Introduction to Electrodynamics · Problem 3.19

Potentials — David J. Griffiths

Physics · separation-of-variables-spherical

Problem

The potential at the surface of a sphere (radius

R

) is given by

V_0 = k\cos 3\theta,

where

k

is a constant. Find the potential inside and outside the sphere, as well as the surface charge density

\sigma(\theta)

on the sphere. (Assume there's no charge inside or outside the sphere.)