Question

Shown in the figure are two point charges $+Q$ and $-Q$ inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If $\sigma _{1}$ is the surface charge on the inner surface and $Q_{1}$ net charge on it and $\sigma _{2}$ the surface charge on the outer surface and $Q_{2}$ net charge on it then:

• A. $\sigma _{1}=0, \, Q_{1}=0$ , $\sigma _{2}=0, \, Q_{2}=0$
• B. $\sigma _{1}\neq 0, \, Q_{1}=0$ , $\sigma _{2}\neq 0, \, Q_{2}=0$
• C. $\sigma _{1}\neq 0,Q_{1}\neq 0$ , $\sigma _{2}\neq 0, \, Q_{2}\neq 0$
• D. $\sigma_{1}=0, Q_{1}=0 \quad \sigma_{2}=0, Q_{2}=0$

Answer 1

Answer: (D)

Net charge inside the cavity is zero.
$ \therefore Q_{1}=0 \text { and } \sigma_{1}=0 $
There is no effect of $+Q$, $-Q$ and induced charge on inner surface on the outer surface hence
$ Q _{2}=0, \sigma_{2}=0 $