A technician tests a rolled paper-and-foil capacitor

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 technician tests a rolled paper-and-foil capacitor. Two aluminium foils face each other across a paper layer of uniform thickness

d = 25\,\mu\mathrm{m}

, and the facing area of the foils is

A = 0.42\,\mathrm{m}^2

. Treat the rolled sandwich as a parallel-plate capacitor with a uniform gap, ignore edge effects, and treat the paper as a homogeneous linear dielectric carrying no free charge. The measured capacitance is

C = 0.45\,\mu\mathrm{F}

. The paper maker quotes a breakdown field of

16\,\mathrm{MV\,m^{-1}}

. ((a)) Find the relative permittivity

\varepsilon_r

, the electric susceptibility

\chi_e

and the permittivity

\varepsilon

of the paper. ((b)) With a steady potential difference of

250\,\mathrm{V}

across the capacitor, find the electric field in the paper, the polarisation

P

, and the bound surface charge density on each face of the paper layer. ((c)) Find the largest steady voltage the capacitor can take before the paper breaks down, and say whether

250\,\mathrm{V}

is safe.

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