Two point charges q and –q are located on the z axis at z = + a and z = –a, respectively.

(a) Find the electrostatic potential as an expansion in spherical harmonics and powers of r for both r > a and r < a.

 (b) Keeping the product qa = p/2 constant, take the limit of a → 0 and find the potential for г ≠ 0. This is by definition a dipole along the z axis and its potential.

(c) Suppose now that the dipole of part b is surrounded by a grounded spherical shell of radius b concentric with the origin. By linear superposition find the potential everywhere inside the shell