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Question
A metallic spherical shell has an inner radius R1 and outer radius R2. A charge Q is placed at the centre of the spherical cavity. What will be surface charge density on (i) the inner surface, and (ii) the outer surface?
Solution
A charge Q is placed at the centre of the spherical cavity. So, the charge induced at the inner surface of the sphere will be –Q and at outer surface of the sphere is +Q.
The surface charge density on the inner surface `sigma_1 = "Charge"/"Area" = (-Q)/(4pi R_1^2)`
Surface charge density on the outer surface `sigma_2 = (+Q)/(4piR_2^2)`
Hence, (i) `(-Q)/(4pi R_1^2)` (ii) `(+Q)/(4pi R_2^2)`
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