A metal ball of radius carrying is held at the centre of a thick spherical metal…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Conductors, capacitance and boundary-value electrostatics · Conductors, capacitance and boundary-value electrostatics

Electricity, Magnetism and Electromagnetism, Ch Conductors, screening and capacitance

Problem

A metal ball of radius

a = 2.0\,\mathrm{cm}

carrying

+5.0\,\mathrm{nC}

is held at the centre of a thick spherical metal shell of inner radius

b = 5.0\,\mathrm{cm}

and outer radius

6.0\,\mathrm{cm}

that carries no net charge. The gap is vacuum, no other charges are nearby, and equilibrium has been reached. The capacitance of a pair of concentric spheres of radii

a

and

b

C = 4\pi\varepsilon_0ab/(b-a)

, as derived in this chapter. ((a)) State the total charge on the inner surface of the shell and on its outer surface. ((b)) Find the capacitance of the ball-and-inner-surface pair, and the energy stored in the field in the gap between them. ((c)) Find the outward electrostatic pressure on the surface of the ball.

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