Page 117 - Engineering Electromagnetics, 8th Edition

CHAPTER 4 Energy and Potential 99

Figure 4.9 The electrostatic field of a point dipole with its moment in the a z
direction. Six equipotential surfaces are labeled with relative values of V.

and then define the dipole moment as Qd and assign it the symbol p. Thus

p = Qd (36)

The units of p are C · m.
Because d · a r = d cos θ,we then have
p · a r
V = (37)
4π 0 r 2
This result may be generalized as
1 r − r
V = p · (38)
2

4π 0 |r − r | |r − r |
where r locates the field point P, and r determines the dipole center. Equation (38)

is independent of any coordinate system.