A spherical shell of charge +Q, has outer radius `r_2` and inner radius `r_1` . If a charge +q is placed at the centre of shell then what are the values of surface charge density of inner and outer surfaces?

Explanation

Here charge +Q resides on the outer surface. As +q charge is placed at centre, a charge – q is induced on inner surface and a charge +q is induced on outer surface.

Hence, total charge on outer surface =Q + q , and surface charge density of outer surface, ltbgt `sigma_2=(Q+q)/(4pir_2^2)`
Surface charge density of inner surface, `sigma_1=q/(4pir_1^2)`