/f}{v_1/f} =
\frac{v_2}{v_1}=\frac{n_1}{n_2}.
\end{displaymath}">|; 

$key = q/(AB);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$(AB)$">|; 

$key = q/{displaymath}{{bf{a}times({{bf{b}times{{bf{c})neq({{bf{a}times{{bf{b})times{{bf{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="\begin{displaymath}
{\bf a}\times({\bf b} \times{\bf c})\neq ({\bf a}\times{\bf b}) \times{\bf c}.
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{C,V^2}{2}=frac{epsilon_0,A,E^2,d^2}{2,d}=frac{epsilon_0,E^2,Ad}{2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img556.png"
 ALT="\begin{displaymath}
W = \frac{C V^2}{2} = \frac{\epsilon_0 A E^2 d^2}{2 d} =
\frac{\epsilon_0 E^2 Ad}{2},
\end{displaymath}">|; 

$key = q/63%;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1104.png"
 ALT="$63\%$">|; 

$key = q/{calE}>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img897.png"
 ALT="${\cal E}&gt;0$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{circuit1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="288" BORDER="0"
 SRC="|."$dir".q|img635.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{circuit1.eps}}
\end{figure}">|; 

$key = q/{displaymath}c=frac{1}{sqrt{(4pitimes10^{-7}),(8.854times10^{-12})}}=2.998times10^8,{{rm{m},{{rm{s}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="443" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img1253.png"
 ALT="\begin{displaymath}
c = \frac{1}{\sqrt{(4\pi\times 10^{-7}) (8.854\times 10^{-12})} }= 2.998
\times 10^8  {\rm m} {\rm s}^{-1}.
\end{displaymath}">|; 

$key = q/R=r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img685.png"
 ALT="$R=r$">|; 

$key = q/{displaymath}P={calE},I=frac{{calE},(V-{calE})}{R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img979.png"
 ALT="\begin{displaymath}
P = {\cal E}  I = \frac{{\cal E}  (V - {\cal E})}{R}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{d{mitPhi}_B}{dt}=frac{{mitPhi}_{B,2}-{mitPhi}_{B,1}}{{mitDeltafrac{(2.039-0.408)}{(10)}=0.163,{{rm{Wb,s}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="439" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img992.png"
 ALT="\begin{displaymath}
\frac{d{\mit\Phi}_B}{dt} = \frac{{\mit\Phi}_{B 2}-
{\mit\P...
...Delta}t} = \frac{(2.039-0.408)}{(10)}=0.163 {\rm Wb s}^{-1}.
\end{displaymath}">|; 

$key = q/{displaymath}B_0=sqrt{frac{2,mu_0,S}{c}}=sqrt{frac{(2),(4pitimes10^{-7}),(140)}{(3times10^8)}}=1.083times10^{-6},{{rm{T}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="65" BORDER="0"
 SRC="|."$dir".q|img1293.png"
 ALT="\begin{displaymath}
B_0 = \sqrt{\frac{2 \mu_0 S}{c}} = \sqrt{\frac{(2) (4\pi\...
...-7}) (140)}
{(3\times 10^8)}} = 1.083\times 10^{-6} {\rm T}.
\end{displaymath}">|; 

$key = q/mu_0=4pitimes10^{-7},{{rm{N},{{rm{s}^2,{{rm{C}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1251.png"
 ALT="$\mu_0 = 4\pi\times 10^{-7} {\rm N} {\rm s}^2  {\rm C}^{-2}$">|; 

$key = q/{displaymath}{mitPhi}=L,I,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1071.png"
 ALT="\begin{displaymath}
{\mit\Phi} = L I,
\end{displaymath}">|; 

$key = q/displaystylefrac{Q_b}{Q};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img493.png"
 ALT="$\displaystyle \frac{Q_b}{Q}$">|; 

$key = q/displaystyleB_0,cos[2pi,(zslashlambda-f,t)].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1243.png"
 ALT="$\displaystyle B_0 \cos[2\pi (z/\lambda-f t)].$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig2.2.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="282" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig2.2.eps}}
\end{figure}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{shunt1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="470" HEIGHT="229" BORDER="0"
 SRC="|."$dir".q|img858.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{shunt1.eps}}
\end{figure}">|; 

$key = q/{figure*}{epsfysize{=3in{centerline{epsffile{kirchhof.eps}}{{figure*};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="346" BORDER="0"
 SRC="|."$dir".q|img713.png"
 ALT="\begin{figure*}
\epsfysize =3in
\centerline{\epsffile{kirchhof.eps}}
\end{figure*}">|; 

$key = q/{displaymath}I=frac{V-{calE}}{R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img978.png"
 ALT="\begin{displaymath}
I = \frac{V-{\cal E}}{R}.
\end{displaymath}">|; 

$key = q/d{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$d{\bf S}$">|; 

$key = q/{displaymath}V({{bf{r})=frac{q}{4piepsilon_0,r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img432.png"
 ALT="\begin{displaymath}
V({\bf r}) = \frac{q}{4\pi\epsilon_0 r}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{mutual.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="496" HEIGHT="340" BORDER="0"
 SRC="|."$dir".q|img1043.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{mutual.eps}}
\end{figure}">|; 

$key = q/B=1.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1016.png"
 ALT="$B=1.0$">|; 

$key = q/m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img615.png"
 ALT="$m$">|; 

$key = q/630;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1484.png"
 ALT="$630$">|; 

$key = q/theta_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$\theta_x$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{prism.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="427" HEIGHT="289" BORDER="0"
 SRC="|."$dir".q|img1337.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{prism.eps}}
\end{figure}">|; 

$key = q/c=1slashsqrt{mu_0,epsilon_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1270.png"
 ALT="$c= 1/\sqrt{\mu_0 \epsilon_0}$">|; 

$key = q/{{bf{E}'({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="${\bf E}'({\bf r})$">|; 

$key = q/{{bf{e}_xtimes{{bf{e}_y={{bf{e}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="${\bf e}_x\times
{\bf e}_y={\bf e}_z$">|; 

$key = q/S,cosalpha_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$S \cos\alpha_x$">|; 

$key = q/E(R)=qslash(4piepsilon_0,R^2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img323.png"
 ALT="$E(R) = q/(4\pi\epsilon_0 R^2)$">|; 

$key = q/dx=v,dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img908.png"
 ALT="$dx=v dt$">|; 

$key = q/{{rm{e}^{-1}simeq0.37;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1106.png"
 ALT="${\rm e}^{-1} \simeq 0.37$">|; 

$key = q/{displaymath}w=frac{B^2}{2,mu_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1090.png"
 ALT="\begin{displaymath}
w = \frac{B^2}{2 \mu_0}.
\end{displaymath}">|; 

$key = q/{displaymath}f'=k_e,frac{q_2,q_3}{|x_2|^{2}}=(8.988times10^9),frac{(-5times10^{-es10^{-6})}{(3.4times10^{-2})^2}=-77.75,{{rm{N}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="529" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="\begin{displaymath}
f' = k_e  \frac{q_2  q_3}{\vert x_2\vert^{2}} = (8.988\tim...
...,(2\times
10^{-6})}{(3.4\times 10^{-2})^2} =
-77.75 {\rm N}.
\end{displaymath}">|; 

$key = q/{displaymath}{calE}_2=-M,frac{dI_1}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1057.png"
 ALT="\begin{displaymath}
{\cal E}_2 = - M  \frac{d I_1}{d t}.
\end{displaymath}">|; 

$key = q/l,x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img906.png"
 ALT="$l x$">|; 

$key = q/f_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img270.png"
 ALT="$f_3$">|; 

$key = q/{displaymath}c'=frac{c}{sqrt{K}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1267.png"
 ALT="\begin{displaymath}
c' = \frac{c}{\sqrt{K}},
\end{displaymath}">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img954.png"
 ALT="$T$">|; 

$key = q/{displaymath}y_m=frac{m,lambda,L}{d},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1507.png"
 ALT="\begin{displaymath}
y_m = \frac{m \lambda L}{d},
\end{displaymath}">|; 

$key = q/displaystyle(a_y,b_z-a_z,b_y)^2+(a_z,b_x-a_x,b_z)^2+(a_x,b_z-a_y,b_x)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="408" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$\displaystyle (a_y  b_z-a_z  b_y)^2 +(a_z  b_x - a_x  b_z)^2 +(a_x  b_z
-a_y  b_x)^2$">|; 

$key = q/{displaymath}I=frac{P}{V}=frac{(150)}{(120)}=1.25,{{rm{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img733.png"
 ALT="\begin{displaymath}
I = \frac{P}{V} = \frac{(150)}{(120)} = 1.25 {\rm A}.
\end{displaymath}">|; 

$key = q/sigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img341.png"
 ALT="$\sigma$">|; 

$key = q/displaystylea_{y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\displaystyle a_{y'}$">|; 

$key = q/{{bf{a},{{rm{x},{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="${\bf a}  {\rm x}  {\bf b}$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{converge.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="698" HEIGHT="284" BORDER="0"
 SRC="|."$dir".q|img1427.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{converge.eps}}
\end{figure}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{axis.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="568" HEIGHT="345" BORDER="0"
 SRC="|."$dir".q|img1368.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{axis.eps}}
\end{figure}">|; 

$key = q/{displaymath}v=sqrt{frac{2,e,V}{m_e}}=sqrt{frac{(2),(1.6times10^{-19}),(10^3)}{(times10^{-31})}}=1.87times10^{7},{{rm{m,s}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="65" BORDER="0"
 SRC="|."$dir".q|img874.png"
 ALT="\begin{displaymath}
v = \sqrt{\frac{2 e V}{m_e}} = \sqrt{\frac{(2) (1.6\times...
...{(9.11\times 10^{-31})}} = 1.87\times 10^{7} {\rm m s}^{-1}.
\end{displaymath}">|; 

$key = q/{displaymath}t=(120),(ln10)=276.3,,{{rm{s}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1198.png"
 ALT="\begin{displaymath}
t = (120)  (\ln 10)= 276.3  {\rm s}.
\end{displaymath}">|; 

$key = q/1slashfrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1401.png"
 ALT="$1/f\rightarrow 0$">|; 

$key = q/eta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1041.png"
 ALT="$\eta$">|; 

$key = q/{displaymath}I=I_{{rm{max},sin(2pi,f,t){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img966.png"
 ALT="\begin{displaymath}
I = I_{\rm max}   \sin (2\pi  f  t)
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{fig31.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="686" HEIGHT="342" BORDER="0"
 SRC="|."$dir".q|img821.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{fig31.eps}}
\end{figure}">|; 

$key = q/I';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img741.png"
 ALT="$I'$">|; 

$key = q/{displaymath}V={calE}-I,r.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img638.png"
 ALT="\begin{displaymath}
V = {\cal E} - I r.
\end{displaymath}">|; 

$key = q/displaystylec_x,costheta+c_y,sintheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$\displaystyle c_x \cos\theta
+c_y \sin\theta.$">|; 

$key = q/f';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="$f'$">|; 

$key = q/{displaymath}E_x(x)=frac{q}{4piepsilon_0,x^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img427.png"
 ALT="\begin{displaymath}
E_x(x)= \frac{q}{4\pi\epsilon_0 x^2}.
\end{displaymath}">|; 

$key = q/50,{{rm{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img997.png"
 ALT="$50 {\rm A}$">|; 

$key = q/{displaymath}(R_1R_2+R_2R_3+R_1R_3),I_3=-R_1,{calE}_1-(R_1+R_2),{calE}_2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="420" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img722.png"
 ALT="\begin{displaymath}
(R_1 R_2 + R_2 R_3+ R_1 R_3) I_3 = - R_1 {\cal E}_1 -
(R_1+R_2) {\cal E}_2,
\end{displaymath}">|; 

$key = q/{displaymath}I_0=frac{calE}{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img639.png"
 ALT="\begin{displaymath}
I_0=\frac{\cal E}{r},
\end{displaymath}">|; 

$key = q/B_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1282.png"
 ALT="$B_0$">|; 

$key = q/{displaymath}C_0=frac{epsilon_0,A}{d}=frac{(8.85times10^{-12}),(50times10^{-4})}{(1times10^{-2})}=4.4,{{rm{pF}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="400" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img573.png"
 ALT="\begin{displaymath}
C_0=\frac{\epsilon_0 A}{d} = \frac{(8.85\times 10^{-12}) (50\times 10^{-4})}
{(1\times 10^{-2})} = 4.4 {\rm pF}.
\end{displaymath}">|; 

$key = q/q_2=-5.0,mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="$q_2=-5.0 \mu{\rm C}$">|; 

$key = q/-infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1396.png"
 ALT="$-\infty$">|; 

$key = q/I'=1.7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img863.png"
 ALT="$I'=1.7$">|; 

$key = q/B=10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img860.png"
 ALT="$B=10^{-4}$">|; 

$key = q/{displaymath}c=f,lambda.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1247.png"
 ALT="\begin{displaymath}
c = f \lambda.
\end{displaymath}">|; 

$key = q/D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img827.png"
 ALT="$D$">|; 

$key = q/1,{{rm{kWh}equiv3.6times10^6,{{rm{J};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img737.png"
 ALT="$1 {\rm kWh} \equiv 3.6\times 10^6 {\rm J}$">|; 

$key = q/{displaymath}I=frac{dQ}{dt}=frac{q^2,N,tau}{2,m},frac{A}{L},V.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img624.png"
 ALT="\begin{displaymath}
I= \frac{dQ}{d t} = \frac{q^2 N \tau}{2 m}  \frac{A}{L}  V.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{fish.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="577" HEIGHT="342" BORDER="0"
 SRC="|."$dir".q|img1335.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{fish.eps}}
\end{figure}">|; 

$key = q/{displaymath}frac{1}{p}+frac{1}{q}=frac{1}{f}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1395.png"
 ALT="\begin{displaymath}
\frac{1}{p} + \frac{1}{q} = \frac{1}{f}.
\end{displaymath}">|; 

$key = q/{displaymath}Q_0=C_0V_0=(4.4times10^{-12}),(200)=8.8times10^{-10},{{rm{C}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img576.png"
 ALT="\begin{displaymath}
Q_0 = C_0 V_0 = (4.4\times 10^{-12}) (200) = 8.8\times 10^{-10}  {\rm C}.
\end{displaymath}">|; 

$key = q/2,mu{{rm{F};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img582.png"
 ALT="$2 \mu{\rm F}$">|; 

$key = q/10^{-6};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1256.png"
 ALT="$10^{-6}$">|; 

$key = q/2,P_B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img380.png"
 ALT="$2  P_B$">|; 

$key = q/R_3=5,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img709.png"
 ALT="$R_3=5 \Omega$">|; 

$key = q/{displaymath}{mitPhi}_E=E,A=frac{-Q}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img330.png"
 ALT="\begin{displaymath}
{\mit\Phi}_E = E A = \frac{-Q}{\epsilon_0},
\end{displaymath}">|; 

$key = q/{displaymath}P_R=I^2,R=frac{{calE}^2,R}{(r+R)^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img674.png"
 ALT="\begin{displaymath}
P_R = I^2 R = \frac{ {\cal E}^2 R}{(r+R)^2}.
\end{displaymath}">|; 

$key = q/{displaymath}2,E(a),A=frac{sigma,A}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img346.png"
 ALT="\begin{displaymath}
2  E(a)  A = \frac{\sigma  A}{\epsilon_0},
\end{displaymath}">|; 

$key = q/f_{23}=-77.75,{{rm{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img269.png"
 ALT="$f_{23} = - 77.75 {\rm N}$">|; 

$key = q/{displaymath}P_R=frac{P^2,R}{V^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1162.png"
 ALT="\begin{displaymath}
P_R = \frac{P^2 R}{V^2}.
\end{displaymath}">|; 

$key = q/I_S=I-I_G;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img838.png"
 ALT="$I_S= I-I_G$">|; 

$key = q/633,{{rm{nm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1521.png"
 ALT="$633 {\rm nm}$">|; 

$key = q/{bf{r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$\bf r$">|; 

$key = q/{displaymath}{{bf{r}=(x,,y,,z),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="\begin{displaymath}
{\bf r} = (x,  y,  z),
\end{displaymath}">|; 

$key = q/theta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1300.png"
 ALT="$\theta_1$">|; 

$key = q/37%;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1117.png"
 ALT="$37\%$">|; 

$key = q/Q_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img486.png"
 ALT="$Q_b$">|; 

$key = q/{{bf{f}_a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="${\bf f}_a$">|; 

$key = q/{displaymath}w_B=frac{1}{2},frac{B^2}{mu_0}=frac{(0.5),(1.0times10^{-2})^2}{(4pitimes10^{-7})}=40,,{{rm{J,m}^{-3}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1180.png"
 ALT="\begin{displaymath}
w_B = \frac{1}{2}  \frac{B^2}{\mu_0} = \frac{(0.5) (1.0\times 10^{-2})^2}
{(4\pi\times 10^{-7})} = 40  {\rm J m}^{-3}.
\end{displaymath}">|; 

$key = q/Q=(a,0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="$Q=(a,0,0)$">|; 

$key = q/{displaymath}oint{{bf{E}cdotd{{bf{S}=frac{Q}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img352.png"
 ALT="\begin{displaymath}
\oint {\bf E}\cdot d{\bf S} = \frac{Q}{\epsilon_0},
\end{displaymath}">|; 

$key = q/{displaymath}W=-qsum_{i=1}^NE_i,{mitDelta}r_i,costheta_i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img368.png"
 ALT="\begin{displaymath}
W =- q\sum_{i=1}^N E_i {\mit\Delta}r_i \cos\theta_i.
\end{displaymath}">|; 

$key = q/{displaymath}E=frac{q}{4piepsilon,r^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img525.png"
 ALT="\begin{displaymath}
E = \frac{q}{4\pi\epsilon  r^2},
\end{displaymath}">|; 

$key = q/displaystyleint_Vz,dV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="$\displaystyle \int_V z dV$">|; 

$key = q/|a|=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$\vert a\vert=0$">|; 

$key = q/V_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img851.png"
 ALT="$V_{\rm max}$">|; 

$key = q/{displaymath}B(r)=frac{mu_0,I,r}{2pi,a^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img886.png"
 ALT="\begin{displaymath}
B(r) = \frac{\mu_0 I r}{2\pi a^2}.
\end{displaymath}">|; 

$key = q/{displaymath}P={calE},I=(100),(5.0)=500,{{rm{W}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1040.png"
 ALT="\begin{displaymath}
P= {\cal E} I = (100) (5.0) = 500 {\rm W}.
\end{displaymath}">|; 

$key = q/-1.7times10^{11}~{{rm{C,kg}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img778.png"
 ALT="$-1.7\times 10^{11}&nbsp;{\rm C kg}^{-1}$">|; 

$key = q/{displaymath}P=V,I,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img665.png"
 ALT="\begin{displaymath}
P = V I,
\end{displaymath}">|; 

$key = q/RC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$RC$">|; 

$key = q/{displaymath}dV=-E_x,dx-E_y,dy-E_z,dy,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img419.png"
 ALT="\begin{displaymath}
dV =- E_x dx - E_y  dy -E_z dy,
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a},&,{{bf{b}=a_x,b_y+a_y,b_z+a_z,b_x={{rm{scalar~number},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="368" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="\begin{displaymath}
{\bf a} \&amp; {\bf b} = a_x  b_y + a_y  b_z + a_z  b_x = {\rm scalar&nbsp;number},
\end{displaymath}">|; 

$key = q/v=f,lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1320.png"
 ALT="$v=f \lambda$">|; 

$key = q/{displaymath}W'=q,v,B,l=q,{calE},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img913.png"
 ALT="\begin{displaymath}
W' = q v B l = q {\cal E},
\end{displaymath}">|; 

$key = q/a_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$a_z$">|; 

$key = q/{displaymath}frac{d{{bf{a}}{dt}=lim_{deltatrightarrow0}left[frac{{{bf{a}(t+deltat)-{{bf{a}(t)}{deltat}right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="\begin{displaymath}
\frac{d {\bf a}}{dt} = \lim_{\delta t\rightarrow 0} \left[\frac{{\bf a}(t+\delta t) - {\bf a}(t)}
{\delta t}\right].
\end{displaymath}">|; 

$key = q/{displaymath}alpha=90^circ-(90^circ-i_1)=i_1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1355.png"
 ALT="\begin{displaymath}
\alpha = 90^\circ-(90^\circ - i_1) = i_1.
\end{displaymath}">|; 

$key = q/q_c=+2.0,mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img277.png"
 ALT="$q_c = +2.0 \mu{\rm C}$">|; 

$key = q/f_{ac};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img280.png"
 ALT="$f_{ac}$">|; 

$key = q/10^{42};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$10^{42}$">|; 

$key = q/{displaymath}{calE}_1=-M,frac{dI_2}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1059.png"
 ALT="\begin{displaymath}
{\cal E}_1 = - M  \frac{d I_2}{d t}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{convex1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="570" HEIGHT="341" BORDER="0"
 SRC="|."$dir".q|img1398.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{convex1.eps}}
\end{figure}">|; 

$key = q/L_2=mu_0,N_2^{~2},Aslashl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1157.png"
 ALT="$L_2= \mu_0 N_2^{&nbsp;2}  A/l$">|; 

$key = q/{mitDelta}theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img829.png"
 ALT="${\mit\Delta}\theta$">|; 

$key = q/{displaymath}tau=tau_{{rm{max},sin^2(2pi,f,t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img952.png"
 ALT="\begin{displaymath}
\tau = \tau_{\rm max} \sin^2(2\pi  f t),
\end{displaymath}">|; 

$key = q/{displaymath}costheta=frac{{{bf{a}cdot{{bf{b}}{|a|,|b|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="\begin{displaymath}
\cos\theta = \frac{{\bf a} \cdot {\bf b}}{\vert a\vert  \vert b\vert }.
\end{displaymath}">|; 

$key = q/S'T'F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1434.png"
 ALT="$S'T'F$">|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$r$">|; 

$key = q/{{bf{a}times{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="${\bf a}\times{\bf b}$">|; 

$key = q/{displaymath}{mitPhi}_B=N,A,B_perp.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img889.png"
 ALT="\begin{displaymath}
{\mit\Phi}_B = N A B_\perp.
\end{displaymath}">|; 

$key = q/1-1slashK;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img521.png"
 ALT="$1-1/K$">|; 

$key = q/theta_1=theta_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1329.png"
 ALT="$\theta_1=\theta_c$">|; 

$key = q/stackrel{displaystylerightarrow}{PS};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="28" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\stackrel{\displaystyle \rightarrow}{PS}$">|; 

$key = q/R_{{rm{eq}=sum_{i=1}^NR_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img653.png"
 ALT="$R_{\rm eq} = \sum_{i=1}^N R_i$">|; 

$key = q/{displaymath}W={{bf{f}cdotd{{bf{r}=f,dr,costheta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img783.png"
 ALT="\begin{displaymath}
W = {\bf f}\cdot d{\bf r} =
f dr \cos\theta,
\end{displaymath}">|; 

$key = q/E_a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img312.png"
 ALT="$E_a$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{comm.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="632" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img959.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{comm.eps}}
\end{figure}">|; 

$key = q/{displaymath}(I_{{rm{max}-I_{{rm{fsd}),R_S=I_{{rm{fsd},R_G,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img842.png"
 ALT="\begin{displaymath}
(I_{\rm max}-I_{\rm fsd}) R_S = I_{\rm fsd} R_G,
\end{displaymath}">|; 

$key = q/displaystylef_{c,y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img299.png"
 ALT="$\displaystyle f_{c y}$">|; 

$key = q/1.7times10^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img631.png"
 ALT="$1.7\times 10^{-8} $">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{compare.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="490" HEIGHT="286" BORDER="0"
 SRC="|."$dir".q|img820.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{compare.eps}}
\end{figure}">|; 

$key = q/{displaymath}W=-q,int_A^B{{bf{E}cdotd{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img369.png"
 ALT="\begin{displaymath}
W = - q \int_A^B{\bf E}\cdot d{\bf r}.
\end{displaymath}">|; 

$key = q/{displaymath}rho=frac{m_e,v}{e,B}=frac{(9.11times10^{-31}),(1.87times10^{7})}{(16times10^{-19}),(1.2)}=8.87times10^{-5},{{rm{m}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="461" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img875.png"
 ALT="\begin{displaymath}
\rho = \frac{m_e v}{e B} = \frac{ (9.11\times 10^{-31}) (...
...}
{(1.6\times 10^{-19}) (1.2)} = 8.87\times 10^{-5} {\rm m}.
\end{displaymath}">|; 

$key = q/4pi,R^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img322.png"
 ALT="$4\pi  R^2$">|; 

$key = q/{figure*}{epsfysize{=2in{centerline{epsffile{fig1.eps}}{{figure*};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="345" HEIGHT="228" BORDER="0"
 SRC="|."$dir".q|img274.png"
 ALT="\begin{figure*}
\epsfysize =2in
\centerline{\epsffile{fig1.eps}}
\end{figure*}">|; 

$key = q/{displaymath}W=frac{C,V^2}{2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img602.png"
 ALT="\begin{displaymath}
W = \frac{C V^2}{2}
\end{displaymath}">|; 

$key = q/{displaymath}F=frac{mu_0,I_1,I_2}{2pi,r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img756.png"
 ALT="\begin{displaymath}
F= \frac{\mu_0  I_1  I_2}{2\pi  r}.
\end{displaymath}">|; 

$key = q/a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$a$">|; 

$key = q/{displaymath}V_a=k_e,frac{q_a}{c}=(8.988times10^9),frac{(-6times10^{-6})}{(sqrt{4^2+3^2})}=-1.08times10^4,{{rm{V},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="465" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img469.png"
 ALT="\begin{displaymath}
V_a = k_e \frac{q_a}{c} = (8.988\times 10^9) \frac{(-6\times 10^{-6})}{(\sqrt{4^2+3^2})}= - 1.08 \times 10^4 {\rm V},
\end{displaymath}">|; 

$key = q/V=V(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img431.png"
 ALT="$V = V(r)$">|; 

$key = q/n=2.42;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1338.png"
 ALT="$n=2.42$">|; 

$key = q/dP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img397.png"
 ALT="$dP$">|; 

$key = q/{displaymath}F=I',B,sin90^circ=I',B=(1.7),(10^{-4})=1.7times10^{-4},{{rm{N,m}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img864.png"
 ALT="\begin{displaymath}
F = I' B \sin 90^\circ = I' B = (1.7)  (10^{-4})= 1.7\times 10^{-4} {\rm N m}^{-1}.
\end{displaymath}">|; 

$key = q/{displaymath}{mitPhi}_B=B,l,x.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img907.png"
 ALT="\begin{displaymath}
{\mit\Phi}_B = B l x.
\end{displaymath}">|; 

$key = q/dI_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1054.png"
 ALT="$d I_1$">|; 

$key = q/{displaymath}{calE}=i,R,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1112.png"
 ALT="\begin{displaymath}
{\cal E} = i R,
\end{displaymath}">|; 

$key = q/4.8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img574.png"
 ALT="$4.8$">|; 

$key = q/q,{calE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img898.png"
 ALT="$q {\cal E}$">|; 

$key = q/E_bggE_a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img501.png"
 ALT="$E_b\gg E_a$">|; 

$key = q/R_{{rm{eq};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img650.png"
 ALT="$R_{\rm eq}$">|; 

$key = q/{displaymath}C=frac{(8.85times10^{-12}),(150times10^{-4})}{(0.6times10^{-2})}=2.21times10^{-11}=22.1,{{rm{pF}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img565.png"
 ALT="\begin{displaymath}
C= \frac{(8.85\times 10^{-12}) (150\times 10^{-4})}{(0.6\times 10^{-2})}
=2.21\times 10^{-11} = 22.1 {\rm pF}.
\end{displaymath}">|; 

$key = q/sigmaslashepsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img554.png"
 ALT="$\sigma/\epsilon_0$">|; 

$key = q/{displaymath}q=-M,p,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1460.png"
 ALT="\begin{displaymath}
q = - M p,
\end{displaymath}">|; 

$key = q/dV=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img424.png"
 ALT="$dV=0$">|; 

$key = q/PQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1318.png"
 ALT="$PQ$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{radius.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="617" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img1413.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{radius.eps}}
\end{figure}">|; 

$key = q/{displaymath}V_H=v_d,w,B.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img801.png"
 ALT="\begin{displaymath}
V_H = v_d w B.
\end{displaymath}">|; 

$key = q/{displaymath}R_S=frac{1times10^{-5}}{1-1times10^{-5}},40simeq4.0times10^{-4},Omega.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img847.png"
 ALT="\begin{displaymath}
R_S = \frac{ 1\times 10^{-5}}{1 - 1\times 10^{-5}}  40 \simeq 4.0\times 10^{-4}
 \Omega.
\end{displaymath}">|; 

$key = q/{{bf{F}=-{{bf{r}slash|r^3|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="${\bf F} = - {\bf r}/ \vert r^3\vert$">|; 

$key = q/dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img395.png"
 ALT="$dx$">|; 

$key = q/{displaymath}k_e=8.988times10^9,,{{rm{N,m^2,C^{-2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="\begin{displaymath}
k_e = 8.988\times 10^9  {\rm N m^2 C^{-2}}.
\end{displaymath}">|; 

$key = q/{displaymath}epsilon=K,epsilon_0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img517.png"
 ALT="\begin{displaymath}
\epsilon = K \epsilon_0
\end{displaymath}">|; 

$key = q/{displaymath}L=frac{mu_0,N^2,A}{l}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1080.png"
 ALT="\begin{displaymath}
L = \frac{\mu_0 N^2 A}{l}.
\end{displaymath}">|; 

$key = q/b=3.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img279.png"
 ALT="$b=3.0$">|; 

$key = q/C=15,mu{{rm{F};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1189.png"
 ALT="$C= 15 \mu{\rm F}$">|; 

$key = q/{displaymath}sintheta_m'=frac{mitDelta}{d}=frac{(m+1slash2),lambda}{d}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1504.png"
 ALT="\begin{displaymath}
\sin\theta_m' = \frac{\mit\Delta}{d} = \frac{(m+1/2) \lambda}{d}.
\end{displaymath}">|; 

$key = q/di'=di;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1100.png"
 ALT="$di'=di$">|; 

$key = q/{{bf{r}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img434.png"
 ALT="${\bf r}_i$">|; 

$key = q/displaystyle-f_{ac},costheta=-(4.31times10^{-3}),(0.6)=-2.59times10^{-3},{{rm{N},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="432" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img293.png"
 ALT="$\displaystyle -f_{ac} \cos\theta = -(4.31 \times 10^{-3}) (0.6)=-2.59\times 10^{-3} {\rm N},$">|; 

$key = q/a=4.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img278.png"
 ALT="$a=4.0$">|; 

$key = q/R_2=10,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img708.png"
 ALT="$R_2=10 \Omega$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{induction.eps}}{{{.{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="582" HEIGHT="367" BORDER="0"
 SRC="|."$dir".q|img904.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{induction.eps}}
.\end{figure}">|; 

$key = q/{displaymath}{calE}=N,B,A,omega,sin(omega,t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img937.png"
 ALT="\begin{displaymath}
{\cal E} = N B A \omega \sin( \omega  t),
\end{displaymath}">|; 

$key = q/{{bf{E}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img920.png"
 ALT="${\bf E}_0$">|; 

$key = q/f_{bc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img283.png"
 ALT="$f_{bc}$">|; 

$key = q/B_1=mu_0,N_1,I_1slashl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1061.png"
 ALT="$B_1 = \mu_0 N_1 I_1/l$">|; 

$key = q/{displaymath}P=epsilon_0,c,E,(c,B)=epsilon_0,c^2,E,B=frac{E,B}{mu_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1279.png"
 ALT="\begin{displaymath}
P = \epsilon_0 c E (c B) = \epsilon_0 c^2 E B = \frac{E B}{\mu_0}.
\end{displaymath}">|; 

$key = q/{displaymath}Phi_B=oint_S{{bf{B}cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img824.png"
 ALT="\begin{displaymath}
\Phi_B = \oint_S {\bf B}\cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/dlll;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img775.png"
 ALT="$d\ll l$">|; 

$key = q/{displaymath}w=B,L.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img815.png"
 ALT="\begin{displaymath}
w = B L.
\end{displaymath}">|; 

$key = q/140,{{rm{W},{{rm{m}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1291.png"
 ALT="$140 {\rm W} {\rm m}^{-2}$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{mirror.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="512" HEIGHT="289" BORDER="0"
 SRC="|."$dir".q|img1298.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{mirror.eps}}
\end{figure}">|; 

$key = q/{figure}{epsfysize{=1.5in{centerline{epsffile{lens.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="173" BORDER="0"
 SRC="|."$dir".q|img1407.png"
 ALT="\begin{figure}
\epsfysize =1.5in
\centerline{\epsffile{lens.eps}}
\end{figure}">|; 

$key = q/C_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img529.png"
 ALT="$C_2$">|; 

$key = q/{displaymath}v_2=L_2,frac{di_2}{dt}+M,frac{di_1}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1146.png"
 ALT="\begin{displaymath}
v_2 = L_2 \frac{di_2}{d t} + M \frac{di_1}{d t}.
\end{displaymath}">|; 

$key = q/r_1=i_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1351.png"
 ALT="$r_1=i_1$">|; 

$key = q/f=35;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1466.png"
 ALT="$f=35$">|; 

$key = q/f=q,E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img616.png"
 ALT="$f=q E$">|; 

$key = q/v=qslashC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1217.png"
 ALT="$v=q/C$">|; 

$key = q/{displaymath}frac{S'T'}{OP}=frac{FS'}{OF},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1435.png"
 ALT="\begin{displaymath}
\frac{S'T'}{OP} = \frac{FS'}{OF},
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=1.25in{centerline{epsffile{series.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="421" HEIGHT="145" BORDER="0"
 SRC="|."$dir".q|img646.png"
 ALT="\begin{figure}
\epsfysize =1.25in
\centerline{\epsffile{series.eps}}
\end{figure}">|; 

$key = q/R_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img725.png"
 ALT="$R_3$">|; 

$key = q/{displaymath}{mitPhi}_B=N_2,A_1,mu_0,n_1,I_1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1008.png"
 ALT="\begin{displaymath}
{\mit\Phi}_B = N_2 A_1 \mu_0 n_1 I_1.
\end{displaymath}">|; 

$key = q/q_1=+6.0,mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$q_1=+6.0 \mu{\rm C}$">|; 

$key = q/{displaymath}C_{{rm{eq}=frac{Q}{V}=frac{Q_1+Q_2}{V}=frac{Q_1}{V}+frac{Q_2}{V},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img535.png"
 ALT="\begin{displaymath}
C_{\rm eq} = \frac{Q}{V} = \frac{Q_1+Q_2}{V} = \frac{Q_1}{V} + \frac{Q_2}{V},
\end{displaymath}">|; 

$key = q/x=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img682.png"
 ALT="$x=1$">|; 

$key = q/f=60;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img957.png"
 ALT="$f=60$">|; 

$key = q/S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$S$">|; 

$key = q/{displaymath}1,{{rm{H}equiv1,{{rm{V,s,A}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1053.png"
 ALT="\begin{displaymath}
1 {\rm H} \equiv 1 {\rm V s A}^{-1}.
\end{displaymath}">|; 

$key = q/displaystylef_{ac,x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img292.png"
 ALT="$\displaystyle f_{ac x}$">|; 

$key = q/3times10^8,{{rm{m},{{rm{s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1254.png"
 ALT="$3\times 10^8 {\rm m} {\rm s}^{-1}$">|; 

$key = q/{displaymath}sintheta_2=frac{n_1}{n_2},sintheta_1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1323.png"
 ALT="\begin{displaymath}
\sin\theta_2 = \frac{n_1}{n_2}  \sin\theta_1.
\end{displaymath}">|; 

$key = q/99%;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1108.png"
 ALT="$99\%$">|; 

$key = q/p=,25;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1449.png"
 ALT="$p= 25$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{descartes.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="427" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img1492.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{descartes.eps}}
\end{figure}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{galvo.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="344" BORDER="0"
 SRC="|."$dir".q|img828.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{galvo.eps}}
\end{figure}">|; 

$key = q/{displaymath}I=frac{{calE}}{r+R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img671.png"
 ALT="\begin{displaymath}
I = \frac{{\cal E}}{r+R}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{parallel.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="355" HEIGHT="231" BORDER="0"
 SRC="|."$dir".q|img654.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{parallel.eps}}
\end{figure}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig2.8.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="281" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig2.8.eps}}
\end{figure}">|; 

$key = q/{displaymath}2pi,r,B(r)=mu_0,I,frac{r^2}{a^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img885.png"
 ALT="\begin{displaymath}
2\pi  r B(r) = \mu_0 I \frac{r^2}{a^2},
\end{displaymath}">|; 

$key = q/d_zV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img416.png"
 ALT="$d_z V$">|; 

$key = q/6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img584.png"
 ALT="$6$">|; 

$key = q/1slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img681.png"
 ALT="$1/4$">|; 

$key = q/x=Rslashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img677.png"
 ALT="$x=R/r$">|; 

$key = q/9.1times10^{-31};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img781.png"
 ALT="$9.1\times 10^{-31}$">|; 

$key = q/{displaymath}tau=frac{L}{R}=frac{(0.1)}{(5.0)}=0.020,{{rm{s}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1187.png"
 ALT="\begin{displaymath}
\tau = \frac{L}{R} = \frac{(0.1)}{(5.0)} = 0.020 {\rm s}.
\end{displaymath}">|; 

$key = q/{displaymath}oint_C{{bf{B}cdotd{{bf{r}=mu_0int_{S'}{{bf{j}cdotd{{bf{S}'+mu_0,epsilon_0,frac{d}{dt}int_{S'}{{bf{E}cdotd{{bf{S}',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1232.png"
 ALT="\begin{displaymath}
\oint_C {\bf B}\cdot d{\bf r} = \mu_0\int_{S'} {\bf j} \cdot...
...u_0 \epsilon_0 \frac{d}{dt}\int_{S'} {\bf E}\cdot d{\bf S}',
\end{displaymath}">|; 

$key = q/0.06;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img514.png"
 ALT="$0.06$">|; 

$key = q/lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img333.png"
 ALT="$\lambda$">|; 

$key = q/{displaymath}q'(t)=-Q,{{rm{e}^{-tslashR,C}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1128.png"
 ALT="\begin{displaymath}
q'(t) = -Q  {\rm e}^{-t/R C}.
\end{displaymath}">|; 

$key = q/{displaymath}{mitPhi}_B=A,B_perp=A,B,costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img888.png"
 ALT="\begin{displaymath}
{\mit\Phi}_B = A B_\perp= A  B  \cos\theta.
\end{displaymath}">|; 

$key = q/42^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1343.png"
 ALT="$42^\circ$">|; 

$key = q/{displaymath}dP=q,dV{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img398.png"
 ALT="\begin{displaymath}
dP = q  dV
\end{displaymath}">|; 

$key = q/{displaymath}frac{dq}{dt}=C,d,frac{dE}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1222.png"
 ALT="\begin{displaymath}
\frac{dq}{d t} = C d \frac{dE}{dt}.
\end{displaymath}">|; 

$key = q/lambda=0.76;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1257.png"
 ALT="$\lambda= 0.76$">|; 

$key = q/{displaymath}{calE}=frac{d{mitPhi}_B}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img893.png"
 ALT="\begin{displaymath}
{\cal E} = \frac{d{\mit\Phi}_B}{dt}.
\end{displaymath}">|; 

$key = q/h=4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1440.png"
 ALT="$h=4$">|; 

$key = q/{displaymath}V=E,d=frac{sigma,d}{epsilon_0}=frac{Q,d}{epsilon_0,A},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img510.png"
 ALT="\begin{displaymath}
V = E  d = \frac{\sigma d}{\epsilon_0} = \frac{Q d}{\epsilon_0 A},
\end{displaymath}">|; 

$key = q/{displaymath}frac{V_1}{V_2}=frac{I_2}{I_1}=frac{N_1}{N_2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1159.png"
 ALT="\begin{displaymath}
\frac{V_1}{V_2} = \frac{I_2}{I_1} = \frac{N_1}{N_2}.
\end{displaymath}">|; 

$key = q/lambda=589;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\lambda =589$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{hall.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="654" HEIGHT="229" BORDER="0"
 SRC="|."$dir".q|img795.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{hall.eps}}
\end{figure}">|; 

$key = q/{calE},I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img951.png"
 ALT="${\cal E} I$">|; 

$key = q/{displaymath}I_D=epsilon_0,frac{d{mitPhi}_E}{dt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1230.png"
 ALT="\begin{displaymath}
I_D = \epsilon_0 \frac{d{\mit\Phi}_E}{d t},
\end{displaymath}">|; 

$key = q/{displaymath}frac{da_x}{dt}=frac{d}{dt}!left(phi,b_xright)=frac{dphi}{dt},b_x+phi,frac{db_x}{dt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="\begin{displaymath}
\frac{d a_x}{dt} = \frac{d}{dt}\!\left(\phi  b_x\right) = \frac{d\phi}{dt}  b_x + \phi  
\frac{d b_x}{dt},
\end{displaymath}">|; 

$key = q/1.25times10^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img603.png"
 ALT="$1.25\times 10^{-8}$">|; 

$key = q/q_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img433.png"
 ALT="$q_i$">|; 

$key = q/A_2=100,{{rm{cm}^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1000.png"
 ALT="$A_2= 100 {\rm cm}^2$">|; 

$key = q/R=4.0,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1031.png"
 ALT="$R=4.0 \Omega$">|; 

$key = q/C=QslashV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img513.png"
 ALT="$C=Q/V$">|; 

$key = q/{displaymath}frac{Q_a}{Q_b}=frac{a}{b}gg1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img496.png"
 ALT="\begin{displaymath}
\frac{Q_a}{Q_b} = \frac{a}{b} \gg 1.
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{Q^2}{2,C}=frac{C,V^2}{2}=frac{Q,V}{2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img553.png"
 ALT="\begin{displaymath}
W = \frac{Q^2}{2 C} = \frac{C V^2}{2} = \frac{Q  V}{2}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{sheet.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="428" HEIGHT="286" BORDER="0"
 SRC="|."$dir".q|img342.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{sheet.eps}}
\end{figure}">|; 

$key = q/{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="${\bf E}$">|; 

$key = q/q,{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img359.png"
 ALT="$q {\bf E}$">|; 

$key = q/{displaymath}E=frac{sigma}{epsilon_0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img351.png"
 ALT="\begin{displaymath}
E= \frac{\sigma}{\epsilon_0}
\end{displaymath}">|; 

$key = q/{displaymath}c=(0.9),(0.08)=0.072,,{{rm{dollars}=7.2,,{{rm{cents}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="350" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img739.png"
 ALT="\begin{displaymath}
c = (0.9) (0.08) = 0.072  {\rm dollars} = 7.2  {\rm cents}.
\end{displaymath}">|; 

$key = q/P=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1199.png"
 ALT="$P=1$">|; 

$key = q/S'T'C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1385.png"
 ALT="$S'T'C$">|; 

$key = q/{displaymath}{mitDelta}=m,lambda,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1498.png"
 ALT="\begin{displaymath}
{\mit\Delta} = m \lambda,
\end{displaymath}">|; 

$key = q/{{bf{a},&,{{bf{b}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="${\bf a} \&amp; {\bf b}= 1$">|; 

$key = q/qslashm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img791.png"
 ALT="$q/m$">|; 

$key = q/B_perp=B,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img912.png"
 ALT="$B_\perp = B \cos\theta$">|; 

$key = q/{displaymath}M=frac{mu_0,N_1,N_2,A}{l}=frac{(1.26times10^{-6}),(100),(300),(0.05)}{0.1}=0.0188,{{rm{H}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="513" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1175.png"
 ALT="\begin{displaymath}
M = \frac{\mu_0 N_1 N_2 A}{l} = \frac{(1.26\times 10^{-6}) (100) (300) (0.05)}{0.1}
= 0.0188 {\rm H}.
\end{displaymath}">|; 

$key = q/{displaymath}P_{calE}={calE},I=frac{{calE}^2}{r+R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img672.png"
 ALT="\begin{displaymath}
P_{\cal E} = {\cal E} I = \frac{{\cal E}^2}{r+R}.
\end{displaymath}">|; 

$key = q/{displaymath}P=epsilon_0,E^2,c.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1277.png"
 ALT="\begin{displaymath}
P = \epsilon_0 E^2  c.
\end{displaymath}">|; 

$key = q/v_2,{mitDelta}t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1314.png"
 ALT="$v_2 {\mit\Delta} t$">|; 

$key = q/q,V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img604.png"
 ALT="$q V$">|; 

$key = q/{displaymath}V_B-V_A=frac{W}{q},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img381.png"
 ALT="\begin{displaymath}
V_B - V_A = \frac{W}{q},
\end{displaymath}">|; 

$key = q/R_G;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img833.png"
 ALT="$R_G$">|; 

$key = q/{displaymath}{mitPhi}=N,B,A=frac{mu_0,N^2,A,I}{l}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1078.png"
 ALT="\begin{displaymath}
{\mit\Phi}= N B A = \frac{\mu_0 N^2 A I}{l}.
\end{displaymath}">|; 

$key = q/(I_{{rm{max}-I_{{rm{fsd}),R_S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img840.png"
 ALT="$(I_{\rm max}-I_{\rm fsd}) R_S$">|; 

$key = q/40^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img861.png"
 ALT="$40^\circ$">|; 

$key = q/M_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1049.png"
 ALT="$M_{12}$">|; 

$key = q/{displaymath}tau=R,C{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1130.png"
 ALT="\begin{displaymath}
\tau = R C
\end{displaymath}">|; 

$key = q/A,d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img557.png"
 ALT="$A d$">|; 

$key = q/V_{12}=6-2.57=3.43,{{rm{V};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img592.png"
 ALT="$V_{12}=6-2.57 = 3.43 {\rm V}$">|; 

$key = q/I_{{rm{max}-I_{{rm{fsd};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img839.png"
 ALT="$I_{\rm max}-I_{\rm fsd}$">|; 

$key = q/{displaymath}v_1=V_1,cos(omega,t){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1137.png"
 ALT="\begin{displaymath}
v_1 = V_1 \cos (\omega  t)
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{diagram.eps}}{{{{figure};MSF=1.6;LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="402" BORDER="0"
 SRC="|."$dir".q|img1319.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{diagram.eps}}
\end{figure}">|; 

$key = q/displaystylef_{bc,y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img288.png"
 ALT="$\displaystyle f_{bc y}$">|; 

$key = q/1.5,{{rm{V};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img642.png"
 ALT="$1.5 {\rm V}$">|; 

$key = q/{displaymath}V_H=frac{I,B}{q,n,d}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img803.png"
 ALT="\begin{displaymath}
V_H = \frac{I B}{q n d}.
\end{displaymath}">|; 

$key = q/M=0.0667;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1480.png"
 ALT="$M=0.0667$">|; 

$key = q/{displaymath}frac{1}{C_{{rm{eq}}=frac{V}{Q}=frac{V_1+V_2}{Q}=frac{V_1}{Q}+frac{V_2}{Q},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="259" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img543.png"
 ALT="\begin{displaymath}
\frac{1}{C_{\rm eq}}=\frac{V}{Q}=\frac{V_1+ V_2}{Q} = \frac{V_1}{Q} + \frac{V_2}{Q},
\end{displaymath}">|; 

$key = q/displaystyle(a_x^{~2}+a_y^{~2}+a_z^{~2}),(b_x^{~2}+b_y^{~2}+b_z^{~2})-(a_x,b_x+a_y,b_y+a_z,b_z)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$\displaystyle (a_x^{&nbsp;2}+a_y^{&nbsp;2}+a_z^{&nbsp;2}) (b_x^{&nbsp;2}+b_y^{&nbsp;2}+b_z^{&nbsp;2}) -
(a_x  b_x + a_y  b_y + a_z  b_z)^2$">|; 

$key = q/{mitDelta}P=q,{mitDelta}V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img390.png"
 ALT="${\mit\Delta}P = q {\mit\Delta} V$">|; 

$key = q/{figure}{epsfysize{=1.5in{centerline{epsffile{fig2.1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="165" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="\begin{figure}
\epsfysize =1.5in
\centerline{\epsffile{fig2.1.eps}}
\end{figure}">|; 

$key = q/{{bf{a}equiv(a_x,a_y,a_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="${\bf a} \equiv (a_x, a_y, a_z)$">|; 

$key = q/dV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img396.png"
 ALT="$dV$">|; 

$key = q/V=QslashC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img566.png"
 ALT="$V = Q/C$">|; 

$key = q/c'=f,lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1289.png"
 ALT="$c'=f \lambda$">|; 

$key = q/W';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img450.png"
 ALT="$W'$">|; 

$key = q/50,{{rm{Hz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1032.png"
 ALT="$50 {\rm Hz}$">|; 

$key = q/1%;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1118.png"
 ALT="$1\%$">|; 

$key = q/{displaymath}lambda_m=frac{2,n,t}{m},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1529.png"
 ALT="\begin{displaymath}
\lambda_m = \frac{2 n t}{m},
\end{displaymath}">|; 

$key = q/+infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1439.png"
 ALT="$+\infty$">|; 

$key = q/dq=i,dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1123.png"
 ALT="$d q = i dt$">|; 

$key = q/{displaymath}V_1=frac{N_1}{N_2},V_2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1164.png"
 ALT="\begin{displaymath}
V_1 = \frac{N_1}{N_2} V_2,
\end{displaymath}">|; 

$key = q/Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img611.png"
 ALT="$\Omega$">|; 

$key = q/{displaymath}i_1,v_1=i_2,v_2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1150.png"
 ALT="\begin{displaymath}
i_1 v_1= i_2 v_2,
\end{displaymath}">|; 

$key = q/displaystylemu_0,epsilon_0,frac{d}{dt}int_{S'}{{bf{E}cdotd{{bf{S}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1239.png"
 ALT="$\displaystyle \mu_0 
\epsilon_0 \frac{d}{dt}\int_{S'} {\bf E}\cdot d {\bf S}',$">|; 

$key = q/{displaymath}2,t=m,lambda.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1517.png"
 ALT="\begin{displaymath}
2 t = m \lambda.
\end{displaymath}">|; 

$key = q/v_2=cslashn_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1310.png"
 ALT="$v_2=c/n_2$">|; 

$key = q/I_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img656.png"
 ALT="$I_2$">|; 

$key = q/lambda=0.40;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1255.png"
 ALT="$\lambda= 0.40$">|; 

$key = q/{mitPhi}_{1}=N_1,B_2,A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1065.png"
 ALT="${\mit\Phi}_{1} = N_1 B_2 A$">|; 

$key = q/{calE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="${\cal E}$">|; 

$key = q/{displaymath}1,{{rm{T}equiv1,{{rm{Wb,m}^{-2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img891.png"
 ALT="\begin{displaymath}
1 {\rm T} \equiv 1 {\rm Wb  m}^{-2}.
\end{displaymath}">|; 

$key = q/b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img484.png"
 ALT="$b$">|; 

$key = q/V=I,R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img614.png"
 ALT="$V=I R$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{orbit.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="481" HEIGHT="286" BORDER="0"
 SRC="|."$dir".q|img790.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{orbit.eps}}
\end{figure}">|; 

$key = q/{displaymath}{{bf{E}_0={{bf{v}times{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img921.png"
 ALT="\begin{displaymath}
{\bf E}_0 = {\bf v} \times {\bf B}.
\end{displaymath}">|; 

$key = q/B_1=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img984.png"
 ALT="$B_1=1$">|; 

$key = q/{displaymath}lnleft(frac{Q}{q}right)=frac{t}{R,C}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1194.png"
 ALT="\begin{displaymath}
\ln\left(\frac{Q}{q}\right) = \frac{t}{R C}.
\end{displaymath}">|; 

$key = q/x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$x$">|; 

$key = q/{displaymath}mu_0=4pitimes10^{-7},{{rm{N,A^{-2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img749.png"
 ALT="\begin{displaymath}
\mu_0 = 4\pi \times 10^{-7} {\rm N A^{-2}}.
\end{displaymath}">|; 

$key = q/{displaymath}B=mu_0,n_1,I_1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1007.png"
 ALT="\begin{displaymath}
B = \mu_0 n_1 I_1,
\end{displaymath}">|; 

$key = q/{displaymath}V_2=k_e,frac{q_2}{|x_2|}=(8.988times10^9),frac{(-5times10^{-6})}{(3.4times10^{-2})}=-1.32times10^6,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img464.png"
 ALT="\begin{displaymath}
V_2 = k_e \frac{q_2}{\vert x_2\vert} = (8.988\times 10^9) ...
...imes 10^{-6})}{(3.4\times 10^{-2})}=-1.32\times 10^6 {\rm V}.
\end{displaymath}">|; 

$key = q/n,{{bf{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$n {\bf a}$">|; 

$key = q/{{bf{B}_1+{{bf{B}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img753.png"
 ALT="${\bf B}_1+{\bf B}_2$">|; 

$key = q/{displaymath}E(R)=frac{lambda}{2piepsilon_0,R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img338.png"
 ALT="\begin{displaymath}
E(R) = \frac{\lambda}{2\pi\epsilon_0 R}.
\end{displaymath}">|; 

$key = q/{displaymath}V=I,R+{calE},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img970.png"
 ALT="\begin{displaymath}
V = I  R + {\cal E},
\end{displaymath}">|; 

$key = q/{displaymath}f_3=f_{13}+f_{23}=-41.69-77.75=-119.22,{{rm{N}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img271.png"
 ALT="\begin{displaymath}
f_3 = f_{13} + f_{23} = - 41.69 - 77.75 =-119.22 {\rm N}.
\end{displaymath}">|; 

$key = q/F_o;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1426.png"
 ALT="$F_o$">|; 

$key = q/50,{{rm{cm}^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img568.png"
 ALT="$50 {\rm cm}^2$">|; 

$key = q/dI_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1058.png"
 ALT="$d I_2$">|; 

$key = q/{displaymath}{mitDelta}=(m+1slash2),lambda,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1502.png"
 ALT="\begin{displaymath}
{\mit\Delta} = (m+1/2) \lambda,
\end{displaymath}">|; 

$key = q/{displaymath}I_1=I_2+I_3.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img712.png"
 ALT="\begin{displaymath}
I_1 = I_2 + I_3.
\end{displaymath}">|; 

$key = q/T';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1372.png"
 ALT="$T'$">|; 

$key = q/1.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img569.png"
 ALT="$1.0$">|; 

$key = q/I=I_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img837.png"
 ALT="$I=I_{\rm max}$">|; 

$key = q/BQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1311.png"
 ALT="$BQ$">|; 

$key = q/{mitDelta}=2,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1512.png"
 ALT="${\mit\Delta}=2 t$">|; 

$key = q/{displaymath}q=frac{1}{1slashf-1slashp}=frac{1}{(1slash20-1slash25)}=100,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="344" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1450.png"
 ALT="\begin{displaymath}
q = \frac{1}{1/f - 1/p} = \frac{1}{(1/20-1/25)} = 100 {\rm cm}.
\end{displaymath}">|; 

$key = q/0.1,{{rm{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img643.png"
 ALT="$0.1 {\rm A}$">|; 

$key = q/{displaymath}W=frac{1}{2},L,I^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1085.png"
 ALT="\begin{displaymath}
W = \frac{1}{2} L I^2.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{b}=a_x,b_x+a_y,b_y+a_z,b_z={{rm{scalar~number}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="361" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="\begin{displaymath}
{\bf a} \cdot {\bf b} = a_x  b_x + a_y  b_y + a_z  b_z = {\rm scalar&nbsp;number}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{wf.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="345" BORDER="0"
 SRC="|."$dir".q|img1297.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{wf.eps}}
\end{figure}">|; 

$key = q/dE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1221.png"
 ALT="$dE$">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{b}=a_x^{~2}+a_y^{~2}+a_z^{~2}={{rm{Length}~(OP)^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="322" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="\begin{displaymath}
{\bf a} \cdot {\bf b} = a_x^{&nbsp;2}+a_y^{&nbsp;2} + a_z^{&nbsp;2} = {\rm Length}&nbsp;(OP)^2,
\end{displaymath}">|; 

$key = q/infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="$\infty$">|; 

$key = q/E=sigmaslashepsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img509.png"
 ALT="$E= \sigma/\epsilon_0$">|; 

$key = q/B_2=mu_0,N_2,I_2slashl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1066.png"
 ALT="$B_2 = \mu_0 N_2 I_2/l$">|; 

$key = q/{displaymath}frac{1}{2},m_e,v^2=e,V.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img873.png"
 ALT="\begin{displaymath}
\frac{1}{2} m_e v^2 = e V.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{huygens.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="325" HEIGHT="344" BORDER="0"
 SRC="|."$dir".q|img1494.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{huygens.eps}}
\end{figure}">|; 

$key = q/{displaymath}h'=M,h=-(9.636),(7)=-4.45,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="302" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1477.png"
 ALT="\begin{displaymath}
h' = M h = -(9.636) (7) = -4.45 {\rm cm}.
\end{displaymath}">|; 

$key = q/I,r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img636.png"
 ALT="$I r$">|; 

$key = q/{displaymath}q'=q-Q.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1126.png"
 ALT="\begin{displaymath}
q' = q -Q.
\end{displaymath}">|; 

$key = q/{displaymath}W=q_3,V=(-7times10^{-6}),(-2.64times10^5)=1.85,{{rm{J}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="393" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img467.png"
 ALT="\begin{displaymath}
W = q_3  V = (-7\times 10^{-6}) (-2.64\times 10^5) = 1.85 {\rm J}.
\end{displaymath}">|; 

$key = q/{displaymath}q=-M,p=-(0.0667),(630)=-42,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1485.png"
 ALT="\begin{displaymath}
q = -M p = -(0.0667) (630) = -42 {\rm cm}.
\end{displaymath}">|; 

$key = q/displaystylef_{bc,x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img286.png"
 ALT="$\displaystyle f_{bc x}$">|; 

$key = q/E=Qslash(4piepsilon_0,a^2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img479.png"
 ALT="$E = Q/(4\pi\epsilon_0 a^2)$">|; 

$key = q/{displaymath}{mitPhi}_{B,1}=N,A,B_1,costheta=(15),(0.0314),(1),(0.8660)=0.408,{{rm{Wb}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="490" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img990.png"
 ALT="\begin{displaymath}
{\mit\Phi}_{B 1} = N A B_1 \cos\theta = (15) (0.0314) (1) (0.8660) = 0.408 {\rm Wb}.
\end{displaymath}">|; 

$key = q/{displaymath}I_{{rm{fsd}=frac{V_{{rm{max}}{R_S+R_G},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img854.png"
 ALT="\begin{displaymath}
I_{\rm fsd} = \frac{V_{\rm max}}{R_S+R_G},
\end{displaymath}">|; 

$key = q/{displaymath}I=frac{V}{R_{{rm{eq}}=frac{(6)}{(4.667)}=1.29,{{rm{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img700.png"
 ALT="\begin{displaymath}
I = \frac{V}{R_{\rm eq}} = \frac{(6)}{(4.667)} = 1.29 {\rm A}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=1in{centerline{epsffile{cap2.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="112" BORDER="0"
 SRC="|."$dir".q|img538.png"
 ALT="\begin{figure}
\epsfysize =1in
\centerline{\epsffile{cap2.eps}}
\end{figure}">|; 

$key = q/{displaymath}q=-p.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1403.png"
 ALT="\begin{displaymath}
q = -p.
\end{displaymath}">|; 

$key = q/P=I,V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1160.png"
 ALT="$P=I  V$">|; 

$key = q/0^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$0^\circ $">|; 

$key = q/{displaymath}f_{bc}=k_e,frac{q_bq_c}{b^2}=(8.988times10^9),frac{(4times10^{-6}),2times10^{-6})}{(3^2)}=7.99times10^{-3},{{rm{N}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="549" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img285.png"
 ALT="\begin{displaymath}
f_{bc} = k_e \frac{q_b q_c}{b^2}= (8.988\times 10^9) \frac...
...) (2\times 10^{-6})}
{(3^2)} = 7.99 \times 10^{-3}  {\rm N}.
\end{displaymath}">|; 

$key = q/R_f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1411.png"
 ALT="$R_f$">|; 

$key = q/{displaymath}{{bf{v}=frac{d{{bf{r}}{dt}=lim_{deltatrightarrow0}frac{{{bf{r}(t+deltat)-{{bf{r}(t)}{deltat}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="\begin{displaymath}
{\bf v} = \frac{d {\bf r}}{dt} = \lim_{\delta t\rightarrow 0}
\frac{ {\bf r}(t+\delta t) - {\bf r}(t) }{\delta t}.
\end{displaymath}">|; 

$key = q/{displaymath}I=I_1+I_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img657.png"
 ALT="\begin{displaymath}
I = I_1 + I_2.
\end{displaymath}">|; 

$key = q/n,t=(m+1slash2),lambdaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1532.png"
 ALT="$n t=(m+1/2) \lambda/2$">|; 

$key = q/h';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1381.png"
 ALT="$h'$">|; 

$key = q/{displaymath}i_2=90^circ-r_1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1350.png"
 ALT="\begin{displaymath}
i_2 = 90^\circ - r_1.
\end{displaymath}">|; 

$key = q/q_3=+2.0,mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="$q_3=+2.0 \mu{\rm C}$">|; 

$key = q/dV=A,c,dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1274.png"
 ALT="$dV = A c d t$">|; 

$key = q/{displaymath}{{bf{a},{{rm{x},{{bf{b}=(a_x,b_x,,a_y,b_y,,a_z,b_z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="\begin{displaymath}
{\bf a}  {\rm x}  {\bf b} = (a_x  b_x,  a_y  b_y,  a_z  b_z).
\end{displaymath}">|; 

$key = q/{displaymath}frac{1}{2},m,v_B^{~2}=-{mitDelta}P,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img460.png"
 ALT="\begin{displaymath}
\frac{1}{2} m v_B^{&nbsp;2} = - {\mit\Delta}P,
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{Q^2}{2,C}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img600.png"
 ALT="\begin{displaymath}
W = \frac{Q^2}{2 C}
\end{displaymath}">|; 

$key = q/Q=Q_1+Q_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img534.png"
 ALT="$Q=Q_1+Q_2$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig3.10.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="417" HEIGHT="274" BORDER="0"
 SRC="|."$dir".q|img754.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig3.10.eps}}\end{figure}">|; 

$key = q/STC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1384.png"
 ALT="$STC$">|; 

$key = q/{{bf{f}_{ab};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="${\bf f}_{ab}$">|; 

$key = q/{displaymath}{{bf{a}+{{bf{b}equiv(a_x+b_x,,a_y+b_y,,a_z+b_z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="\begin{displaymath}
{\bf a} + {\bf b} \equiv (a_x+b_x,  a_y+b_y,  a_z+b_z).
\end{displaymath}">|; 

$key = q/W_1-W_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img374.png"
 ALT="$W_1-W_2$">|; 

$key = q/{displaymath}dW=frac{q,dq}{C}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img551.png"
 ALT="\begin{displaymath}
dW =\frac{q dq}{C}.
\end{displaymath}">|; 

$key = q/{displaymath}q=frac{1}{1slashf-1slashp}=frac{1}{(1slash35-1slash25)}=-87.5,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1468.png"
 ALT="\begin{displaymath}
q = \frac{1}{1/f - 1/p} = \frac{1}{(1/35-1/25)} = - 87.5 {\rm cm}.
\end{displaymath}">|; 

$key = q/theta=0^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img932.png"
 ALT="$\theta = 0^\circ$">|; 

$key = q/{displaymath}V_1=omega,(L_1,I_1+M,I_2),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1143.png"
 ALT="\begin{displaymath}
V_1 = \omega (L_1 I_1 + M I_2),
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{trans.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="580" HEIGHT="290" BORDER="0"
 SRC="|."$dir".q|img1136.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{trans.eps}}
\end{figure}">|; 

$key = q/{displaymath}V=frac{(1.00times10^{-9})}{(2.21times10^{-11})}=45.2,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img567.png"
 ALT="\begin{displaymath}
V = \frac{ (1.00\times 10^{-9})}{(2.21\times 10^{-11})} = 45.2  {\rm V}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{lenses.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="512" HEIGHT="402" BORDER="0"
 SRC="|."$dir".q|img1424.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{lenses.eps}}
\end{figure}">|; 

$key = q/{displaymath}oint_C{{bf{B}cdotd{{bf{r}=mu_0,(I+I_D),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1231.png"
 ALT="\begin{displaymath}
\oint_C {\bf B}\cdot d{\bf r} = \mu_0 (I + I_D),
\end{displaymath}">|; 

$key = q/dW;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img549.png"
 ALT="$dW$">|; 

$key = q/alpha_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\alpha_y$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{aberr.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="618" HEIGHT="340" BORDER="0"
 SRC="|."$dir".q|img1369.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{aberr.eps}}
\end{figure}">|; 

$key = q/w=Wslash(l,A);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1089.png"
 ALT="$w = W/(l A)$">|; 

$key = q/V_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1438.png"
 ALT="$V_i$">|; 

$key = q/v=omega,wslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img926.png"
 ALT="$v = \omega w/2$">|; 

$key = q/E,costheta=E_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img400.png"
 ALT="$E \cos\theta=E_x$">|; 

$key = q/A_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1004.png"
 ALT="$A_2$">|; 

$key = q/{displaymath}V=i,R+L,frac{di}{dt}=(2.0),(5.0)+(0.1),(20)=12,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="391" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1186.png"
 ALT="\begin{displaymath}
V = i R + L \frac{di}{d t}
= (2.0) (5.0) + (0.1) (20) = 12 {\rm V}.
\end{displaymath}">|; 

$key = q/displaystyle{{bf{a}cdot({{bf{b}+{{bf{c});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$\displaystyle {\bf a}\cdot({\bf b}+{\bf c})$">|; 

$key = q/w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img797.png"
 ALT="$w$">|; 

$key = q/displaystylef_{ac,y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img294.png"
 ALT="$\displaystyle f_{ac y}$">|; 

$key = q/{displaymath}E(R),4pi,R^2=frac{q}{4piepsilon_0,R^2},4pi,R^2=frac{q}{epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img324.png"
 ALT="\begin{displaymath}
E(R) 4\pi  R^2 = \frac{q}{4\pi\epsilon_0 R^2}  4\pi  R^2 = \frac{q}{\epsilon_0}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig3.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="286" HEIGHT="285" BORDER="0"
 SRC="|."$dir".q|img425.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig3.eps}}
\end{figure}">|; 

$key = q/{displaymath}M=frac{mu_0,N_1,N_2,A}{l}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1069.png"
 ALT="\begin{displaymath}
M = \frac{\mu_0 N_1 N_2 A}{l}.
\end{displaymath}">|; 

$key = q/{{bf{b}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="${\bf b}(t)$">|; 

$key = q/{displaymath}S=bar{P}=frac{E_0,B_0}{2,mu_0}=frac{epsilon_0,c,E_0^{~2}}{2}=frac{c,B_0^{~2}}{2,mu_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1283.png"
 ALT="\begin{displaymath}
S= \bar{P} = \frac{E_0 B_0}{2 \mu_0} = \frac{\epsilon_0 c E_0^{&nbsp;2}}{2}
= \frac{c B_0^{&nbsp;2}}{2 \mu_0}.
\end{displaymath}">|; 

$key = q/{displaymath}P_B=q,V_B.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img384.png"
 ALT="\begin{displaymath}
P_B = q V_B.
\end{displaymath}">|; 

$key = q/{displaymath}I_2=frac{V_{12}}{R_2}=frac{(0.857)}{(2)}=0.429,{{rm{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img704.png"
 ALT="\begin{displaymath}
I_2 = \frac{V_{12}}{R_2} = \frac{(0.857)}{(2)}= 0.429 {\rm A}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig3.7.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="579" HEIGHT="279" BORDER="0"
 SRC="|."$dir".q|img742.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig3.7.eps}}
\end{figure}">|; 

$key = q/Omega,{{rm{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img628.png"
 ALT="$\Omega {\rm m}$">|; 

$key = q/z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$z$">|; 

$key = q/{displaymath}V({{bf{r})=sum_{i=1}^Nfrac{q_i}{4piepsilon_0,|{{bf{r}-{{bf{r}_i|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img435.png"
 ALT="\begin{displaymath}
V({\bf r}) = \sum_{i=1}^N \frac{q_i}{4\pi\epsilon_0 \vert{\bf r} - {\bf r}_i\vert}.
\end{displaymath}">|; 

$key = q/N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img363.png"
 ALT="$N$">|; 

$key = q/V({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img411.png"
 ALT="$V({\bf r})$">|; 

$key = q/{displaymath}{mitPhi}_B=int_S{{bf{B}cdotd{{bf{S}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img896.png"
 ALT="\begin{displaymath}
{\mit\Phi}_B = \int_S {\bf B}\cdot d{\bf S}
\end{displaymath}">|; 

$key = q/{displaymath}w=frac{epsilon,E^2}{2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img559.png"
 ALT="\begin{displaymath}
w = \frac{\epsilon  E^2}{2},
\end{displaymath}">|; 

$key = q/r+R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img670.png"
 ALT="$r+R$">|; 

$key = q/OQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$OQ$">|; 

$key = q/d{{bf{r}=(dx,dy,dz);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$d{\bf r} = (dx,dy,dz)$">|; 

$key = q/E=V_Hslashw;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img798.png"
 ALT="$E= V_H/w$">|; 

$key = q/9.4times10^{-31};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img780.png"
 ALT="$9.4\times 10^{-31}$">|; 

$key = q/dVslashdx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img405.png"
 ALT="$dV/dx$">|; 

$key = q/L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img335.png"
 ALT="$L$">|; 

$key = q/{displaymath}i(t)=I,(1-{{rm{e}^{-R,tslashL}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1103.png"
 ALT="\begin{displaymath}
i(t) = I (1-{\rm e}^{-R t/L}).
\end{displaymath}">|; 

$key = q/{calE}_2=6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img711.png"
 ALT="${\cal E}_2=6$">|; 

$key = q/{displaymath}W(Q)=int_0^Qfrac{q,dq}{C}=frac{Q^2}{2,C}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img552.png"
 ALT="\begin{displaymath}
W(Q) = \int_0^Q\frac{q dq}{C}= \frac{Q^2}{2 C}.
\end{displaymath}">|; 

$key = q/displaystyle{{bf{a}cdot{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$\displaystyle {\bf a} \cdot {\bf b}$">|; 

$key = q/A=1200,{{rm{cm}^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1027.png"
 ALT="$A= 1200 {\rm cm}^2$">|; 

$key = q/+{calE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img634.png"
 ALT="$+{\cal E}$">|; 

$key = q/displaystyle{{bf{a}cdot{{bf{b}+{{bf{a}cdot{{bf{c}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle {\bf a} \cdot {\bf b} + {\bf a}\cdot {\bf c}.$">|; 

$key = q/{displaymath}eta=frac{P}{P_1}=frac{500}{600}=0.83=83,%.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1042.png"
 ALT="\begin{displaymath}
\eta = \frac{P}{P_1} = \frac{500}{600} = 0.83 = 83 \%.
\end{displaymath}">|; 

$key = q/{bf{b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$\bf b$">|; 

$key = q/{displaymath}q'(t=0)=-Q.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1127.png"
 ALT="\begin{displaymath}
q'(t=0) = -Q.
\end{displaymath}">|; 

$key = q/d^3{{bf{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="$d^3{\bf r}$">|; 

$key = q/SOT;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1430.png"
 ALT="$SOT$">|; 

$key = q/10,mu,{{rm{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img832.png"
 ALT="$10 \mu {\rm A}$">|; 

$key = q/{{bf{j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1215.png"
 ALT="${\bf j}$">|; 

$key = q/{displaymath}Q_1=C_1,V_{12}=(1times10^{-6}),(3.43)=3.42,mu{{rm{C}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="346" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img593.png"
 ALT="\begin{displaymath}
Q_1 = C_1 V_{12} = (1\times 10^{-6}) (3.43) = 3.42 \mu{\rm C}.
\end{displaymath}">|; 

$key = q/{displaymath}(R_1+R_2),I_2+R_1,I_3={calE}_1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img719.png"
 ALT="\begin{displaymath}
(R_1+R_2) I_2 + R_1 I_3 = {\cal E}_1.
\end{displaymath}">|; 

$key = q/{displaymath}B=mu_0,n,I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img819.png"
 ALT="\begin{displaymath}
B =\mu_0 n I.
\end{displaymath}">|; 

$key = q/{displaymath}I_3=-frac{(100),(12)+(110),(6)}{(1000+50+500)}=-frac{(1860)}{(1550)}=-1.2,{{rm{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="411" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img724.png"
 ALT="\begin{displaymath}
I_3 = - \frac{ (100) (12)+(110) (6)}{(1000+50 + 500)} =- \frac{(1860)}{(1550)}=
-1.2 {\rm A}.
\end{displaymath}">|; 

$key = q/-theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$-\theta$">|; 

$key = q/{displaymath}I=frac{V}{R}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1092.png"
 ALT="\begin{displaymath}
I = \frac{V}{R}
\end{displaymath}">|; 

$key = q/theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\theta$">|; 

$key = q/{displaymath}V_4=frac{Q}{C_4}=frac{(10.3times10^{-6})}{(4times10^{-6})}=2.57,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img591.png"
 ALT="\begin{displaymath}
V_4 = \frac{Q}{C_4} = \frac{(10.3\times 10^{-6})}{(4\times 10^{-6})}=2.57 {\rm V}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{L_1}{L_2}=left(frac{N_1}{N_2}right)^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1158.png"
 ALT="\begin{displaymath}
\frac{L_1}{L_2} = \left(\frac{N_1}{N_2}\right)^2,
\end{displaymath}">|; 

$key = q/6.67;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1453.png"
 ALT="$6.67$">|; 

$key = q/AB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$AB$">|; 

$key = q/theta_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1301.png"
 ALT="$\theta_2$">|; 

$key = q/{displaymath}P_r=I^2,r=frac{{calE}^2,r}{(r+R)^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img673.png"
 ALT="\begin{displaymath}
P_r = I^2 r = \frac{ {\cal E}^2 r}{(r+R)^2}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{motor.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="494" HEIGHT="342" BORDER="0"
 SRC="|."$dir".q|img969.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{motor.eps}}
\end{figure}">|; 

$key = q/{displaymath}{mitPhi}_{B,2}=N,A,B_2,costheta=(15),(0.0314),(5),(0.8660)=2.039,{{rm{Wb}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="490" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img991.png"
 ALT="\begin{displaymath}
{\mit\Phi}_{B 2} = N A B_2 \cos\theta =
(15) (0.0314) (5) (0.8660) = 2.039 {\rm Wb}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{E_b}{E_a}=frac{Q_b}{Q_a}frac{a^2}{b^2}=frac{a}{b}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img499.png"
 ALT="\begin{displaymath}
\frac{E_b}{E_a} = \frac{Q_b}{Q_a}\frac{a^2}{b^2}=\frac{a}{b}.
\end{displaymath}">|; 

$key = q/B=Eslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1269.png"
 ALT="$B=E/c$">|; 

$key = q/p=90;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1467.png"
 ALT="$p=90$">|; 

$key = q/E_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img520.png"
 ALT="$E_1$">|; 

$key = q/m=0,1,2,cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1499.png"
 ALT="$m=0,1,2,\cdots$">|; 

$key = q/{displaymath}I=frac{{calE}}{R}=frac{(0.163)}{(15)}=0.011,{{rm{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img994.png"
 ALT="\begin{displaymath}
I = \frac{{\cal E}}{R} = \frac{(0.163)}{(15)} = 0.011 {\rm A}.
\end{displaymath}">|; 

$key = q/|n|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\vert n\vert$">|; 

$key = q/{{bf{a}={{bf{a}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="${\bf a} = {\bf a} (t)$">|; 

$key = q/displaystyle0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$\displaystyle 0.$">|; 

$key = q/{displaymath}f=frac{R}{2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1394.png"
 ALT="\begin{displaymath}
f = \frac{R}{2}.
\end{displaymath}">|; 

$key = q/41^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1336.png"
 ALT="$41^\circ$">|; 

$key = q/{displaymath}{calE}=-frac{d{mitPhi}_B}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img895.png"
 ALT="\begin{displaymath}
{\cal E} = -\frac{d{\mit\Phi}_B}{dt}.
\end{displaymath}">|; 

$key = q/2,{calE}_{ab};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img935.png"
 ALT="$2 {\cal E}_{ab}$">|; 

$key = q/{displaymath}t=tau,lnleft(frac{Q}{q}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1195.png"
 ALT="\begin{displaymath}
t = \tau \ln\left(\frac{Q}{q}\right),
\end{displaymath}">|; 

$key = q/{displaymath}1,{{rm{W}equiv1,{{rm{V}cdot1,{{rm{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img667.png"
 ALT="\begin{displaymath}
1 {\rm W} \equiv 1 {\rm V}\cdot 1 {\rm A}.
\end{displaymath}">|; 

$key = q/L_1=mu_0,N_1^{~2},Aslashl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1156.png"
 ALT="$L_1=\mu_0 N_1^{&nbsp;2}  A/l$">|; 

$key = q/{figure}{epsfysize{=1.75in{centerline{epsffile{fig2.5.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="398" HEIGHT="201" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="\begin{figure}
\epsfysize =1.75in
\centerline{\epsffile{fig2.5.eps}}
\end{figure}">|; 

$key = q/{displaymath}int_{S}{{bf{v}cdotd{{bf{S}=lim_{d{{bf{S}rightarrow0}left[sumv,costheta,dSright],{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="\begin{displaymath}
\int_{S} {\bf v}\cdot d{\bf S} = \lim_{d{\bf S}\rightarrow 0}\left[ \sum v \cos\theta
 dS\right],
\end{displaymath}">|; 

$key = q/1000;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img856.png"
 ALT="$1000$">|; 

$key = q/{displaymath}W=frac{1}{2},L,I^2=frac{mu_0,N^2,A}{2,l},left(frac{B,l}{mu_0,N}right)^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1086.png"
 ALT="\begin{displaymath}
W = \frac{1}{2}  L I^2 =\frac{\mu_0 N^2 A}{2 l}  \left(\frac{B l}{\mu_0 N}
\right)^2,
\end{displaymath}">|; 

$key = q/P=(infty,0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="$P=(\infty, 0, 0)$">|; 

$key = q/{displaymath}{calE}_2=-frac{d{mitPhi}_B}{dt}=-1.26times10^{-4},{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1012.png"
 ALT="\begin{displaymath}
{\cal E}_2 = -\frac{ d{\mit\Phi}_B}{dt} =
-1.26\times 10^{-4} {\rm V}.
\end{displaymath}">|; 

$key = q/f=-25;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1456.png"
 ALT="$f=-25$">|; 

$key = q/-V_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img473.png"
 ALT="$-V_c$">|; 

$key = q/{displaymath}{{bf{f}=q,{{bf{E},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="\begin{displaymath}
{\bf f} = q  {\bf E},
\end{displaymath}">|; 

$key = q/1+2=3,mu{{rm{F};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img585.png"
 ALT="$1+2= 3 \mu{\rm F}$">|; 

$key = q/{displaymath}frac{-h'}{h}=frac{q}{p}=frac{q-f}{f}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1436.png"
 ALT="\begin{displaymath}
\frac{-h'}{h} = \frac{q}{p} = \frac{q-f}{f}.
\end{displaymath}">|; 

$key = q/+cslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img311.png"
 ALT="$+c/2$">|; 

$key = q/n_2<n_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1322.png"
 ALT="$n_2&lt; n_1$">|; 

$key = q/{displaymath}W=Lint_0^Ii,di,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1084.png"
 ALT="\begin{displaymath}
W = L\int_0^I i di,
\end{displaymath}">|; 

$key = q/{displaymath}q,dV=-q,E_x,dx,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img403.png"
 ALT="\begin{displaymath}
q  dV = -q E_x dx,
\end{displaymath}">|; 

$key = q/{displaymath}I_3=-frac{R_1,{calE}_1+(R_1+R_2),{calE}_2}{R_1R_2+R_2R_3+R_1R_3},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img723.png"
 ALT="\begin{displaymath}
I_3 = - \frac{ R_1 {\cal E}_1 +
(R_1+R_2) {\cal E}_2}{R_1 R_2 + R_2 R_3+ R_1 R_3},
\end{displaymath}">|; 

$key = q/{{bf{S}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="${\bf S} = {\bf0}$">|; 

$key = q/stackrel{displaystylerightarrow}{PR},=,stackrel{displaystylerightarrow}{PQ}+stackrel{displaystylerightarrow}{QR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\stackrel{\displaystyle \rightarrow}{PR}
 = 
\stackrel{\displaystyle \rightarrow}{PQ}+ \stackrel{\displaystyle \rightarrow}{QR}$">|; 

$key = q/V(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img426.png"
 ALT="$V(x)$">|; 

$key = q/{calE}=B,l,v.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img917.png"
 ALT="${\cal E}=B l v.$">|; 

$key = q/K=4.3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1285.png"
 ALT="$K=4.3$">|; 

$key = q/{{bf{e}_zequiv(0,0,1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="${\bf e}_z \equiv
(0,0,1)$">|; 

$key = q/I_{{rm{fsd}=10,mu{{rm{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img844.png"
 ALT="$I_{\rm fsd}=10 \mu{\rm A}$">|; 

$key = q/E_r(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img355.png"
 ALT="$E_r(r)$">|; 

$key = q/a=q,Eslashm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img617.png"
 ALT="$a= q E/m$">|; 

$key = q/{displaymath}int_S{{bf{B}cdotd{{bf{S}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1210.png"
 ALT="\begin{displaymath}
\int_S {\bf B} \cdot d{\bf S} = 0,
\end{displaymath}">|; 

$key = q/f<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="$f&lt;0$">|; 

$key = q/displaystyleE_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1240.png"
 ALT="$\displaystyle E_x$">|; 

$key = q/a_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$a_x$">|; 

$key = q/1.36;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1527.png"
 ALT="$1.36$">|; 

$key = q/abcd;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img714.png"
 ALT="$abcd$">|; 

$key = q/R_f<R_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1421.png"
 ALT="$R_f&lt;R_b$">|; 

$key = q/d_yV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img415.png"
 ALT="$d_y V$">|; 

$key = q/{displaymath}{calE}=frac{d{mitPhi}_B}{dt}=0.163,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img993.png"
 ALT="\begin{displaymath}
{\cal E} = \frac{d{\mit\Phi}_B}{dt} = 0.163 {\rm V}.
\end{displaymath}">|; 

$key = q/4pitimes10^{-7};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img759.png"
 ALT="$4\pi\times 10^{-7}$">|; 

$key = q/S';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1212.png"
 ALT="$S'$">|; 

$key = q/{displaymath}frac{di}{dt}=-i,frac{R}{L}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1113.png"
 ALT="\begin{displaymath}
\frac{di}{dt} = -i \frac{R}{L}.
\end{displaymath}">|; 

$key = q/r<a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img883.png"
 ALT="$r&lt;a$">|; 

$key = q/1.0times10^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1177.png"
 ALT="$1.0\times 10^{-2}$">|; 

$key = q/{mitPhi}_{1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1047.png"
 ALT="${\mit\Phi}_{1}$">|; 

$key = q/{displaymath}B=frac{mu_0,I}{2pi,r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img747.png"
 ALT="\begin{displaymath}
B = \frac{\mu_0 I}
{2 \pi  r}.
\end{displaymath}">|; 

$key = q/{displaymath}lambda_1'=frac{(2),(1.36),(250times10^{-9})}{(1slash2)}=1360,{{rm{nm},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1534.png"
 ALT="\begin{displaymath}
\lambda_1' = \frac{(2) (1.36) (250\times 10^{-9})}{(1/2)} = 1360 {\rm nm},
\end{displaymath}">|; 

$key = q/Rrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1399.png"
 ALT="$R\rightarrow \infty$">|; 

$key = q/{displaymath}w=oint_C{{bf{B}cdotd{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img806.png"
 ALT="\begin{displaymath}
w =\oint_C{\bf B}\cdot d{\bf r}.
\end{displaymath}">|; 

$key = q/P_R=I^2,R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1161.png"
 ALT="$P_R= I^2  R$">|; 

$key = q/dq=C,d,dE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1220.png"
 ALT="$dq = C d d E$">|; 

$key = q/{displaymath}dW=P,dt=-{calE},i,dt=i,L,frac{di}{dt},dt=L,i,di.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1082.png"
 ALT="\begin{displaymath}
d W = P dt = -{\cal E} i dt
= i L \frac{d i}{d t}  d t = L i di.
\end{displaymath}">|; 

$key = q/costheta_irightarrow-costheta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img371.png"
 ALT="$\cos\theta_i\rightarrow
-\cos\theta_i$">|; 

$key = q/10%;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1192.png"
 ALT="$10\%$">|; 

$key = q/d_xV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img414.png"
 ALT="$d_x V$">|; 

$key = q/{displaymath}v_2=V_2,cos(omega,t){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1139.png"
 ALT="\begin{displaymath}
v_2= V_2 \cos (\omega  t)
\end{displaymath}">|; 

$key = q/{displaymath}alpha=90^circ-r_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1354.png"
 ALT="\begin{displaymath}
\alpha = 90^\circ - r_2.
\end{displaymath}">|; 

$key = q/v,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="$v \cos\theta$">|; 

$key = q/{displaymath}{{bf{a}equiv(a_x,,a_y,,a_z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="\begin{displaymath}
{\bf a} \equiv (a_x,  a_y,  a_z).
\end{displaymath}">|; 

$key = q/{displaymath}{calE}_{ab}=frac{B,w,l,omega,sintheta}{2}=frac{B,A,omega,sintheta}{2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img930.png"
 ALT="\begin{displaymath}
{\cal E}_{ab} = \frac{B  w  l  \omega \sin\theta}{2} = \frac{B A 
\omega \sin\theta}{2},
\end{displaymath}">|; 

$key = q/|M|=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1406.png"
 ALT="$\vert M\vert=1$">|; 

$key = q/E_1=(1-1slashK),E_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img522.png"
 ALT="$E_1 = (1-1/K) E_0$">|; 

$key = q/{{bf{a}={{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="${\bf a} = {\bf b}$">|; 

$key = q/M=+0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1458.png"
 ALT="$M=+0.1$">|; 

$key = q/{displaymath}E_0=sqrt{frac{2,S}{epsilon_0,c}}=sqrt{frac{(2),(140)}{(8.85times10^12}),(3times10^8)}}=324.7,,{{rm{V},{{rm{m}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="458" HEIGHT="65" BORDER="0"
 SRC="|."$dir".q|img1292.png"
 ALT="\begin{displaymath}
E_0 = \sqrt{\frac{2 S}{\epsilon_0 c}} = \sqrt{\frac{(2) (...
... 10^{-12}) (3\times 10^8)}} = 324.7  {\rm V} {\rm m}^{-1}.
\end{displaymath}">|; 

$key = q/m=1,2,3,cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1503.png"
 ALT="$m=1,2,3,\cdots$">|; 

$key = q/10^{-9};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1261.png"
 ALT="$10^{-9}$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig2.4.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="224" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig2.4.eps}}
\end{figure}">|; 

$key = q/E_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img401.png"
 ALT="$E_x$">|; 

$key = q/displaystylea_x,(a_y,b_z-a_z,b_y)+a_y,(a_z,b_x-a_x,b_z)+a_z,(a_x,b_y-a_y,b_x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="449" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$\displaystyle a_x (a_y  b_z-a_z  b_y) + a_y  (a_z  b_x- a_x  b_z)
+a_z (a_x  b_y - a_y  b_x)$">|; 

$key = q/stackrel{displaystylerightarrow}{SR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="28" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\stackrel{\displaystyle \rightarrow}{SR}$">|; 

$key = q/{displaymath}R=rho,frac{L}{A},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img625.png"
 ALT="\begin{displaymath}
R = \rho \frac{L}{A},
\end{displaymath}">|; 

$key = q/T({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$T({\bf r})$">|; 

$key = q/{displaymath}sintheta_2=frac{AP}{AQ}=frac{v_2,{mitDelta}t}{AQ}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1316.png"
 ALT="\begin{displaymath}
\sin\theta_2 = \frac{AP}{AQ} = \frac{ v_2 {\mit\Delta} t}{AQ}.
\end{displaymath}">|; 

$key = q/displaystylef_{c,x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img297.png"
 ALT="$\displaystyle f_{c x}$">|; 

$key = q/4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1447.png"
 ALT="$4$">|; 

$key = q/{displaymath}i=epsilon_0,A,frac{dE_perp}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1226.png"
 ALT="\begin{displaymath}
i =\epsilon_0 A  \frac{d E_\perp}{dt}.
\end{displaymath}">|; 

$key = q/{displaymath}R'=left(frac{N_1}{N_2}right)^2,R.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1168.png"
 ALT="\begin{displaymath}
R' = \left(\frac{N_1}{N_2}\right)^2 R.
\end{displaymath}">|; 

$key = q/STV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1377.png"
 ALT="$STV$">|; 

$key = q/q';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="$q'$">|; 

$key = q/{displaymath}f_c=sqrt{(f_{c,x})^2+(f_{c,y})^2}=6.4times10^{-3},{{rm{N}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img301.png"
 ALT="\begin{displaymath}
f_c = \sqrt{(f_{c x})^2 + (f_{c y})^2} = 6.4\times 10^{-3} {\rm N}.
\end{displaymath}">|; 

$key = q/B=1.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img870.png"
 ALT="$B=1.2$">|; 

$key = q/lambda_1=589;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1357.png"
 ALT="$\lambda_1 = 589$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{lr1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="490" HEIGHT="227" BORDER="0"
 SRC="|."$dir".q|img1093.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{lr1.eps}}
\end{figure}">|; 

$key = q/{displaymath}V=V_1+V_2=-2.64times10^5,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img465.png"
 ALT="\begin{displaymath}
V = V_1 + V_2 = -2.64\times 10^5 {\rm V}.
\end{displaymath}">|; 

$key = q/dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img412.png"
 ALT="$dy$">|; 

$key = q/{displaymath}{mitPhi}_B=int_S{{bf{B}cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img890.png"
 ALT="\begin{displaymath}
{\mit\Phi}_B = \int_S {\bf B}\cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{eclipse.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="609" HEIGHT="336" BORDER="0"
 SRC="|."$dir".q|img1296.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{eclipse.eps}}
\end{figure}">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$R$">|; 

$key = q/{displaymath}f=q_c,E=(20times10^{-6}),(-1.8times10^6)=-36,{{rm{N}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img318.png"
 ALT="\begin{displaymath}
f = q_c E = (20\times 10^{-6}) (-1.8\times 10^6)=-36  {\rm N}.
\end{displaymath}">|; 

$key = q/dQ=q,N,(A,v_d,dt);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img622.png"
 ALT="$dQ = q N (A v_d dt)$">|; 

$key = q/displaystylef_{ac},cos(90^circ-theta)=f_{ac},sintheta=(4.31times10^{-3}),(0.8)=3.45times10^{-3},{{rm{N}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="538" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img295.png"
 ALT="$\displaystyle f_{ac} \cos(90^\circ -\theta) = f_{ac}  \sin\theta = (4.31 \times 10^{-3}) (0.8) = 3.45 \times 10^{-3} {\rm N}.$">|; 

$key = q/4,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img693.png"
 ALT="$4 \Omega$">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{convex.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="452" HEIGHT="402" BORDER="0"
 SRC="|."$dir".q|img1397.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{convex.eps}}
\end{figure}">|; 

$key = q/epsilon_0=8.854times10^{-12},{{rm{C}^2,{{rm{N}^{-1},{{rm{m}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1252.png"
 ALT="$\epsilon_0 = 8.854\times 10^{-12} {\rm C}^2 {\rm N}^{-1}  {\rm m}^{-2}$">|; 

$key = q/(K-1),epsilon_0,E^2slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img561.png"
 ALT="$(K-1) \epsilon_0 E^2/2$">|; 

$key = q/{displaymath}E(R),2pi,R,L=frac{lambda,L}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img336.png"
 ALT="\begin{displaymath}
E(R) 2\pi  R  L = \frac{\lambda  L}{\epsilon_0},
\end{displaymath}">|; 

$key = q/2.0times10^6,{{rm{V,m}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1178.png"
 ALT="$2.0\times 10^6 {\rm V m}^{-1}$">|; 

$key = q/k_e=1slash4piepsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="$k_e=1/4\pi\epsilon_0$">|; 

$key = q/{displaymath}oint_C{{bf{E}cdotd{{bf{S}=-frac{d}{dt}int_{S'}{{bf{B}cdotd{{bf{S}',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1211.png"
 ALT="\begin{displaymath}
\oint_C {\bf E}\cdot d {\bf S} = -\frac{d}{dt}\int_{S'} {\bf B}\cdot d {\bf S}',
\end{displaymath}">|; 

$key = q/50^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img866.png"
 ALT="$50^\circ$">|; 

$key = q/1.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img731.png"
 ALT="$1.2$">|; 

$key = q/W;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$W$">|; 

$key = q/{{bf{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="${\bf a}$">|; 

$key = q/displaystylefrac{a}{a+b},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img492.png"
 ALT="$\displaystyle \frac{a}{a+b},$">|; 

$key = q/displaystylec_{x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$\displaystyle c_{x'}$">|; 

$key = q/theta_1>theta_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1328.png"
 ALT="$\theta_1&gt;\theta_c$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{disp.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="490" HEIGHT="227" BORDER="0"
 SRC="|."$dir".q|img1216.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{disp.eps}}
\end{figure}">|; 

$key = q/v_1=n_1,c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1489.png"
 ALT="$v_1=n_1 c$">|; 

$key = q/theta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img366.png"
 ALT="$\theta_i$">|; 

$key = q/I=Vslash(R_S+R_G);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img853.png"
 ALT="$I= V/(R_S+R_G)$">|; 

$key = q/{displaymath}P_{{rm{max}={calE}_{{rm{max},I_{{rm{max}=frac{{calE}_{{rm{max},(V_{{rm{max}-{calE}_{{rm{max})}{R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="318" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img974.png"
 ALT="\begin{displaymath}
P_{\rm max} = {\cal E}_{\rm max}  I_{\rm max} = \frac{ {\cal E}_{\rm max} 
(V_{\rm max} - {\cal E}_{\rm max})}{R}.
\end{displaymath}">|; 

$key = q/R_b=infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1419.png"
 ALT="$R_b=\infty$">|; 

$key = q/{displaymath}{{bf{a}times{{bf{b}=(a_y,b_z-a_z,b_y,,a_z,b_x-a_x,b_z,,a_x,b_y-a_y,b_x)={{bf{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="438" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="\begin{displaymath}
{\bf a}\times{\bf b} = (a_y   b_z-a_z  b_y,  a_z  b_x - a_x  b_z,  a_x  b_y - a_y  b_x)
={\bf c}.
\end{displaymath}">|; 

$key = q/theta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img421.png"
 ALT="$\theta=0$">|; 

$key = q/>10^1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1266.png"
 ALT="$&gt;10^1$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{refract.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="346" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img1305.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{refract.eps}}
\end{figure}">|; 

$key = q/{displaymath}h'=M,h=(3.5),(7)=24.5,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1472.png"
 ALT="\begin{displaymath}
h' = M h =(3.5) (7) =24.5 {\rm cm}.
\end{displaymath}">|; 

$key = q/1slashC_{{rm{eq}=sum_{i=1}^N(1slashC_i).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img545.png"
 ALT="$1/C_{\rm eq}
=\sum_{i=1}^N (1/C_i).$">|; 

$key = q/V=V_0slashK;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img579.png"
 ALT="$V=V_0/K$">|; 

$key = q/{displaymath}y=frac{x}{(1+x)^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img678.png"
 ALT="\begin{displaymath}
y = \frac{x}{(1+x)^2}.
\end{displaymath}">|; 

$key = q/tanalpha=-h'slash(R-q);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1387.png"
 ALT="$\tan \alpha = -h'/(R-q)$">|; 

$key = q/A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img345.png"
 ALT="$A$">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img364.png"
 ALT="$i$">|; 

$key = q/I_D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1227.png"
 ALT="$I_D$">|; 

$key = q/epsilon_0,E^2slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img560.png"
 ALT="$\epsilon_0 E^2/2$">|; 

$key = q/{displaymath}tau=N,I,B_parallel,A,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img946.png"
 ALT="\begin{displaymath}
\tau = N I B_\parallel A,
\end{displaymath}">|; 

$key = q/{displaymath}{mitPhi}_E=oint{{bf{E}cdotd{{bf{S}=frac{Q}{epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img478.png"
 ALT="\begin{displaymath}
{\mit\Phi}_E= \oint {\bf E}\cdot d{\bf S} = \frac{Q}{\epsilon_0}.
\end{displaymath}">|; 

$key = q/{displaymath}v_1-L_1,frac{di_1}{dt}-M,frac{di_2}{dt}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1141.png"
 ALT="\begin{displaymath}
v_1 - L_1 \frac{di_1}{d t} - M \frac{di_2}{d t}=0,
\end{displaymath}">|; 

$key = q/n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$n$">|; 

$key = q/{displaymath}w=frac{epsilon_0,E^2}{2}+frac{E^2}{2,mu_0,c^2}=frac{epsilon_0,E^2}{2}+frac{epsilon_0,E^2}{2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="302" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1271.png"
 ALT="\begin{displaymath}
w = \frac{\epsilon_0 E^2}{2} + \frac{E^2}{2 \mu_0 c^2} =
\frac{\epsilon_0 E^2}{2} + \frac{\epsilon_0 E^2}{2},
\end{displaymath}">|; 

$key = q/E_{{rm{crit};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img481.png"
 ALT="$E_{\rm crit}$">|; 

$key = q/{displaymath}lambda_2=frac{n_1}{n_2},lambda_1=frac{(1.00)}{(1.52)},(589)=387.5,{{rm{nm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1365.png"
 ALT="\begin{displaymath}
\lambda_2 = \frac{n_1}{n_2} \lambda_1 = \frac{(1.00)}{(1.52)} (589)
= 387.5 {\rm nm}.
\end{displaymath}">|; 

$key = q/tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\tau $">|; 

$key = q/q_a=50,mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img306.png"
 ALT="$q_a=50 \mu{\rm C}$">|; 

$key = q/{{bf{a},&,{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="${\bf a} \&amp; {\bf b}$">|; 

$key = q/{displaymath}lambda_1=frac{(2),(1.36),(250times10^{-9})}{(1)}=680,{{rm{nm},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1530.png"
 ALT="\begin{displaymath}
\lambda_1 = \frac{(2) (1.36) (250\times 10^{-9})}{(1)} = 680 {\rm nm},
\end{displaymath}">|; 

$key = q/{displaymath}M=-frac{q}{p}=-frac{(-87.5)}{(25)}=3.5.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1470.png"
 ALT="\begin{displaymath}
M = -\frac{q}{p} = -\frac{(-87.5)}{(25)} = 3.5.
\end{displaymath}">|; 

$key = q/v=(q,Eslashm),t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img618.png"
 ALT="$v = (q E/m) t$">|; 

$key = q/{figure*}{epsfysize{=2.5in{centerline{epsffile{earth.eps}}{{figure*};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="483" HEIGHT="288" BORDER="0"
 SRC="|."$dir".q|img859.png"
 ALT="\begin{figure*}
\epsfysize =2.5in
\centerline{\epsffile{earth.eps}}
\end{figure*}">|; 

$key = q/dV=dx,dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$dV = dx  dy  dz$">|; 

$key = q/{displaymath}B_perp=B,costheta=B,cos30^circ=0.8660,B,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img989.png"
 ALT="\begin{displaymath}
B_\perp = B \cos\theta = B \cos 30^\circ = 0.8660 B,
\end{displaymath}">|; 

$key = q/{displaymath}B(r)=frac{mu_0,I}{2pi,r}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img882.png"
 ALT="\begin{displaymath}
B(r) = \frac{\mu_0 I}{2\pi r}
\end{displaymath}">|; 

$key = q/y=P_Rslash({calE}^2slashr);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img676.png"
 ALT="$y = P_R/({\cal E}^2/r)$">|; 

$key = q/{displaymath}n,{{bf{a}equiv(n,a_x,,n,a_y,,n,a_z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="\begin{displaymath}
n {\bf a} \equiv (n a_x,  n a_y,  n a_z).
\end{displaymath}">|; 

$key = q/{displaymath}P_B-P_A=W.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img376.png"
 ALT="\begin{displaymath}
P_B - P_A = W.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}times({{bf{b}+{{bf{c})={{bf{a}times{{bf{b}+{{bf{a}times{{bf{c},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="\begin{displaymath}
{\bf a}\times({\bf b} +{\bf c})= {\bf a} \times{\bf b}+{\bf a}\times{\bf c},
\end{displaymath}">|; 

$key = q/{displaymath}i=frac{dq}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1124.png"
 ALT="\begin{displaymath}
i = \frac{d q}{d t}.
\end{displaymath}">|; 

$key = q/lambdaslashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1518.png"
 ALT="$\lambda/n$">|; 

$key = q/{displaymath}{calE}=B,l,v=(1),(0.2),(0.1)=0.020,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1018.png"
 ALT="\begin{displaymath}
{\cal E} = B l v = (1) (0.2) (0.1) = 0.020 {\rm V}.
\end{displaymath}">|; 

$key = q/R';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1166.png"
 ALT="$R'$">|; 

$key = q/n_1slashn_2>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1324.png"
 ALT="$n_1/n_2&gt;1$">|; 

$key = q/displaystyleE_0,cos[2pi,(zslashlambda-f,t)],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1241.png"
 ALT="$\displaystyle E_0 \cos[2\pi (z/\lambda - f t)],$">|; 

$key = q/V,I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img666.png"
 ALT="$V I$">|; 

$key = q/x=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$x=0$">|; 

$key = q/C_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1410.png"
 ALT="$C_b$">|; 

$key = q/{displaymath}I=q,n,w,d,v_d,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img802.png"
 ALT="\begin{displaymath}
I = q n w d v_d,
\end{displaymath}">|; 

$key = q/q=-1.6times10^{-19};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img391.png"
 ALT="$q=-1.6\times 10^{-19}$">|; 

$key = q/{displaymath}lambda_{{rm{quartz}=frac{c'}{f}=frac{(1.4times10^8)}{(1times10^9)}=14,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1290.png"
 ALT="\begin{displaymath}
\lambda_{\rm quartz} = \frac{c'}{f} = \frac{(1.4\times 10^8)}
{(1\times 10^9)} = 14 {\rm cm}.
\end{displaymath}">|; 

$key = q/displaystylexcostheta+ysintheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$\displaystyle x\cos\theta + y\sin \theta,$">|; 

$key = q/displaystyle(a_x,costheta+a_y,sintheta),(b_x,costheta+b_y,sintheta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="322" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$\displaystyle (a_x  \cos\theta+a_y \sin\theta) (b_x \cos\theta + b_y \sin\theta)$">|; 

$key = q/{displaymath}P_0=frac{E_0,B_0}{mu_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1281.png"
 ALT="\begin{displaymath}
P_0 = \frac{E_0 B_0}{\mu_0},
\end{displaymath}">|; 

$key = q/{displaymath}R_{{rm{eq}=frac{1}{(1slashR_G)+(1slashR_S)}=frac{I_{{rm{fsd}}{I_{{rm{max}},R_G.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img849.png"
 ALT="\begin{displaymath}
R_{\rm eq} = \frac{1}{(1/R_G)+(1/R_S)} = \frac{I_{\rm fsd}}{I_{\rm max}} R_G.
\end{displaymath}">|; 

$key = q/z=h(l);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$z=h(l)$">|; 

$key = q/stackrel{displaystylerightarrow}{QR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\stackrel{\displaystyle \rightarrow}{QR}$">|; 

$key = q/{displaymath}oint_S{{bf{E}cdotd{{bf{S}=frac{1}{epsilon_0}int_Vrho,dV,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1209.png"
 ALT="\begin{displaymath}
\oint_S {\bf E}\cdot d{\bf S}= \frac{1}{\epsilon_0}\int_V \rho dV,
\end{displaymath}">|; 

$key = q/{displaymath}d{mitPhi}_B=B,l,dx=B,l,v,dt.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img909.png"
 ALT="\begin{displaymath}
d{\mit\Phi}_B = B l dx = B l v dt.
\end{displaymath}">|; 

$key = q/E_b=Q_bslash(4piepsilon_0,b^2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img498.png"
 ALT="$E_b= Q_b/(4\pi\epsilon_0 b^2)$">|; 

$key = q/p=15;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1441.png"
 ALT="$p=15$">|; 

$key = q/{mitDelta}t=10;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img986.png"
 ALT="${\mit\Delta}t=10$">|; 

$key = q/q,v,B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img915.png"
 ALT="$q v B$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{eddy.eps}}{{{.{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="464" HEIGHT="367" BORDER="0"
 SRC="|."$dir".q|img923.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{eddy.eps}}
.\end{figure}">|; 

$key = q/W_1=W_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img375.png"
 ALT="$W_1=W_2$">|; 

$key = q/q_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="$q_b$">|; 

$key = q/{displaymath}i(t)=I,{{rm{e}^{-tslashR,C},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1134.png"
 ALT="\begin{displaymath}
i(t) = I {\rm e}^{-t/R C},
\end{displaymath}">|; 

$key = q/q=f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1392.png"
 ALT="$q=f$">|; 

$key = q/dQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img607.png"
 ALT="$dQ$">|; 

$key = q/|b|=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$\vert b\vert=0$">|; 

$key = q/F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="$F$">|; 

$key = q/R=15,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img987.png"
 ALT="$R=15 \Omega$">|; 

$key = q/{{rm{N,C}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="${\rm N  C}^{-1}$">|; 

$key = q/{displaymath}P=frac{dW}{A,dt}=frac{epsilon_0,E^2,A,c,dt}{A,dt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1276.png"
 ALT="\begin{displaymath}
P = \frac{d W}{A d t} = \frac{ \epsilon_0 E^2  A c d t}{A dt},
\end{displaymath}">|; 

$key = q/V_o;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1437.png"
 ALT="$V_o$">|; 

$key = q/{displaymath}overline{z}=left.int_Vz,dVrightslashint_VdV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="\begin{displaymath}
\overline{z} = \left. \int_V z dV\right/ \int_V dV.
\end{displaymath}">|; 

$key = q/-{calE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img661.png"
 ALT="$-{\cal E}$">|; 

$key = q/R_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1412.png"
 ALT="$R_b$">|; 

$key = q/{{bf{f}_{bc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img284.png"
 ALT="${\bf f}_{bc}$">|; 

$key = q/displaystylex';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$\displaystyle x'$">|; 

$key = q/|F|,|r|,sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$\vert F\vert \vert r\vert \sin\theta$">|; 

$key = q/{mitPhi}_{2}=N_2,B_1,A=mu_0,N_1,N_2,A,I_1slashl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1063.png"
 ALT="${\mit\Phi}_{2}
= N_2 B_1 A = \mu_0 N_1 N_2 A I_1/l$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{lenz.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img894.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{lenz.eps}}
\end{figure}">|; 

$key = q/{displaymath}dV=d_xV+d_yV+d_zV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img417.png"
 ALT="\begin{displaymath}
dV = d_x V + d_y V + d_z V.
\end{displaymath}">|; 

$key = q/{displaymath}overline{z}=frac{pi,a^4}{4}frac{3}{2pi,a^3}=frac{3,a}{8}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="\begin{displaymath}
\overline{z} = \frac{ \pi  a^4}{4}\frac{3}{2\pi  a^3}= \frac{3 a}{8}.
\end{displaymath}">|; 

$key = q/{displaymath}q(t)=Q,{{rm{e}^{-tslashR,C},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1135.png"
 ALT="\begin{displaymath}
q(t) = Q {\rm e}^{-t/R C},
\end{displaymath}">|; 

$key = q/S'T';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1373.png"
 ALT="$S'T'$">|; 

$key = q/d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img506.png"
 ALT="$d$">|; 

$key = q/lambda_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1359.png"
 ALT="$\lambda_2$">|; 

$key = q/1.5times10^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img630.png"
 ALT="$1.5\times 10^{-8}$">|; 

$key = q/x';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$x'$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{rainbow.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="661" HEIGHT="338" BORDER="0"
 SRC="|."$dir".q|img1344.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{rainbow.eps}}
\end{figure}">|; 

$key = q/2,{{rm{Omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img692.png"
 ALT="$2 {\rm\Omega}$">|; 

$key = q/{displaymath}W=-q,E,dx,costheta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img399.png"
 ALT="\begin{displaymath}
W = -q E dx \cos\theta,
\end{displaymath}">|; 

$key = q/{{bf{a}=(1slashsqrt{2},,-1slashsqrt{2},,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="${\bf a} = (1/\sqrt{2},  -1/\sqrt{2},  0)$">|; 

$key = q/{displaymath}tau=frac{L}{R}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1105.png"
 ALT="\begin{displaymath}
\tau = \frac{L}{R}
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{gauss.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="452" HEIGHT="401" BORDER="0"
 SRC="|."$dir".q|img329.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{gauss.eps}}
\end{figure}">|; 

$key = q/C_{{rm{eq};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img532.png"
 ALT="$C_{\rm eq}$">|; 

$key = q/+x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="$+x$">|; 

$key = q/q=-1.6times10^{-19},{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img449.png"
 ALT="$q=-1.6\times 10^{-19} {\rm C}$">|; 

$key = q/F=I,B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1020.png"
 ALT="$F= I B$">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{image.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="508" HEIGHT="402" BORDER="0"
 SRC="|."$dir".q|img1374.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{image.eps}}
\end{figure}">|; 

$key = q/y_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1524.png"
 ALT="$y_4$">|; 

$key = q/I,R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img637.png"
 ALT="$I R$">|; 

$key = q/blla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img495.png"
 ALT="$b\ll a$">|; 

$key = q/{displaymath}{{bf{F}={{bf{I}'times{{bf{B}=q,n,A,{{bf{v}times{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img764.png"
 ALT="\begin{displaymath}
{\bf F} = {\bf I}'\times {\bf B} = q n  A  {\bf v}\times{\bf B}.
\end{displaymath}">|; 

$key = q/{{bf{e}_yequiv(0,1,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="${\bf e}_y \equiv (0,1,0)$">|; 

$key = q/f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$f$">|; 

$key = q/dq;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img546.png"
 ALT="$dq$">|; 

$key = q/{{bf{a},&,{{bf{b}=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="${\bf a} \&amp; {\bf b} = 1/2$">|; 

$key = q/di;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1094.png"
 ALT="$di$">|; 

$key = q/{displaymath}w=frac{epsilon_0,E^2}{2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img558.png"
 ALT="\begin{displaymath}
w = \frac{\epsilon_0 E^2}{2}.
\end{displaymath}">|; 

$key = q/q(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img356.png"
 ALT="$q(r)$">|; 

$key = q/{displaymath}(AB)^2=(OA)^2+(OB)^2-2,(OA),(OB),costheta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="375" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="\begin{displaymath}
(AB)^2 = (OA)^2 + (OB)^2 - 2  (OA) (OB) \cos\theta,
\end{displaymath}">|; 

$key = q/{mitDelta}=m,lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1513.png"
 ALT="${\mit \Delta}=m \lambda$">|; 

$key = q/B_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img928.png"
 ALT="$B_\perp$">|; 

$key = q/c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img305.png"
 ALT="$c$">|; 

$key = q/{displaymath}c'=frac{c}{sqrt{K}}=frac{(3times10^8)}{sqrt{4.3}}=1.4times10^8,{{rm{m},{{rm{s}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1288.png"
 ALT="\begin{displaymath}
c' = \frac{c}{\sqrt{K}} = \frac{(3\times 10^8)}{\sqrt{4.3}} = 1.4\times
10^8 {\rm m} {\rm s}^{-1}.
\end{displaymath}">|; 

$key = q/{displaymath}w=frac{epsilon_0,E^2}{2}+frac{B^2}{2,mu_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1091.png"
 ALT="\begin{displaymath}
w = \frac{\epsilon_0 E^2}{2} + \frac{B^2}{2 \mu_0}.
\end{displaymath}">|; 

$key = q/P_B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img378.png"
 ALT="$P_B$">|; 

$key = q/{displaymath}V_1=k_e,frac{q_1}{x_1}=(8.988times10^9),frac{(6times10^{-6})}{(5.1times10^{-2})}=1.06times10^6,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="452" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img463.png"
 ALT="\begin{displaymath}
V_1 = k_e \frac{q_1}{x_1} = (8.988\times 10^9) \frac{(6\times 10^{-6})}{(5.1\times 10^{-2})}= 1.06 \times 10^6 {\rm V}.
\end{displaymath}">|; 

$key = q/{displaymath}oint_C{{bf{B}cdotd{{bf{r}=mu_0,I,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1213.png"
 ALT="\begin{displaymath}
\oint_C {\bf B}\cdot d{\bf r} = \mu_0 I,
\end{displaymath}">|; 

$key = q/0<x<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img680.png"
 ALT="$0&lt;x&lt;1$">|; 

$key = q/{displaymath}C=frac{Q}{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img503.png"
 ALT="\begin{displaymath}
C = \frac{Q}{V}.
\end{displaymath}">|; 

$key = q/E(a)=-E(-a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img347.png"
 ALT="$E(a)=-E(-a)$">|; 

$key = q/{{bf{e}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="${\bf e}_y$">|; 

$key = q/K>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1268.png"
 ALT="$K&gt;1$">|; 

$key = q/{calE}=B,l,v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img914.png"
 ALT="${\cal E} = B l v$">|; 

$key = q/{displaymath}sintheta_msimeqfrac{y_m}{L},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1505.png"
 ALT="\begin{displaymath}
\sin\theta_m \simeq \frac{y_m}{L},
\end{displaymath}">|; 

$key = q/R=50;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1455.png"
 ALT="$R=50$">|; 

$key = q/q_b=100,mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img307.png"
 ALT="$q_b = 100 \mu{\rm C}$">|; 

$key = q/{displaymath}R_{{rm{eq}=frac{V}{I}=frac{V_1+V_2}{I}=frac{V_1}{I}+frac{V_2}{I},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img651.png"
 ALT="\begin{displaymath}
R_{\rm eq} = \frac{V}{I} = \frac{V_1+V_2}{I} = \frac{V_1}{I} + \frac{V_2}{I},
\end{displaymath}">|; 

$key = q/{{bf{v}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="${\bf v} \cdot d{\bf S}$">|; 

$key = q/V_{{rm{max}<{calE}_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img976.png"
 ALT="$V_{\rm max} &lt; {\cal E}_{\rm max}$">|; 

$key = q/{displaymath}C=frac{epsilon_0,A}{d}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img511.png"
 ALT="\begin{displaymath}
C = \frac{\epsilon_0 A}{d}.
\end{displaymath}">|; 

$key = q/P_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img377.png"
 ALT="$P_A$">|; 

$key = q/{displaymath}A(r),E_r(r)=frac{q(r)}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img353.png"
 ALT="\begin{displaymath}
A(r) E_r(r) = \frac{q(r)}{\epsilon_0},
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{it.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="228" BORDER="0"
 SRC="|."$dir".q|img1111.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{it.eps}}
\end{figure}">|; 

$key = q/displaystylez.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle z.$">|; 

$key = q/epsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img325.png"
 ALT="$\epsilon_0$">|; 

$key = q/{figure}{epsfysize{=1.in{centerline{epsffile{fig3.9.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="523" HEIGHT="110" BORDER="0"
 SRC="|."$dir".q|img793.png"
 ALT="\begin{figure}
\epsfysize =1.in
\centerline{\epsffile{fig3.9.eps}}
\end{figure}">|; 

$key = q/{displaymath}Q=C_{{rm{eq}V=(1.71times10^{-6}),(6)=10.3,mu{{rm{C}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="332" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img590.png"
 ALT="\begin{displaymath}
Q = C_{\rm eq} V = (1.71\times 10^{-6}) (6) = 10.3 \mu{\rm C}.
\end{displaymath}">|; 

$key = q/q_c=20,mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img308.png"
 ALT="$q_c=20 \mu{\rm C}$">|; 

$key = q/{displaymath}E_x=-frac{dV}{dx}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img404.png"
 ALT="\begin{displaymath}
E_x = - \frac{dV}{dx}.
\end{displaymath}">|; 

$key = q/nequivsqrt{K};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1487.png"
 ALT="$n\equiv \sqrt{K}$">|; 

$key = q/180^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img933.png"
 ALT="$180^\circ$">|; 

$key = q/W_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img373.png"
 ALT="$W_2$">|; 

$key = q/2,q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img379.png"
 ALT="$2 q$">|; 

$key = q/{displaymath}{calE}=-L,frac{di}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1095.png"
 ALT="\begin{displaymath}
{\cal E} = - L \frac{d i}{d t}.
\end{displaymath}">|; 

$key = q/E=VslashL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img613.png"
 ALT="$E = V/L$">|; 

$key = q/M=+0.0667;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1481.png"
 ALT="$M=+0.0667$">|; 

$key = q/{displaymath}1,Omegaequiv1,{{rm{V,A}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img612.png"
 ALT="\begin{displaymath}
1 \Omega \equiv 1 {\rm V A}^{-1}.
\end{displaymath}">|; 

$key = q/Q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$Q$">|; 

$key = q/{displaymath}theta_c=sin^{-1}(1.00slash1.33)=48.8^circ,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1333.png"
 ALT="\begin{displaymath}
\theta_c = \sin^{-1}(1.00/1.33) = 48.8^\circ,
\end{displaymath}">|; 

$key = q/lambda>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img339.png"
 ALT="$\lambda&gt;0$">|; 

$key = q/{displaymath}frac{-h'}{h}=frac{OS'}{OS}=frac{q}{p}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1432.png"
 ALT="\begin{displaymath}
\frac{-h'}{h} = \frac{OS'}{OS} = \frac{q}{p}.
\end{displaymath}">|; 

$key = q/displaystyle{{bf{b}cdot{{bf{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$\displaystyle {\bf b} \cdot {\bf a},$">|; 

$key = q/I_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img655.png"
 ALT="$I_1$">|; 

$key = q/B_perp=B,sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img929.png"
 ALT="$B_\perp = B \sin\theta$">|; 

$key = q/{displaymath}dw={{bf{B}cdotd{{bf{r}=B,dr,costheta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img804.png"
 ALT="\begin{displaymath}
dw = {\bf B}\cdot d{\bf r}
= B d r \cos\theta,
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig2.6.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="223" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig2.6.eps}}
\end{figure}">|; 

$key = q/h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$h$">|; 

$key = q/{mitDelta}thetaproptoI;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img830.png"
 ALT="${\mit\Delta}\theta \propto I$">|; 

$key = q/B,L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img813.png"
 ALT="$B L$">|; 

$key = q/Q_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img531.png"
 ALT="$Q_2$">|; 

$key = q/K=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img515.png"
 ALT="$K=1$">|; 

$key = q/omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img876.png"
 ALT="$\omega$">|; 

$key = q/{displaymath}frac{dq'}{dt}=-frac{q'}{R,C},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1125.png"
 ALT="\begin{displaymath}
\frac{d q'}{dt} = - \frac{q'}{R C},
\end{displaymath}">|; 

$key = q/n_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1302.png"
 ALT="$n_1$">|; 

$key = q/displaystylea_{z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\displaystyle a_{z'}$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$\textstyle =$">|; 

$key = q/lslashv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img774.png"
 ALT="$l/v$">|; 

$key = q/{displaymath}oint{{bf{A}cdotd{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="\begin{displaymath}
\oint {\bf A}\cdot d{\bf r}.
\end{displaymath}">|; 

$key = q/q,{{bf{v}times{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img792.png"
 ALT="$q {\bf v}\times{\bf B}$">|; 

$key = q/i_2=r_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1352.png"
 ALT="$i_2=r_2$">|; 

$key = q/{{bf{e}_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="${\bf e}_x$">|; 

$key = q/{displaymath}{{bf{f}_a={{bf{f}_{ba}+{{bf{f}_{ca}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="\begin{displaymath}
{\bf f}_a = {\bf f}_{ba} + {\bf f}_{ca}.
\end{displaymath}">|; 

$key = q/x=+a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img344.png"
 ALT="$x=+a$">|; 

$key = q/q_a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="$q_a$">|; 

$key = q/{displaymath}i'(t=0)=-I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1101.png"
 ALT="\begin{displaymath}
i'(t=0)=-I.
\end{displaymath}">|; 

$key = q/{displaymath}sintheta_c=frac{n_2}{n_1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1331.png"
 ALT="\begin{displaymath}
\sin\theta_c = \frac{n_2}{n_1}.
\end{displaymath}">|; 

$key = q/{displaymath}p=fleft(1-frac{1}{M}right)=-(25),(1-10)=225,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1461.png"
 ALT="\begin{displaymath}
p = f\left(1-\frac{1}{M}\right) = -(25) (1-10) = 225 {\rm cm}.
\end{displaymath}">|; 

$key = q/V_H;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img794.png"
 ALT="$V_H$">|; 

$key = q/{{bf{v}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="${\bf v}({\bf r})$">|; 

$key = q/Q=C,V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img664.png"
 ALT="$Q=C V$">|; 

$key = q/E_x=1.40times10^3,{{rm{N,C^{-1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img438.png"
 ALT="$E_x=1.40\times 10^3 {\rm N C^{-1}}$">|; 

$key = q/{{bf{I}'propto{{bf{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img762.png"
 ALT="${\bf I}'\propto {\bf v}$">|; 

$key = q/v_2=n_2,c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1490.png"
 ALT="$v_2=n_2 c$">|; 

$key = q/I_{{rm{fsd};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img831.png"
 ALT="$I_{\rm fsd}$">|; 

$key = q/B=mu_0,I_2slash2pi,r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img757.png"
 ALT="$B= \mu_0  I_2/2\pi  r$">|; 

$key = q/l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$l$">|; 

$key = q/{displaymath}rho=frac{m,v}{q,B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img788.png"
 ALT="\begin{displaymath}
\rho = \frac{m v}{q B}.
\end{displaymath}">|; 

$key = q/{{bf{a}cdot{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="${\bf a} \cdot {\bf b}$">|; 

$key = q/{calE}_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1029.png"
 ALT="${\cal E}_{\rm max}$">|; 

$key = q/{displaymath}P=f,v=(0.20),(0.10)=0.020,{{rm{W}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1023.png"
 ALT="\begin{displaymath}
P = f v = (0.20) (0.10) = 0.020 {\rm W}.
\end{displaymath}">|; 

$key = q/d=(1slash2),a_z,t^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img772.png"
 ALT="$d=(1/2) a_z t^2$">|; 

$key = q/{displaymath}tantheta=frac{h}{p}=frac{-h'}{q}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1382.png"
 ALT="\begin{displaymath}
\tan\theta = \frac{h}{p}= \frac{-h'}{q}.
\end{displaymath}">|; 

$key = q/45;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1478.png"
 ALT="$45$">|; 

$key = q/90^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img784.png"
 ALT="$90^\circ$">|; 

$key = q/{displaymath}v_d=frac{q,E,tau}{2,m}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img620.png"
 ALT="\begin{displaymath}
v_d = \frac{q E \tau}{2 m}.
\end{displaymath}">|; 

$key = q/{displaymath}d=frac{1}{2}frac{q,E}{m},t^2=frac{q}{m}frac{E,l^2}{2,v^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img773.png"
 ALT="\begin{displaymath}
d = \frac{1}{2}\frac{q E}{m} t^2 = \frac{q}{m} \frac{E l^2}{2 v^2},
\end{displaymath}">|; 

$key = q/{{bf{F}=-q,{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img360.png"
 ALT="${\bf F}=-
q {\bf E}$">|; 

$key = q/1.6times10^{-19};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img392.png"
 ALT="$1.6\times 10^{-19}$">|; 

$key = q/M_{21}=M_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1068.png"
 ALT="$M_{21} = M_{12}$">|; 

$key = q/displaystyleoint_S{{bf{B}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1235.png"
 ALT="$\displaystyle \oint_S {\bf B}\cdot d{\bf S}$">|; 

$key = q/E_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img519.png"
 ALT="$E_0$">|; 

$key = q/{displaymath}{mitPhi}_{1}=M_{12},I_2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1048.png"
 ALT="\begin{displaymath}
{\mit\Phi}_{1} = M_{12} I_2,
\end{displaymath}">|; 

$key = q/{displaymath}V_{{rm{max},sin(2pi,f,t)=I_{{rm{max},R,sin(2pi,f,t)+{calE}_{{rm{max},sin(2pi,f,t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="442" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img971.png"
 ALT="\begin{displaymath}
V_{\rm max}  \sin (2\pi  f  t) = I_{\rm max}  R \sin (2\pi  f  t) + {\cal E}_{\rm max} 
\sin (2\pi  f  t),
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{cap1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img527.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{cap1.eps}}
\end{figure}">|; 

$key = q/{displaymath}{{bf{M}={{bf{r}times{{bf{F}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="\begin{displaymath}
{\bf M} = {\bf r}\times{\bf F}.
\end{displaymath}">|; 

$key = q/{displaymath}f=frac{q,q'}{4piepsilon,r^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img524.png"
 ALT="\begin{displaymath}
f = \frac{q q'}{4\pi\epsilon r^2},
\end{displaymath}">|; 

$key = q/c=-3.50;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img439.png"
 ALT="$c=-3.50$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{young2.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="340" BORDER="0"
 SRC="|."$dir".q|img1496.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{young2.eps}}
\end{figure}">|; 

$key = q/{calE}_1=12;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img710.png"
 ALT="${\cal E}_1=12$">|; 

$key = q/R=8,{{rm{M}Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1191.png"
 ALT="$R=8 {\rm M}\Omega$">|; 

$key = q/W=q,{mitDelta}V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img389.png"
 ALT="$W=q {\mit\Delta} V$">|; 

$key = q/displaystyle+(-a_x,sintheta+a_y,costheta),(-b_x,sintheta+b_y,costheta)+a_z,b_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\displaystyle +(-a_x \sin\theta + a_y \cos\theta) (-b_x \sin \theta + b_y \cos\theta)
+a_z  b_z$">|; 

$key = q/{bf{F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$\bf F$">|; 

$key = q/d{mitPhi}_{2}=M,dI_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1055.png"
 ALT="$d{\mit\Phi}_{2} = M d I_1$">|; 

$key = q/v=0.1,{{rm{m,s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1015.png"
 ALT="$v=0.1 {\rm m s}^{-1}$">|; 

$key = q/N_2=300;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1172.png"
 ALT="$N_2=300$">|; 

$key = q/V=V_1+V_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img541.png"
 ALT="$V=V_1+V_2$">|; 

$key = q/n_1=400;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img995.png"
 ALT="$n_1=400$">|; 

$key = q/displaystyle-xsintheta+ycostheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\displaystyle -x\sin\theta + y\cos\theta,$">|; 

$key = q/bc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img810.png"
 ALT="$bc$">|; 

$key = q/N=10;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1026.png"
 ALT="$N=10$">|; 

$key = q/{displaymath}r_2=90^circ-i_1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1353.png"
 ALT="\begin{displaymath}
r_2=90^\circ - i_1.
\end{displaymath}">|; 

$key = q/OPF;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1433.png"
 ALT="$OPF$">|; 

$key = q/m,v^2slashrho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img785.png"
 ALT="$m v^2/\rho$">|; 

$key = q/r=10;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img981.png"
 ALT="$r=10$">|; 

$key = q/{displaymath}w_E=frac{1}{2},epsilon_0,E^2=(0.5),(8.85times10^{-12}),(2.0times10^6)^2=18,,{{rm{J,m}^{-3}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="488" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1179.png"
 ALT="\begin{displaymath}
w_E = \frac{1}{2} \epsilon_0 E^2 =
(0.5) (8.85\times 10^{-12})  (2.0\times 10^6)^2 = 18  {\rm J m}^{-3}.
\end{displaymath}">|; 

$key = q/{displaymath}(P_R)_{{rm{max}=frac{{calE}^2}{4,r}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img684.png"
 ALT="\begin{displaymath}
(P_R)_{\rm max} = \frac{{\cal E}^2}{4  r}
\end{displaymath}">|; 

$key = q/{displaymath}theta=tan^{-1}(aslashb)=tan^{-1}(4slash3)=53.1^circ{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img289.png"
 ALT="\begin{displaymath}
\theta =\tan^{-1} (a/b) = \tan^{-1}(4/3) = 53.1^\circ
\end{displaymath}">|; 

$key = q/{displaymath}w=epsilon_0,E^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1272.png"
 ALT="\begin{displaymath}
w = \epsilon_0 E^2.
\end{displaymath}">|; 

$key = q/q<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="$q&lt;0$">|; 

$key = q/E(R);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img337.png"
 ALT="$E(R)$">|; 

$key = q/R_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img647.png"
 ALT="$R_1$">|; 

$key = q/{displaymath}frac{1}{C_{{rm{eq}}=frac{1}{(3times10^{-6})}+frac{1}{(4times10^{-6})}=frac{(7)}{(12times10^{-6})},,{{rm{F}^{-1},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="416" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img588.png"
 ALT="\begin{displaymath}
\frac{1}{C_{\rm eq}} = \frac{1}{(3\times 10^{-6})} + \frac{1...
...es 10^{-6})} = \frac{(7)}{(12\times 10^{-6})}  {\rm F}^{-1},
\end{displaymath}">|; 

$key = q/v_1,{mitDelta}t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1312.png"
 ALT="$v_1 {\mit\Delta} t$">|; 

$key = q/1slashr^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img320.png"
 ALT="$1/r^2$">|; 

$key = q/r>a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img878.png"
 ALT="$r&gt;a$">|; 

$key = q/{displaymath}{mitPhi}_{2}=M_{21},I_1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1045.png"
 ALT="\begin{displaymath}
{\mit\Phi}_{2} = M_{21} I_1,
\end{displaymath}">|; 

$key = q/{displaymath}frac{1}{f}=(n-1)left(frac{1}{R_f}-frac{1}{R_b}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1414.png"
 ALT="\begin{displaymath}
\frac{1}{f} = (n-1)\left(\frac{1}{R_f} - \frac{1}{R_b}\right),
\end{displaymath}">|; 

$key = q/displaystyle1.26times10^{-4},{{rm{Wb,,s}^{-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1011.png"
 ALT="$\displaystyle 1.26\times 10^{-4} {\rm Wb  s}^{-1}.$">|; 

$key = q/displaystyle(-a_x,sintheta+a_y,costheta),b_z-a_z,(-b_x,sintheta+b_y,costheta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$\displaystyle (-a_x  \sin\theta + a_y \cos\theta) b_z - a_z (-b_x  \sin\theta + b_y \cos\theta)$">|; 

$key = q/r=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="$r=$">|; 

$key = q/R=V_2slashI_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1163.png"
 ALT="$R= V_2/I_2$">|; 

$key = q/f=-45;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1479.png"
 ALT="$f=-45$">|; 

$key = q/{mitDeltaP}=W;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img402.png"
 ALT="${\mit\Delta P} = W$">|; 

$key = q/QgeqQ_{{rm{crit};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img483.png"
 ALT="$Q\geq Q_{\rm crit}$">|; 

$key = q/V_1=500;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1200.png"
 ALT="$V_1=500$">|; 

$key = q/{displaymath}{calE}_{{rm{max}=2pi,N,B,A,f,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img968.png"
 ALT="\begin{displaymath}
{\cal E}_{\rm max} = 2\pi N B A f,
\end{displaymath}">|; 

$key = q/{displaymath}i_1=I_1,sin(omega,t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1138.png"
 ALT="\begin{displaymath}
i_1 = I_1 \sin (\omega  t),
\end{displaymath}">|; 

$key = q/qslashQ=0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1197.png"
 ALT="$q/Q = 0.1$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{virtual.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="530" HEIGHT="342" BORDER="0"
 SRC="|."$dir".q|img1375.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{virtual.eps}}
\end{figure}">|; 

$key = q/displaystyle({{bf{a}times{{bf{b})^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$\displaystyle ({\bf a}\times{\bf b})^2$">|; 

$key = q/n_2=1.52;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1362.png"
 ALT="$n_2= 1.52$">|; 

$key = q/I_3=-1.2,{{rm{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img730.png"
 ALT="$I_3=-1.2 {\rm A}$">|; 

$key = q/K=4.8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img571.png"
 ALT="$K=4.8$">|; 

$key = q/x_2=-3.4,{{rm{cm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="$x_2=-3.4 {\rm cm}$">|; 

$key = q/0.103,{{rm{mm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1522.png"
 ALT="$0.103 {\rm mm}$">|; 

$key = q/{displaymath}P=I^2,R=(1),(1),(0.020)=0.020,{{rm{W}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1025.png"
 ALT="\begin{displaymath}
P = I^2 R = (1) (1) (0.020) = 0.020 {\rm W}.
\end{displaymath}">|; 

$key = q/{calE}=B_perp,l,v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img927.png"
 ALT="${\cal E} = B_\perp l v$">|; 

$key = q/2,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img695.png"
 ALT="$2 \Omega$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{diverge.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="816" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img1428.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{diverge.eps}}
\end{figure}">|; 

$key = q/{displaymath}Phi_E=oint_S{{bf{E}cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img823.png"
 ALT="\begin{displaymath}
\Phi_E = \oint_S {\bf E}\cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}times{{bf{b}=-{{bf{b}times{{bf{a},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="\begin{displaymath}
{\bf a}\times{\bf b} = - {\bf b} \times{\bf a},
\end{displaymath}">|; 

$key = q/S'OT';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1431.png"
 ALT="$S'OT'$">|; 

$key = q/{displaymath}tau=2,F,frac{D}{2}=I,B,L,D=I,B,A.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img826.png"
 ALT="\begin{displaymath}
\tau = 2 F \frac{D}{2} = I B L D = I B A.
\end{displaymath}">|; 

$key = q/{displaymath}P=frac{E,B}{mu_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1280.png"
 ALT="\begin{displaymath}
P = \frac{E B}{\mu_0}.
\end{displaymath}">|; 

$key = q/3,{{rm{cm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1356.png"
 ALT="$3 {\rm cm}$">|; 

$key = q/{displaymath}M=frac{h'}{h}=-frac{q}{p}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1383.png"
 ALT="\begin{displaymath}
M = \frac{h'}{h} = -\frac{q}{p}.
\end{displaymath}">|; 

$key = q/{displaymath}2,t=(m+1slash2),lambda,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1516.png"
 ALT="\begin{displaymath}
2 t=(m+1/2) \lambda,
\end{displaymath}">|; 

$key = q/R=rho,LslashA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img687.png"
 ALT="$R=\rho L/A$">|; 

$key = q/I_{{rm{max}=1,{{rm{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img845.png"
 ALT="$I_{\rm max} = 1 {\rm A}$">|; 

$key = q/{displaymath}-,I_2,R_2+{calE}_1-I_1,R_1=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img715.png"
 ALT="\begin{displaymath}
- I_2 R_2+{\cal E}_1 - I_1 R_1=0.
\end{displaymath}">|; 

$key = q/B(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img880.png"
 ALT="$B(r)$">|; 

$key = q/phi(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$\phi(t)$">|; 

$key = q/W=q,{calE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img900.png"
 ALT="$W = q {\cal E}$">|; 

$key = q/{{bf{a}cdot{{bf{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="${\bf a} \cdot {\bf a}$">|; 

$key = q/dqslashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1223.png"
 ALT="$dq/d t$">|; 

$key = q/rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img627.png"
 ALT="$\rho$">|; 

$key = q/{{bf{S}=S,(cosalpha,,sinalpha,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="${\bf S} = S (\cos\alpha,  \sin\alpha,  0)$">|; 

$key = q/{displaymath}w(r)=2pi,r,B(r)=mu_0,I,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img881.png"
 ALT="\begin{displaymath}
w(r) = 2\pi  r B(r) = \mu_0 I,
\end{displaymath}">|; 

$key = q/{displaymath}frac{d{{bf{a}}{dt}=frac{dphi}{dt},{{bf{b}+phi,frac{d{{bf{b}}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="\begin{displaymath}
\frac{d {\bf a}}{dt} = \frac{d\phi}{dt}  {\bf b} + \phi  \frac{d {\bf b}}{dt}.
\end{displaymath}">|; 

$key = q/{mitPhi}_E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img327.png"
 ALT="${\mit\Phi}_E$">|; 

$key = q/V_{{rm{max}=220;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img965.png"
 ALT="$V_{\rm max} = 220$">|; 

$key = q/dS;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="$dS$">|; 

$key = q/{displaymath}frac{1}{C_{{rm{eq}}=frac{1}{C_1}+frac{1}{C_2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img544.png"
 ALT="\begin{displaymath}
\frac{1}{C_{\rm eq}} = \frac{1}{C_1} + \frac{1}{C_2}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{z}{lambda}-f,t=N,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1244.png"
 ALT="\begin{displaymath}
\frac{z}{\lambda} - f t = N,
\end{displaymath}">|; 

$key = q/B_1,A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1062.png"
 ALT="$B_1 A$">|; 

$key = q/N_1=100;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1171.png"
 ALT="$N_1=100$">|; 

$key = q/{displaymath}I=frac{dQ}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img609.png"
 ALT="\begin{displaymath}
I= \frac{d Q}{dt}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig3.2.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="292" HEIGHT="284" BORDER="0"
 SRC="|."$dir".q|img319.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig3.2.eps}}
\end{figure}">|; 

$key = q/f_{23};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img267.png"
 ALT="$f_{23}$">|; 

$key = q/q,n,A,v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img761.png"
 ALT="$q n  A v$">|; 

$key = q/dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img608.png"
 ALT="$dt$">|; 

$key = q/{displaymath}tanalpha=frac{h}{p-R}=-frac{h'}{R-q}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1388.png"
 ALT="\begin{displaymath}
\tan\alpha = \frac{h}{p-R} = - \frac{h'}{R-q}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=4in{centerline{epsffile{focus.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="457" HEIGHT="457" BORDER="0"
 SRC="|."$dir".q|img1408.png"
 ALT="\begin{figure}
\epsfysize =4in
\centerline{\epsffile{focus.eps}}
\end{figure}">|; 

$key = q/{displaymath}f=I,B,l=(1),(1),(0.2)=0.20,{{rm{N}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1021.png"
 ALT="\begin{displaymath}
f = I B l = (1) (1) (0.2) = 0.20 {\rm N}.
\end{displaymath}">|; 

$key = q/l,A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1088.png"
 ALT="$l A$">|; 

$key = q/V_{{rm{max}>{calE}_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img975.png"
 ALT="$V_{\rm max} &gt; {\cal E}_{\rm max}$">|; 

$key = q/{calE}=-L,dislashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1081.png"
 ALT="${\cal E} = - L d i/dt$">|; 

$key = q/{displaymath}i'=i-I,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1098.png"
 ALT="\begin{displaymath}
i' = i - I,
\end{displaymath}">|; 

$key = q/dV=r^2,sintheta,dr,dtheta,dphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$dV = r^2 \sin\theta dr d\theta d\phi$">|; 

$key = q/{displaymath}W=int_{infty}^0frac{-y,dy}{(a^2+y^2)^{3slash2}}=left[frac{1}{(y^2+a^2)^{1slash2}}right]^0_infty=frac{1}{a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="366" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="\begin{displaymath}
W = \int_{\infty}^0 \frac{-y dy}{(a^2 + y^2)^{3/2}} = \left[\frac{1}{(y^2+a^2)^{1/2}}
\right]^0_\infty = \frac{1}{a}.
\end{displaymath}">|; 

$key = q/S'T'V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1379.png"
 ALT="$S'T'V$">|; 

$key = q/I={calE}slashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img903.png"
 ALT="$I={\cal E}/R$">|; 

$key = q/M>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1405.png"
 ALT="$M&gt;0$">|; 

$key = q/{displaymath}y_4=frac{4,lambda,L}{d}=frac{4,(633times10^{-9}),(2.65)}{(0.103times10^{-3})}=6.29,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="369" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1525.png"
 ALT="\begin{displaymath}
y_4 = \frac{4 \lambda L}{d} =\frac{4 (633\times 10^{-9}) (2.65)}{(0.103\times
10^{-3})} = 6.29 {\rm cm}.
\end{displaymath}">|; 

$key = q/{displaymath}int_VF(x,y,z),dV,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="\begin{displaymath}
\int_V F(x,y,z) dV,
\end{displaymath}">|; 

$key = q/-cslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img310.png"
 ALT="$-c/2$">|; 

$key = q/{displaymath}W=q,oint_C{{bf{E}cdotd{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img899.png"
 ALT="\begin{displaymath}
W=q \oint_C {\bf E}\cdot d{\bf r},
\end{displaymath}">|; 

$key = q/displaystyleint_0^adrint_0^{pislash2}dthetaint_0^{2pi}dphi,,r,costheta,,r^2sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="$\displaystyle \int_0^a dr\int_0^{\pi/2} d\theta \int_0^{2\pi} d\phi  r \cos\theta 
 
r^2 \sin\theta$">|; 

$key = q/d_xV=-E_x,dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img418.png"
 ALT="$d_x V =- E_x dx$">|; 

$key = q/{figure}{epsfysize{=4in{centerline{epsffile{dispersion1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="462" BORDER="0"
 SRC="|."$dir".q|img1340.png"
 ALT="\begin{figure}
\epsfysize =4in
\centerline{\epsffile{dispersion1.eps}}
\end{figure}">|; 

$key = q/alpha=i_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1348.png"
 ALT="$\alpha=i_1$">|; 

$key = q/f=20;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1442.png"
 ALT="$f=20$">|; 

$key = q/{displaymath}{{bf{S}=sum_idelta{{bf{S}_i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="\begin{displaymath}
{\bf S} = \sum_i \delta {\bf S}_i.
\end{displaymath}">|; 

$key = q/displaystyley';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$\displaystyle y'$">|; 

$key = q/2,N,{calE}_{ab};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img936.png"
 ALT="$2 N {\cal E}_{ab}$">|; 

$key = q/tau=LslashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1110.png"
 ALT="$\tau=L/R$">|; 

$key = q/270^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img934.png"
 ALT="$270^\circ$">|; 

$key = q/{displaymath}Q_2=C_2,V_{12}=(2times10^{-6}),(3.43)=6.84,mu{{rm{C}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="346" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img594.png"
 ALT="\begin{displaymath}
Q_2 = C_2 V_{12} = (2\times 10^{-6}) (3.43) = 6.84 \mu{\rm C}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{I_1}{I_2}=sqrt{frac{L_2}{L_1}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img1154.png"
 ALT="\begin{displaymath}
\frac{I_1}{I_2} = \sqrt{\frac{L_2}{L_1}}.
\end{displaymath}">|; 

$key = q/displaystyle(a_y,b_z-a_z,b_y),costheta+(a_z,b_x-a_x,b_z),sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\displaystyle (a_y  b_z - a_z  b_y)  \cos\theta + (a_z  b_x-a_x  b_z) \sin\theta$">|; 

$key = q/{displaymath}W=q,V({{bf{r}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img436.png"
 ALT="\begin{displaymath}
W = q V({\bf r}).
\end{displaymath}">|; 

$key = q/R=5.0,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1182.png"
 ALT="$R=5.0 \Omega$">|; 

$key = q/{displaymath}V_B-V_A=1000,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img447.png"
 ALT="\begin{displaymath}
V_B - V_A = 1000 {\rm V}.
\end{displaymath}">|; 

$key = q/{displaymath}V_{{rm{max}=I_{{rm{max},R+{calE}_{{rm{max}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img972.png"
 ALT="\begin{displaymath}
V_{\rm max} = I_{\rm max}  R + {\cal E}_{\rm max}.
\end{displaymath}">|; 

$key = q/1,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img691.png"
 ALT="$1 \Omega$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig2.14.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="275" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig2.14.eps}}
\end{figure}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{anal.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="345" BORDER="0"
 SRC="|."$dir".q|img1376.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{anal.eps}}
\end{figure}">|; 

$key = q/B=mu_0,I_1slash2pi,r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img755.png"
 ALT="$B = \mu_0  I_1/2\pi  r$">|; 

$key = q/5.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img596.png"
 ALT="$5.0$">|; 

$key = q/c=1.00;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img309.png"
 ALT="$c=1.00$">|; 

$key = q/{displaymath}lambda_2'=frac{(2),(1.36),(250times10^{-9})}{(3slash2)}=453,{{rm{nm},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1535.png"
 ALT="\begin{displaymath}
\lambda_2' = \frac{(2) (1.36) (250\times 10^{-9})}{(3/2)} = 453 {\rm nm},
\end{displaymath}">|; 

$key = q/L={mitPhi}slashI;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1079.png"
 ALT="$L= {\mit\Phi}/I$">|; 

$key = q/a_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$a_y$">|; 

$key = q/{calE}_{{rm{ext};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img960.png"
 ALT="${\cal E}_{\rm ext}$">|; 

$key = q/n,L,I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img817.png"
 ALT="$n L I$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{motion.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="431" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img905.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{motion.eps}}
\end{figure}">|; 

$key = q/{figure*}{epsfysize{=2in{centerline{epsffile{cap3.eps}}{{figure*};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="230" BORDER="0"
 SRC="|."$dir".q|img580.png"
 ALT="\begin{figure*}
\epsfysize =2in
\centerline{\epsffile{cap3.eps}}
\end{figure*}">|; 

$key = q/{figure*}{epsfysize{=2.5in{centerline{epsffile{cir2.eps}}{{figure*};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="316" HEIGHT="288" BORDER="0"
 SRC="|."$dir".q|img690.png"
 ALT="\begin{figure*}
\epsfysize =2.5in
\centerline{\epsffile{cir2.eps}}
\end{figure*}">|; 

$key = q/-I,R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img662.png"
 ALT="$-I R$">|; 

$key = q/|f|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="$\vert f\vert$">|; 

$key = q/{displaymath}W=int_{infty}^aleft(-frac{1}{x^2}right),dx=left[frac{1}{x}right]_{infty}^a=frac{1}{a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="\begin{displaymath}
W = \int_{\infty}^a \left(-\frac{1}{x^2}\right) dx = \left[\frac{1}{x}\right]_{\infty}^a
=\frac{1}{a}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{prism1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="709" HEIGHT="284" BORDER="0"
 SRC="|."$dir".q|img1342.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{prism1.eps}}
\end{figure}">|; 

$key = q/{displaymath}I_2=frac{{calE}_2}{R_2}=frac{(-1.26times10^{-4})}{(0.050)}=-2.6,{{rm{mA},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="318" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1013.png"
 ALT="\begin{displaymath}
I_2 = \frac{{\cal E}_2}{R_2} = \frac{(-1.26\times 10^{-4})}{(0.050)} = -2.6 {\rm mA},
\end{displaymath}">|; 

$key = q/R_f<|R_b|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1423.png"
 ALT="$R_f&lt;\vert R_b\vert$">|; 

$key = q/defc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img718.png"
 ALT="$defc$">|; 

$key = q/{{bf{a},{{rm{x},{{bf{b}=(1slash2,,-1slash2,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="${\bf a}  {\rm x}  {\bf b} = (1/2,  -1/2, 0)$">|; 

$key = q/{displaymath}m,{{bf{a}=q,{{bf{E}+q,{{bf{v}times{{bf{B},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img768.png"
 ALT="\begin{displaymath}
m {\bf a} = q {\bf E} + q {\bf v} \times{\bf B},
\end{displaymath}">|; 

$key = q/{displaymath}f=-G,frac{m,m'}{r^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="\begin{displaymath}
f = -G \frac{m m'}{r^2},
\end{displaymath}">|; 

$key = q/{displaymath}E_x(x)=-frac{dV(x)}{dx}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img429.png"
 ALT="\begin{displaymath}
E_x(x) = - \frac{dV(x)}{dx}.
\end{displaymath}">|; 

$key = q/{mitPhi}=B,A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1077.png"
 ALT="${\mit\Phi} = B A$">|; 

$key = q/f=q,v,B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img786.png"
 ALT="$f=q v B$">|; 

$key = q/e=1.60times10^{-19};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img872.png"
 ALT="$e=1.60\times 10^{-19}$">|; 

$key = q/119.22,{{rm{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img272.png"
 ALT="$119.22 {\rm N}$">|; 

$key = q/displaystylef_{ac,x}+f_{bc,x}=-2.59times10^{-3}+7.99times10^{-3}=5.40times10^{-3},{{rm{N},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="483" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img298.png"
 ALT="$\displaystyle f_{ac x} + f_{bc x} = -2.59\times 10^{-3} + 7.99 \times 10^{-3} =5.40\times
10^{-3} {\rm N},$">|; 

$key = q/{displaymath}I_1=frac{N_2}{N_1},I_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1165.png"
 ALT="\begin{displaymath}
I_1 =\frac{N_2}{N_1} I_2.
\end{displaymath}">|; 

$key = q/C_f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1409.png"
 ALT="$C_f$">|; 

$key = q/C_{{rm{eq}=sum_{i=1}^NC_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img537.png"
 ALT="$C_{\rm eq} = \sum_{i=1}^N C_i$">|; 

$key = q/{displaymath}V_4=I,R_4=(1.29),(4)=5.14,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img701.png"
 ALT="\begin{displaymath}
V_4 = I R_4 = (1.29) (4) =5.14 {\rm V}.
\end{displaymath}">|; 

$key = q/{displaymath}S_{x'}=S,cos,(alpha-theta)=S,cosalpha,costheta+S,sinalpha,sintheta=S_x,costheta+S_y,sintheta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="557" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="\begin{displaymath}
S_{x'} = S \cos (\alpha-\theta) = S \cos\alpha \cos\thet...
...S \sin\alpha \sin\theta
= S_x \cos\theta + S_y \sin\theta,
\end{displaymath}">|; 

$key = q/displaystylea_xcostheta+a_ysintheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\displaystyle a_x\cos\theta + a_y\sin \theta,$">|; 

$key = q/{{rm{V,m^{-1}});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img406.png"
 ALT="${\rm V  m^{-1}})$">|; 

$key = q/{mitPhi}_{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1044.png"
 ALT="${\mit\Phi}_{2}$">|; 

$key = q/theta_irightarrow180^circ+theta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img370.png"
 ALT="$\theta_i \rightarrow 180^\circ +\theta_i$">|; 

$key = q/V_{{rm{max}=110;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img964.png"
 ALT="$V_{\rm max} = 110$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{shadow.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="487" HEIGHT="340" BORDER="0"
 SRC="|."$dir".q|img1295.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{shadow.eps}}
\end{figure}">|; 

$key = q/R_f<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1422.png"
 ALT="$R_f&lt;0$">|; 

$key = q/C_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img528.png"
 ALT="$C_1$">|; 

$key = q/VproptoQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img504.png"
 ALT="$V\propto Q$">|; 

$key = q/{displaymath}dW=w,dV=epsilon_0,E^2,A,c,dt.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1275.png"
 ALT="\begin{displaymath}
d W = w d V = \epsilon_0 E^2  A c d t.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{torque.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="688" HEIGHT="288" BORDER="0"
 SRC="|."$dir".q|img956.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{torque.eps}}
\end{figure}">|; 

$key = q/13.6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img394.png"
 ALT="$13.6$">|; 

$key = q/E_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img367.png"
 ALT="$E_i$">|; 

$key = q/{displaymath}{{bf{E}=-left(frac{dV}{dx},frac{dV}{dy},frac{dV}{dz}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img410.png"
 ALT="\begin{displaymath}
{\bf E} = - \left(\frac{dV}{dx},
\frac{dV}{dy}, \frac{dV}{dz}
\right).
\end{displaymath}">|; 

$key = q/R_{{rm{eq}=0.667+4=4.667,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img699.png"
 ALT="$R_{\rm eq} = 0.667 + 4 = 4.667 \Omega$">|; 

$key = q/B=0.40;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1028.png"
 ALT="$B=0.40$">|; 

$key = q/{displaymath}f=frac{q_a,q_b}{4piepsilon_0,r^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="\begin{displaymath}
f = \frac{q_a q_b}{4\pi\epsilon_0 r^2},
\end{displaymath}">|; 

$key = q/{displaymath}frac{1}{p}+frac{1}{q}=frac{1}{f}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1402.png"
 ALT="\begin{displaymath}
\frac{1}{p} + \frac{1}{q} = \frac{1}{f} = 0,
\end{displaymath}">|; 

$key = q/v_A=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img459.png"
 ALT="$v_A=0$">|; 

$key = q/{displaymath}P=P_1-P_2=(600)-(100)=500,{{rm{W}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1039.png"
 ALT="\begin{displaymath}
P = P_1 - P_2 = (600) - (100) = 500 {\rm W}.
\end{displaymath}">|; 

$key = q/{displaymath}I=frac{calE}{R}=frac{{calE}_{{rm{max}}{R},sin(2pi,f,t).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img944.png"
 ALT="\begin{displaymath}
I = \frac{\cal E}{R} = \frac{ {\cal E}_{\rm max}}{R}  \sin (2\pi  f  t).
\end{displaymath}">|; 

$key = q/{displaymath}1,{{rm{T}equiv1,{{rm{N},{{rm{A}^{-1},{{rm{m}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img750.png"
 ALT="\begin{displaymath}
1 {\rm T} \equiv 1 {\rm N} {\rm A}^{-1} {\rm m}^{-1}.
\end{displaymath}">|; 

$key = q/pmsigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img350.png"
 ALT="$\pm \sigma$">|; 

$key = q/{displaymath}q,(V_B-V_A)=P_B-P_A=W=-q,E_x,c,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="324" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img444.png"
 ALT="\begin{displaymath}
q (V_B- V_A)= P_B - P_A = W = - q E_x c,
\end{displaymath}">|; 

$key = q/{mitDelta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1497.png"
 ALT="${\mit\Delta}$">|; 

$key = q/f>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="$f&gt;0$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{concave.eps}}{{{.{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="683" HEIGHT="311" BORDER="0"
 SRC="|."$dir".q|img1367.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{concave.eps}}
.\end{figure}">|; 

$key = q/V={calE}+I,R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1035.png"
 ALT="$V = {\cal E} + I R$">|; 

$key = q/42;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1486.png"
 ALT="$42$">|; 

$key = q/{displaymath}v_B=sqrt{frac{-2,{mitDelta}P}{m}}=sqrt{frac{-2,(-1.6times10^{-16})}.11times10^{-31}}}=1.87times10^7,{{rm{m,s^{-1}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img461.png"
 ALT="\begin{displaymath}
v_B = \sqrt{\frac{-2 {\mit\Delta}P}{m}} = \sqrt{
\frac{-2 ...
...6})}{9.11\times
10^{-31}}} = 1.87\times 10^7 {\rm m s^{-1}}.
\end{displaymath}">|; 

$key = q/{displaymath}tau=R,C=(8),(15)=120,,{{rm{s}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1196.png"
 ALT="\begin{displaymath}
\tau = R C = (8) (15) = 120  {\rm s}
\end{displaymath}">|; 

$key = q/R_S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img834.png"
 ALT="$R_S$">|; 

$key = q/V_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img540.png"
 ALT="$V_2$">|; 

$key = q/displaystyle|a|^2,|b|^2-|a|^2,|b|^2,cos^2theta=|a|^2,|b|^2,sin^2theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$\displaystyle \vert a\vert^2  \vert b\vert^2 - \vert a\vert^2  \vert b\vert^2  \cos^2\theta = \vert a\vert^2 \vert b\vert^2  \sin^2\theta.$">|; 

$key = q/A_1=10,{{rm{cm}^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img996.png"
 ALT="$A_1= 10 {\rm cm}^2$">|; 

$key = q/{displaymath}int_P^Q{{bf{A}cdotd{{bf{r}=int_P^Q(A_x,dx+A_y,dy+A_z,dz),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="\begin{displaymath}
\int_P^Q {\bf A}\cdot d{\bf r} = \int_P^Q (A_x dx+A_y dy + A_z dz),
\end{displaymath}">|; 

$key = q/{displaymath}frac{1}{R_{{rm{eq}}=frac{I}{V}=frac{I_1+I_2}{V}=frac{I_1}{V}+frac{I_2}{V},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img658.png"
 ALT="\begin{displaymath}
\frac{1}{R_{\rm eq}} = \frac{I}{V} = \frac{I_1+I_2}{V} = \frac{I_1}{V}
+\frac{I_2}{V},
\end{displaymath}">|; 

$key = q/displaystylea_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\displaystyle a_z,$">|; 

$key = q/{displaymath}q=frac{1}{1slashf-1slashp}=frac{1}{(1slash35-1slash90)}=57.27,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="359" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1474.png"
 ALT="\begin{displaymath}
q = \frac{1}{1/f - 1/p} = \frac{1}{(1/35-1/90)} = 57.27 {\rm cm}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{di'}{dt}=-i',frac{R}{L},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1099.png"
 ALT="\begin{displaymath}
\frac{d i'}{d t} = -i' \frac{R}{L},
\end{displaymath}">|; 

$key = q/Q=1.00times10^{-3},mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img564.png"
 ALT="$Q=1.00\times 10^{-3} \mu{\rm C}$">|; 

$key = q/{displaymath}i(t)=I,{{rm{e}^{-R,tslashL}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1115.png"
 ALT="\begin{displaymath}
i(t) = I {\rm e}^{-R t/L}.
\end{displaymath}">|; 

$key = q/f_3<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img273.png"
 ALT="$f_3&lt;0$">|; 

$key = q/{displaymath}sintheta_m=frac{mitDelta}{d}=frac{m,lambda}{d}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1501.png"
 ALT="\begin{displaymath}
\sin\theta_m = \frac{\mit\Delta}{d} = \frac{m \lambda}{d}.
\end{displaymath}">|; 

$key = q/v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img457.png"
 ALT="$v$">|; 

$key = q/{displaymath}I_2=frac{P}{V_2}=frac{(1times10^9)}{(5times10^4)}=20,{{rm{kA}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1205.png"
 ALT="\begin{displaymath}
I_2 = \frac{P}{V_2} = \frac{(1\times 10^9)}{(5\times 10^4)} = 20 {\rm kA}.
\end{displaymath}">|; 

$key = q/costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img743.png"
 ALT="$\cos\theta$">|; 

$key = q/A=150,{{rm{cm}^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img562.png"
 ALT="$A=150 {\rm cm}^2$">|; 

$key = q/{displaymath}V=V_1+V_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img649.png"
 ALT="\begin{displaymath}
V = V_1 + V_2.
\end{displaymath}">|; 

$key = q/n,t=m,lambdaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1528.png"
 ALT="$n t=m \lambda/2$">|; 

$key = q/displaystyle|a|^2,|b|^2-({{bf{a}cdot{{bf{b})^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\displaystyle \vert a\vert^2  \vert b\vert^2 - ({\bf a}\cdot {\bf b})^2$">|; 

$key = q/{{bf{B}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img752.png"
 ALT="${\bf B}_2$">|; 

$key = q/m=9.11times10^{-31};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img456.png"
 ALT="$m=9.11\times 10^{-31}$">|; 

$key = q/I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img606.png"
 ALT="$I$">|; 

$key = q/displaystyle0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1234.png"
 ALT="$\displaystyle 0,$">|; 

$key = q/6,{{rm{V};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img694.png"
 ALT="$6 {\rm V}$">|; 

$key = q/lambda=30;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1284.png"
 ALT="$\lambda = 30$">|; 

$key = q/{displaymath}P={calE},I=P_{{rm{max},sin^2(2pi,f,t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img973.png"
 ALT="\begin{displaymath}
P = {\cal E} I = P_{\rm max}  \sin^2(2\pi  f  t),
\end{displaymath}">|; 

$key = q/{displaymath}R_S=frac{I_{{rm{fsd}}{I_{{rm{max}-I_{{rm{fsd}},R_G.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img843.png"
 ALT="\begin{displaymath}
R_S = \frac{I_{\rm fsd}}{I_{\rm max}-I_{\rm fsd}} R_G.
\end{displaymath}">|; 

$key = q/L_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1145.png"
 ALT="$L_2$">|; 

$key = q/theta_2=90^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1326.png"
 ALT="$\theta_2= 90^\circ$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{gen.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="695" HEIGHT="342" BORDER="0"
 SRC="|."$dir".q|img924.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{gen.eps}}
\end{figure}">|; 

$key = q/{displaymath}f=F,l=(1.30times10^{-4}),(1.2)=1.56times10^{-4},{{rm{N}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="374" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img868.png"
 ALT="\begin{displaymath}
f = F l = (1.30\times 10^{-4}) (1.2) = 1.56\times 10^{-4} {\rm N}.
\end{displaymath}">|; 

$key = q/W(Q);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img548.png"
 ALT="$W(Q)$">|; 

$key = q/{displaymath}{calE}=V-I,R=(120)-(5.0),(4.0)=100,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="349" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1036.png"
 ALT="\begin{displaymath}
{\cal E} = V - I R = (120) - (5.0) (4.0) = 100 {\rm V}.
\end{displaymath}">|; 

$key = q/P=I_1,V_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1203.png"
 ALT="$P=I_1 V_1$">|; 

$key = q/200,{{rm{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img645.png"
 ALT="$200 {\rm A}$">|; 

$key = q/{displaymath}{calE}=-L,frac{dI}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1075.png"
 ALT="\begin{displaymath}
{\cal E} = - L \frac{dI}{d t}.
\end{displaymath}">|; 

$key = q/1slashR_{{rm{eq}=sum_{i=1}^N(1slashR_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img660.png"
 ALT="$1/R_{\rm eq} = \sum_{i=1}^N (1/R_i)$">|; 

$key = q/{displaymath}{{bf{f}=q,{{bf{v}times{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img766.png"
 ALT="\begin{displaymath}
{\bf f} = q {\bf v} \times{\bf B}.
\end{displaymath}">|; 

$key = q/{displaymath}M=-frac{q}{p}=-frac{(-60)}{(15)}=4.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1446.png"
 ALT="\begin{displaymath}
M = -\frac{q}{p} = -\frac{(-60)}{(15)} = 4.
\end{displaymath}">|; 

$key = q/90^circ-phi=57.4^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img303.png"
 ALT="$90^\circ-\phi = 57.4^\circ$">|; 

$key = q/C_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img572.png"
 ALT="$C_0$">|; 

$key = q/n<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$n&lt;0$">|; 

$key = q/L=100,{{rm{mH};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1183.png"
 ALT="$L= 100 {\rm mH}$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{harbour.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="624" HEIGHT="347" BORDER="0"
 SRC="|."$dir".q|img1493.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{harbour.eps}}
\end{figure}">|; 

$key = q/{{bf{b},equiv,stackrel{displaystylerightarrow}{QR},equiv,stackrel{displaystylerightarrow}{PS};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="${\bf b}  \equiv  \stackrel{\displaystyle \rightarrow}{QR} \equiv
 \stackrel{\displaystyle \rightarrow}{PS}$">|; 

$key = q/{displaymath}E=frac{-Q}{epsilon_0,A}=-frac{Q}{4piepsilon_0,R^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img332.png"
 ALT="\begin{displaymath}
E = \frac{-Q}{\epsilon_0 A} =- \frac{Q}{4\pi\epsilon_0 R^2}.
\end{displaymath}">|; 

$key = q/A=0.05,{{rm{m}^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1170.png"
 ALT="$A=0.05 {\rm m}^2$">|; 

$key = q/0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1174.png"
 ALT="$0.1$">|; 

$key = q/{bf{a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$\bf a$">|; 

$key = q/M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1052.png"
 ALT="$M$">|; 

$key = q/{displaymath}frac{Q}{q}={{rm{e}^{,tslashR,C}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1193.png"
 ALT="\begin{displaymath}
\frac{Q}{q} = {\rm e}^{ t/R C}.
\end{displaymath}">|; 

$key = q/{displaymath}v=V-i,R.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1121.png"
 ALT="\begin{displaymath}
v = V - i R.
\end{displaymath}">|; 

$key = q/{{bf{E}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="${\bf E}({\bf r})$">|; 

$key = q/3.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1471.png"
 ALT="$3.5$">|; 

$key = q/<10^{-11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1259.png"
 ALT="$&lt;10^{-11}$">|; 

$key = q/Q_{{rm{crit}=4piepsilon_0,a^2,E_{{rm{crit};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img482.png"
 ALT="$Q_{\rm crit} = 4\pi\epsilon_0 a^2  E_{\rm crit}$">|; 

$key = q/{displaymath}2,n,t=(m+1slash2),lambda,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1519.png"
 ALT="\begin{displaymath}
2 n t=(m+1/2) \lambda,
\end{displaymath}">|; 

$key = q/da;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img811.png"
 ALT="$da$">|; 

$key = q/{displaymath}P_1=V,I=(120),(5.0)=600,{{rm{W}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1037.png"
 ALT="\begin{displaymath}
P_1 = V I = (120) (5.0) = 600 {\rm W}.
\end{displaymath}">|; 

$key = q/-0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1459.png"
 ALT="$-0.1$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{shunt.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="551" HEIGHT="229" BORDER="0"
 SRC="|."$dir".q|img850.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{shunt.eps}}
\end{figure}">|; 

$key = q/2.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img599.png"
 ALT="$2.5$">|; 

$key = q/epsilon=K,epsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img526.png"
 ALT="$\epsilon= K \epsilon_0$">|; 

$key = q/{displaymath}W=-q,E_x,c=-(1.2times10^{-6}),(1.40times10^3),(-3.50times10^{-2})=+5.88times10^{-5},{{rm{J}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="586" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img441.png"
 ALT="\begin{displaymath}
W = -q  E_x  c= -(1.2\times 10^{-6}) (1.40\times 10^3) (-3.50\times 10^{-2}) =
+5.88 \times 10^{-5} {\rm J}.
\end{displaymath}">|; 

$key = q/{displaymath}f=q,v,B=frac{m,v^2}{rho},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img787.png"
 ALT="\begin{displaymath}
f = q v B = \frac{m v^2}{\rho},
\end{displaymath}">|; 

$key = q/n,A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img765.png"
 ALT="$n A$">|; 

$key = q/{displaymath}lambda_3'=frac{(2),(1.36),(250times10^{-9})}{(5slash2)}=272,{{rm{nm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1536.png"
 ALT="\begin{displaymath}
\lambda_3' = \frac{(2) (1.36) (250\times 10^{-9})}{(5/2)} = 272 {\rm nm}.
\end{displaymath}">|; 

$key = q/{mitDelta}V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img388.png"
 ALT="${\mit\Delta}V$">|; 

$key = q/{displaymath}n_1,sintheta_1=n_2,sintheta_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1491.png"
 ALT="\begin{displaymath}
n_1 \sin\theta_1 = n_2 \sin\theta_2.
\end{displaymath}">|; 

$key = q/{displaymath}V_b=k_e,frac{q_b}{b}=(8.988times10^9),frac{(4times10^{-6})}{(3)}=1.20times10^4,{{rm{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="432" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img470.png"
 ALT="\begin{displaymath}
V_b = k_e \frac{q_b}{b} = (8.988\times 10^9) \frac{(4\times 10^{-6})}{(3)}=1.20\times 10^4 {\rm V}.
\end{displaymath}">|; 

$key = q/{displaymath}c=frac{1}{sqrt{mu_0,epsilon_0}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1250.png"
 ALT="\begin{displaymath}
c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}.
\end{displaymath}">|; 

$key = q/{displaymath}q=-M,p=-(0.1),(225)=-22.5,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1463.png"
 ALT="\begin{displaymath}
q = -M p = -(0.1) (225) = -22.5 {\rm cm}.
\end{displaymath}">|; 

$key = q/-Q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img328.png"
 ALT="$-Q$">|; 

$key = q/{displaymath}P_{calE}=P_r+P_R.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img675.png"
 ALT="\begin{displaymath}
P_{\cal E} =P_r + P_R.
\end{displaymath}">|; 

$key = q/lambdaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1515.png"
 ALT="$\lambda/2$">|; 

$key = q/ab;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img814.png"
 ALT="$ab$">|; 

$key = q/E_a=Q_aslash(4piepsilon_0,a^2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img497.png"
 ALT="$E_a = Q_a/(4\pi\epsilon_0 a^2)$">|; 

$key = q/i_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1349.png"
 ALT="$i_1$">|; 

$key = q/{displaymath}B,L=mu_0,n,L,I,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img818.png"
 ALT="\begin{displaymath}
B L = \mu_0  n L I,
\end{displaymath}">|; 

$key = q/Lslashd;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1510.png"
 ALT="$L/d$">|; 

$key = q/{mitDelta}=(m+1slash2),lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1514.png"
 ALT="${\mit\Delta}=(m+1/2) \lambda$">|; 

$key = q/0.667,{{rm{Omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img698.png"
 ALT="$0.667 {\rm\Omega}$">|; 

$key = q/{displaymath}-L,frac{di}{dt}=i,R-V.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1097.png"
 ALT="\begin{displaymath}
-L \frac{d i}{d t} = i R - V.
\end{displaymath}">|; 

$key = q/ST;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1370.png"
 ALT="$ST$">|; 

$key = q/{{bf{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="${\bf v}$">|; 

$key = q/{displaymath}P_2=i_2,v_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1149.png"
 ALT="\begin{displaymath}
P_2 = i_2 v_2.
\end{displaymath}">|; 

$key = q/4,mu{{rm{F};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img583.png"
 ALT="$4 \mu{\rm F}$">|; 

$key = q/{displaymath}E=P+K.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img454.png"
 ALT="\begin{displaymath}
E = P + K.
\end{displaymath}">|; 

$key = q/45^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$45^\circ$">|; 

$key = q/z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$z'$">|; 

$key = q/q>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="$q&gt;0$">|; 

$key = q/q_3=-7.0,mu{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img462.png"
 ALT="$q_3=-7.0 \mu{\rm C}$">|; 

$key = q/{displaymath}q=C,v=C,d,E.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1219.png"
 ALT="\begin{displaymath}
q = C v = C d E.
\end{displaymath}">|; 

$key = q/I_{12}=I_1+I_2=1.29,{{rm{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img705.png"
 ALT="$I_{12} = I_1 + I_2 = 1.29 {\rm A}$">|; 

$key = q/{displaymath}n=sqrt{K}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1306.png"
 ALT="\begin{displaymath}
n = \sqrt{K}.
\end{displaymath}">|; 

$key = q/{displaymath}K=frac{1}{2},m,v^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img455.png"
 ALT="\begin{displaymath}
K = \frac{1}{2}  m  v^2,
\end{displaymath}">|; 

$key = q/{displaymath}f=k_e,frac{q,q'}{r^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="\begin{displaymath}
f = k_e  \frac{q  q'}{r^2},
\end{displaymath}">|; 

$key = q/{displaymath}({{bf{b}-{{bf{a})cdot({{bf{b}-{{bf{a})=|a|^2+|b|^2-2,{{bf{a}cdot{{bf{b}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="\begin{displaymath}
({\bf b} - {\bf a} ) \cdot ({\bf b} - {\bf a} ) = \vert a\vert^2 + \vert b\vert^2 - 2 {\bf a} \cdot
{\bf b}.
\end{displaymath}">|; 

$key = q/v_d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img621.png"
 ALT="$v_d$">|; 

$key = q/{displaymath}i=frac{dq}{dt}=C,d,frac{dE}{dt}=epsilon_0,A,frac{dE}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1225.png"
 ALT="\begin{displaymath}
i = \frac{dq}{d t} = C d \frac{d E}{dt} =\epsilon_0 A  \frac{d E}{d t}.
\end{displaymath}">|; 

$key = q/{displaymath}omega=frac{v}{rho}=frac{q,B}{m}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img789.png"
 ALT="\begin{displaymath}
\omega = \frac{v}{\rho} = \frac{q B}{m}.
\end{displaymath}">|; 

$key = q/n_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1303.png"
 ALT="$n_2$">|; 

$key = q/displaystyleoint_C{{bf{B}cdotd{{bf{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1238.png"
 ALT="$\displaystyle \oint_C {\bf B}\cdot d{\bf r}$">|; 

$key = q/d=5.00;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img440.png"
 ALT="$d=5.00$">|; 

$key = q/{displaymath}1,{{rm{F}equiv1,{{rm{C,V}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img505.png"
 ALT="\begin{displaymath}
1 {\rm F} \equiv 1 {\rm C V}^{-1}.
\end{displaymath}">|; 

$key = q/1,mu{{rm{F};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img581.png"
 ALT="$1 \mu{\rm F}$">|; 

$key = q/{displaymath}{calE}=B_perp,l,v,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img911.png"
 ALT="\begin{displaymath}
{\cal E} = B_\perp l v,
\end{displaymath}">|; 

$key = q/stackrel{displaystylerightarrow}{PQ};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\stackrel{\displaystyle \rightarrow}{PQ}$">|; 

$key = q/{displaymath}F=I',B,sin50^circ=(1.7),(10^{-4}),(0.7660)=1.30times10^{-4},{{rm{N,m}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="494" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img867.png"
 ALT="\begin{displaymath}
F = I' B \sin 50^\circ= (1.7)  (10^{-4}) (0.7660)
= 1.30\times 10^{-4} {\rm N m}^{-1}.
\end{displaymath}">|; 

$key = q/+Q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img477.png"
 ALT="$+Q$">|; 

$key = q/displaystylef_{bc}=7.99times10^{-3},{{rm{N},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img287.png"
 ALT="$\displaystyle f_{bc} = 7.99 \times 10^{-3}  {\rm N},$">|; 

$key = q/{displaymath}W=frac{C,V^2}{2}=frac{(5times10^{-12}),(100)^2}{2}=2.5times10^{-8},{{rm{J}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img598.png"
 ALT="\begin{displaymath}
W = \frac{C V^2}{2} = \frac{(5\times 10^{-12}) (100)^2}{2}= 2.5\times 10^{-8}
 {\rm J}.
\end{displaymath}">|; 

$key = q/N_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1060.png"
 ALT="$N_1$">|; 

$key = q/{displaymath}W=P,t=(150),(6),(60),(60)=3.24times10^6,{{rm{J}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="362" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img736.png"
 ALT="\begin{displaymath}
W = P t = (150) (6) (60) (60) = 3.24\times 10^6 {\rm J}.
\end{displaymath}">|; 

$key = q/{displaymath}|{{bf{a}times{{bf{b}|=|a|,|b|,sintheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="\begin{displaymath}
\vert{\bf a}\times{\bf b}\vert = \vert a\vert \vert b\vert \sin\theta.
\end{displaymath}">|; 

$key = q/W_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img372.png"
 ALT="$W_1$">|; 

$key = q/y';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$y'$">|; 

$key = q/2.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img597.png"
 ALT="$2.0$">|; 

$key = q/{{bf{I}times{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1022.png"
 ALT="${\bf I}\times {\bf B}$">|; 

$key = q/V=E,d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img555.png"
 ALT="$V=E d$">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{rainbow1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="372" HEIGHT="401" BORDER="0"
 SRC="|."$dir".q|img1345.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{rainbow1.eps}}
\end{figure}">|; 

$key = q/R_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img648.png"
 ALT="$R_2$">|; 

$key = q/V_B-V_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img443.png"
 ALT="$V_B- V_A$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig3.8.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="281" BORDER="0"
 SRC="|."$dir".q|img769.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig3.8.eps}}
\end{figure}">|; 

$key = q/f,lambda=c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1286.png"
 ALT="$f \lambda=c$">|; 

$key = q/2pi,a^3slash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$2\pi  a^3/3$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig9a.ps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="220" BORDER="0"
 SRC="|."$dir".q|img1119.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig9a.ps}}
\end{figure}">|; 

$key = q/displaystyleoint_C{{bf{E}cdotd{{bf{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1236.png"
 ALT="$\displaystyle \oint_C {\bf E}\cdot d{\bf r}$">|; 

$key = q/{{bf{v}times{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img922.png"
 ALT="${\bf v}\times{\bf B}$">|; 

$key = q/{displaymath}q(t)=Q,(1-{{rm{e}^{-tslashR,C}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1129.png"
 ALT="\begin{displaymath}
q(t) = Q (1- {\rm e}^{-t/R C}).
\end{displaymath}">|; 

$key = q/V_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img382.png"
 ALT="$V_A$">|; 

$key = q/V_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img409.png"
 ALT="$V_0$">|; 

$key = q/{displaymath}frac{1}{R_{eq}'}=frac{1}{1}+frac{1}{2}=frac{3}{2},Omega^{-1},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img696.png"
 ALT="\begin{displaymath}
\frac{1}{R_{eq}'} = \frac{1}{1} + \frac{1}{2} = \frac{3}{2} \Omega^{-1},
\end{displaymath}">|; 

$key = q/E_0-E_1=E_0slashK;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img523.png"
 ALT="$E_0 - E_1 = E_0/K$">|; 

$key = q/{displaymath}frac{-h'}{h}=frac{R-q}{p-R}=frac{q}{p},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1389.png"
 ALT="\begin{displaymath}
\frac{-h'}{h} = \frac{R-q}{p-R} = \frac{q}{p},
\end{displaymath}">|; 

$key = q/{displaymath}E_0=v,B.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img916.png"
 ALT="\begin{displaymath}
E_0 = v B.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{plate.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="451" HEIGHT="226" BORDER="0"
 SRC="|."$dir".q|img349.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{plate.eps}}
\end{figure}">|; 

$key = q/aefb;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img716.png"
 ALT="$aefb$">|; 

$key = q/{{bf{E}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="${\bf E}'$">|; 

$key = q/{displaymath}C_{{rm{eq}=C_1+C_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img536.png"
 ALT="\begin{displaymath}
C_{\rm eq} = C_1 + C_2.
\end{displaymath}">|; 

$key = q/{figure*}{epsfysize{=1in{centerline{epsffile{fig2.eps}}{{figure*};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="448" HEIGHT="111" BORDER="0"
 SRC="|."$dir".q|img304.png"
 ALT="\begin{figure*}
\epsfysize =1in
\centerline{\epsffile{fig2.eps}}
\end{figure*}">|; 

$key = q/displaystyle{{bf{a}cdot{{bf{a}times{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\displaystyle {\bf a}\cdot {\bf a}\times{\bf b}$">|; 

$key = q/p=25;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1443.png"
 ALT="$p=25$">|; 

$key = q/87.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1469.png"
 ALT="$87.5$">|; 

$key = q/{mitDelta}K=-{mitDelta}P;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img475.png"
 ALT="${\mit\Delta}K= -{\mit\Delta}P$">|; 

$key = q/{mitDelta}t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1308.png"
 ALT="${\mit\Delta} t$">|; 

$key = q/{{bf{b}=(0,,1,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="${\bf b} = (0, 1, 0)$">|; 

$key = q/10^1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1265.png"
 ALT="$10^1$">|; 

1;

