a solid ball of radius r is composed of a dielectric insulator of perm

Question

A solid ball of radius R is composed of a dielectric insulator of permittivity ɛ. The outside surface of the ball carries a static surface charge of(theta). (a) Determine the boundary conditions satisfied by the potential V(r) (i) at the center of the ball, (ii) at the surface of the ball, and (iii) at infinity. (b) Find the voltage V (r) both inside and outside the ball,expressed as an infinite sum with coefficients depending on integrals of of(theta). (c) Suppose that the static charge is concentrated in a ring at polar angle theta = theta0, with total charge qf in the ring. Find the electric field at the center of the ball in terms of qf, theta0 Re and e0 and e- infinity limits (d) Locate the center of charge in the situation described-in part (c) and verify your answer behaves as expected in the e → €, and ɛ → ∞ limits.