Two charges -q and +q are located at points (0, 0, –a) and (0, 0, a), respectively.
(a) What is the electrostatic potential at the points (0, 0, z) and (x, y, 0) ? (b) Obtain the dependence of potential on the distance r of a point from the origin when `r//a gt gt 1`.
(c) How much work is done in moving a small test charge from the point (5,0,0) to (–7,0,0) along the x-axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?

Explanation

(a) On the axis of the dipole, potential is `(+- 1//4 pi epsilon_(0)) p//(x^(2)-a^(2))` where p =2qa is the magnitude of the dipole moment, the + sign when the point is closer to q and the – sign when it is closer to –q. Normal to the axis, at points (x, y, 0), potential is zero.
(b) The dependence on r is `1//r^(2)` type.
(c) Zero. No, because work done by electrostatic field between two points is independent of the path connecting the two points.