Chapter 4Linear Dielectrics: Problem 4.20 + 4.35
Problem 4.20

A sphere of linear dielectric material has embedded in it a uniform free charge density ?. Find the potential at the center of the sphere, if its radius is R and its dielectric constant is K.

Problem 4.35

Prove the following uniqueness theorem: A region S contains a specified free charge distribution rf and various pieces of linear dielectric material, with the susceptibility of each one given. If the potential is specified on the boundary of S (and V = 0 at infinity) then the potential throughout S is uniquely defined.