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Electric Dipoles
Consider a charge
located at position vector
, and a charge
located at position vector
.
In the limit that
, but
remains finite, this combination of charges constitutes an
electric dipole, of dipole moment
|
(195) |
located at position vector
. We have seen that the electric field generated at point
by an electric charge
located
at point
is
|
(196) |
Hence, the electric field generated at point
by an electric dipole of moment
located at point
is
|
(197) |
However, in the limit that
,
|
(198) |
Thus, the electric field due to the dipole becomes
|
(199) |
It follows from Equation (154) that the scalar electric potential due to the dipole is
|
(200) |
(Here,
is a gradient operator expressed in terms of the components of
, but independent of the
components of
.)
Finally, because electric fields are superposable, the electric potential due to a volume distribution of electric dipoles
is
|
(201) |
where
is the electric polarization (i.e., the electric dipole moment per unit volume), and
the integral is over all space.
Next: Charge Sheets and Dipole
Up: Electrostatic Fields
Previous: Electrostatic Energy
Richard Fitzpatrick
2014-06-27