Two conducting plates

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

Two conducting plates, each of width

b = 0.12\,\mathrm{m}

and length

L_p = 0.15\,\mathrm{m}

along the direction a dielectric slab will later be pushed in, are held

d = 5.0\,\mathrm{mm}

apart at a fixed potential difference

V = 1.5\,\mathrm{kV}

by a battery. Air fills the gap and the field between the plates, away from their edges, is uniform. ((a)) A small isolated conducting sphere of radius

a = 0.50\,\mathrm{mm}

, far smaller than the gap, sits in this uniform field. Using its polarisability

\alpha = 4\pi\varepsilon_0a^3

, find its interaction energy with the field, the energy stored in stretching its induced dipole, and its total energy in the field. ((b)) The battery is left connected. A slab of dielectric with

\chi_e = 1.4

, filling the gap across the full width

b

and kept well short of the sphere, so that the field at the sphere is unchanged, is now pushed a distance

x

into the gap alongside the plates. Find the force pulling the slab in, and say whether it depends on

x

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