Electricity and Magnetism · Problem 10.12

MAGNETIC FIELDS IN MATTER — Edward Purcell & David Morin

Physics — E&M · boundary-conditions-displacement

Problem

Using

\mathbf{D} \equiv \epsilon_0 \mathbf{E} + \mathbf{P}

and

\mathrm{div}\,\mathbf{D} = \rho_{\rm free}

, derive the general rules for the discontinuities (if any) in

D_\parallel

and

D_\perp

across the surface of an arbitrarily shaped polarized material (with no free charge).