A spherical conducting sheel of inner redius `s_1` and outer radius `r_2` has a charge Q. (a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell ?

Explanation

(a) The charge of `+Q` resides on the Outer surface of the shell. The charge q placed at the centre of the shell induces charge `-q` on the inner surface and charge +q on the outer surface of the shelll, from figure.
`therefore` Total charge on inner surface of the shell is -q and total charge on the outer surface of the shell is `(Q+q)`
`sigma_1=(q)/(4pir_(1)^(2)) and sigma_(1)(Q_1+q)/(4pir_(2)^(2))`