An infinite dielectric slab is uniformly polarised with magnitude and carries no free…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric fields in matter · Electric fields in matter

The Boundary-Value Problem, Ch Polarisation and bound charge, completed

Problem

An infinite dielectric slab is uniformly polarised with magnitude

P = 3.0\times10^{-6}\,\mathrm{C\,m^{-2}}

and carries no free charge anywhere, on any surface or in the bulk. Edge effects are ignored. Two orientations of the same magnitude of

\mathbf{P}

are considered. ((a)) Case A:

\mathbf{P}

is perpendicular to the flat faces of the slab. Find

\sigma_b

on each face and

\rho_b

in the bulk, then find

\mathbf{E}

and

\mathbf{D}

inside and outside the slab. ((b)) Case B:

\mathbf{P}

has the same magnitude but lies in the plane of the slab (parallel to the flat faces). Find

\sigma_b

on each face and

\rho_b

in the bulk, then find

\mathbf{E}

and

\mathbf{D}

inside and outside the slab. ((c)) Confirm that the free charge is zero everywhere in both cases, and state the values of

\mathbf{D}

inside the slab in each case.