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A point charge is placed at the centre of a hollow conducting sphere of internal radius 'r' and outer radius '2r'. The ratio of the surface charge density of the inner surface to that - Physics

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A point charge is placed at the centre of a hollow conducting sphere of internal radius 'r' and outer radius '2r'. The ratio of the surface charge density of the inner surface to that of the outer surface will be_________.

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Solution

Let the point charge be q.
by gauss's law, the charge on the inner surface will be - q

Surface charge density of the inner surface `sigma_i = - q/(4pir^2)`

by charge conservation, on the hollow sphere, the outer surface will have charge q

Surface charge density of the inner surface `sigma_o = q/(4pi(2r)^2) = q/(16pir^2)`

ratio = `sigma_i/sigma_o = (-q/(4pir^2))/(q/(16pir^2)) = -4/1`

Concept: Electrostatics of Conductors
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