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?

Answer 1

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)`