Question

A positive charge Q=8 mC is placed inside the cavity of a neutral spherical conducting shell with an inner radius a and an outer radius b. Find the charges induced at the inner and outer surfaces of the shell.

Answer 1

Solution;

Given;

$Q=8mC$

$r_1=a$

$r_2=b$

Charge density induced on a surface is;

$\sigma=\frac{Charge}{Area}$

Negative charge is induced on the inner surface. Given by;

$\sigma _1=\frac{-8×10^{-6}}{4πa^2}=-0.6366mC/a^2m^2$

Positive charge is induced on the outside surface. Given by;

$\sigma_2=\frac{8×10^{-3}}{4πb^2}=0.6366mC/b^2m^2$