A parallel-plate capacitor with plates apart sits inside a vacuum chamber and reads…

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 with plates

d = 1.5\,\mathrm{mm}

apart sits inside a vacuum chamber and reads

220.00\,\mathrm{pF}

when the chamber is evacuated. A monatomic gas is then admitted at number density

n = 2.7\times10^{25}\,\mathrm{m^{-3}}

and the capacitance reads

220.11\,\mathrm{pF}

. Throughout, the capacitor is held at

300\,\mathrm{V}

by an ideal supply of zero internal resistance. Edge effects are ignored; the gas is a homogeneous linear dielectric with no free charge, every atom is polarised alike with

\mathbf{p} = \alpha\mathbf{E}

, and each atom feels the field in the gap. ((a)) Find the relative permittivity and the susceptibility of the gas. ((b)) Find the polarisability

\alpha

of one atom and the polarisability volume

\alpha/4\pi\varepsilon_0

. ((c)) Find the field in the gap and the induced dipole moment of one atom. ((d)) Find the change in stored energy on admitting the gas, and the energy the supply delivers.

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