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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
.


(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
20001106