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Question
Fill in the blank.
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_________.
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`
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