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Consider a pair of charges
a small distance
apart
(
is the vector joining the negative charge to the positive
charge and is illustrated in Figure 3.5) such that we can define
Figure 3.5:
A pair of opposite charges are a distance
apart. A dipole is formed
by letting
.
![\includegraphics [scale=0.7]{fundfig33a.eps}](img520.gif) |
 |
(3.14) |
which is called the dipole moment. The resulting dipole
potential is
If we assume that
tends to zero, we may expand the second term in
a Taylor series for small
. Thus, we obtain
Hence,
 |
(3.15) |
The resulting electric field components are given by evaluating
in spherical coordinates. Hence
Thus,
falls off in magnitude like
and
vanishes when
. The electric field for a dipole is
shown in Figure 3.6.
Figure 3.6:
The electric field lines for an electric dipole.
|
Next: Magnetic Fields
Up: Electrostatics
Previous: Continuous distribution of charge,
Prof. Alan Hood
2000-11-06