Question

A metallic spherical shell has an inner radius $R _{1}$ and outer radius $R_{2}$. 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

Answer: (B)

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 $=\frac{-q}{4 \pi R_{1}^{2}}$