A parallel-plate capacitor of plate area and gap is completely filled with a linear…

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

The Boundary-Value Problem, Ch Energy and force in dielectrics

Problem

A parallel-plate capacitor of plate area

S = 0.020\,\mathrm{m^2}

and gap

d = 2.0\,\mathrm{mm}

is completely filled with a linear dielectric of relative permittivity

\varepsilon_r = 6.0

and carries a free charge

Q = 4.0\times10^{-8}\,\mathrm{C}

. ((a)) Find

W_{\rm free}

, the work done by the free sources in charging the capacitor. ((b)) Find the energy held in the field alone,

\tfrac{\varepsilon_0}{2}\int E^2\,d\tau

, and state what accounts for the difference between it and

W_{\rm free}