Introduction to Electrodynamics · Problem 3.27

Potentials — David J. Griffiths

Physics · multipole-expansion

Problem

A sphere of radius

R

, centered at the origin, carries charge density

\rho(r,\theta) = k\frac{R}{r^2}(R - 2r)\sin\theta,

where

k

is a constant, and

r

\theta

are the usual spherical coordinates. Find the approximate potential for points on the

z

axis, far from the sphere.