Question

A thick walled hollow spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge Q. A charge q is placed at the centre of sphere. The surface charge densities on inner and outer surfaces of the sphere will be respectively

• A. $\frac{-q}{4\pi r^2_1},\frac{q}{4\pi r^2_2}$
• B. $-\frac{q}{4\pi r^2_1},\frac{Q+q}{4\pi r^2_2}$
• C. $-\frac{q}{4\pi r^2_1},\frac{Q-q}{4\pi r^2_2}$
• D. $- \frac{q}{4\pi r^2_1},\frac{Q}{4\pi r^2_2}$

Answer 1

Answer: (B)

By induction charge on inner surface is (-q)
$\sigma_{in}=-\frac{q}{4\pi r^2_1}$
$\sigma_{out} = - \frac{Q+q}{4\pi R^2_2}$