A parallel-plate capacitor with plates of area is filled with a linear dielectric of…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric fields in matter · Maxwell's equations and conservation laws

Electricity, Magnetism and Electromagnetism, Ch Displacement current, Maxwell's equations and boundary conditions

Problem

A parallel-plate capacitor with plates of area A=0.015 m2A = 0.015\,\mathrm{m^2} is filled with a linear dielectric of relative permittivity εr=3.0\varepsilon_r = 3.0. It is charged by a current I=0.20 AI = 0.20\,\mathrm{A} in the wires. Take the fields between the plates to be uniform and perpendicular to them, with no fringing, and the free charge to sit only on the plates. ((a)) Find dD/dtdD/dt in the dielectric, where DD is the magnitude of the electric displacement. ((b)) Find dE/dtdE/dt in the dielectric. ((c)) Find the displacement current ∫(∂D/∂t)⋅dA\int(\partial\mathbf{D}/\partial t)\cdot d\mathbf{A} over a flat surface inside the dielectric spanning the whole plate area.

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