A dipole is oriented along the x axis. The dipole moment is p (=qs). (a) Calculate exactly the potential V (relative to infinity) at a location x, 0, 0 on the x axis and at a location 0, y, 0 on the y...

A dipole is oriented along the x axis. The dipole moment is p (=qs).

(a) Calculate exactly the potential V (relative to infinity) at a location x, 0, 0 on the x axis and at a location 0, y, 0

on the y axis, by superposition of the individual 1/r contributions to the potential.

(b) What are the approximate values of V at the locations in part (a) if these locations are far from the dipole?

(c) Using the approximate results of part (b), calculate the gradient of the potential along the x axis, and show that the

negative gradient is equal to the x component Ex of the electric field.

(d) Along the y axis, dV/dy = 0. Why isn't this equal to the magnitude of the electric field E along the y axis?