Introduction to Electrodynamics · Problem 4.10

Electric Fields in Matter — David J. Griffiths

Physics · bound-charges-polarized-sphere

Problem

A sphere of radius

R

carries a polarization

\mathbf{P}(\mathbf{r}) = k\mathbf{r},

where

k

is a constant and

\mathbf{r}

is the vector from the center. (a) Calculate the bound charges

\sigma_b

and

\rho_b

. (b) Find the field inside and outside the sphere.