A parallel-plate capacitor has a gap of between plates large enough for the fields to…

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

Electricity, Magnetism and Electromagnetism, Ch Dielectrics: polarisation, bound charge and the displacement field

Problem

A parallel-plate capacitor has a gap of

d = 4.0\,\mathrm{mm}

between plates large enough for the fields to be treated as uniform (edge effects ignored). A slab of glass of relative permittivity

\varepsilon_r = 5.0

, of thickness

2.0\,\mathrm{mm}

, lies in the gap parallel to the plates and against the negative plate; the remaining

2.0\,\mathrm{mm}

is empty and may be treated as vacuum. The free surface charge density on the positive plate is

\sigma_f = 1.0\times10^{-5}\,\mathrm{C\,m^{-2}}

, with the opposite free charge on the negative plate. The glass is a homogeneous, isotropic, linear dielectric. ((a)) Find the magnitude of

\mathbf{D}

in the empty region and in the glass. ((b)) Find the magnitude of

\mathbf{E}

in the empty region and in the glass. ((c)) Find the potential difference between the plates. ((d)) Find the magnitude of the bound surface charge density on each face of the glass slab, and state

\chi_e

for the glass.

Browse the problem library