A parallel-plate capacitor has plates of area separated by of vacuum

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 plates of area

A = 2.50\times10^{-2}\ \mathrm{m^2}

separated by

d = 0.80\ \mathrm{mm}

of vacuum. Edge effects are ignored. The capacitor is charged to

300\ \mathrm{V}

and then disconnected from the supply, so its free charge is fixed thereafter. The gap is then completely flooded with liquid argon, an ideal insulator, so no charge leaks away. Argon has polarisability volume

\alpha/4\pi\varepsilon_0 = 1.64\times10^{-30}\ \mathrm{m^3}

and the liquid has number density

n = 2.10\times10^{28}

atoms per

\mathrm{m^3}

. Treat the liquid as a linear dielectric in which every atom acquires the moment

p = \alpha E

with

E

the macroscopic field in the liquid, so that

P = n\alpha E

; local-field corrections are ignored. ((a)) Find the relative permittivity of the liquid argon. ((b)) Find the voltage across the capacitor and the energy it stores after flooding. ((c)) Find the induced dipole moment of one argon atom in the flooded gap, and the distance its electron cloud shifts, treating the 18 electrons as a rigid cloud of charge

-18e

that moves bodily.

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