Question

A metallic spherical shell of inner radius $R_1$ and outer radius $R_2$ is shown in figure below. A charge is placed at the centre of the spherical cavity. The surface charge density on the inner surface is:

• A. $\frac{q}{4\pi R_1^2}$
• B. $\frac{-q}{4\pi R_1^2}$
• C. $\frac{q^2}{4\pi R_2^2}$
• D. $\frac{q}{4\pi R_2^2}$

Answer 1

The correct option is B $\frac{-q}{4\pi R_1^2}$

When a charge +q is placed at the centre of spherical cavity as shown in figure.

Charge induced on the inner surface of shell = - q …(i)
Charge induced on the outer surface of shell = + q …(ii)
$\therefore$ Surface charge density on the inner surface = $\frac{-q}{4\pi R_1^2}$