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From Sect. 233, the energy stored per unit volume in an electromagnetic
wave is given by

(331) 
Since, , for an electromagnetic wave, and
,
the above expression yields

(332) 
or

(333) 
It is clear, from the above, that half the energy in an
electromagnetic wave is carried by the electric field, and the other half
is carried by the magnetic field.
As an electromagnetic field propagates it transports energy. Let be the
power per unit area carried by an electromagnetic wave:
i.e., is the energy transported per unit time
across a unit crosssectional area perpendicular to the
direction in which the wave is traveling. Consider a
plane electromagnetic
wave propagating along the axis. The wave propagates
a distance
along the axis in a time interval . If we
consider a crosssectional area at rightangles to the axis, then in
a time the wave sweeps through a volume of
space, where
. The
amount of energy filling this volume is

(334) 
It follows, from the definition of , that the power per unit area carried by
the wave is given by

(335) 
so that

(336) 
Since half the energy in an electromagnetic wave is carried by the
electric field, and the other half is carried by the magnetic field, it
is conventional to convert the above expression into a form involving both
the electric and magnetic field strengths. Since, , we have

(337) 
Thus,

(338) 
Equation (338) specifies the power per unit area transported by an electromagnetic
wave at any given instant of time. The peak power is given by

(339) 
where and are the peak amplitudes of the oscillatory
electric and
magnetic fields, respectively. It is easily demonstrated that
the average power per unit area transported by an electromagnetic wave
is half the peak power, so that

(340) 
The quantity is conventionally termed the intensity of the wave.
Next: Worked Examples
Up: Electromagnetic Waves
Previous: Effect of Dielectric Materials
Richard Fitzpatrick
20070714