Question

A solid conducting sphere of radius ${}^{\prime }{a}^{\prime }$ is surrounded by a thin uncharged concentric conducting shell of radius $2a$. A point charge $q$ is placed at a distance $4a$ from common centre of conducting sphere and shell. The inner sphere is then grounded.
The potential of outer shell is

• A. $\frac{q}{32\pi {ϵ}_{0}a}$
• B. $\frac{q}{16\pi {ϵ}_{0}a}$
• C. $\frac{q}{8\pi {ϵ}_{0}a}$
• D. $\frac{q}{4\pi {ϵ}_{0}a}$

Answer 1

The correct option is C $\frac{q}{8\pi {ϵ}_{0}a}$

The charge $q$ placed inside the shell causes an induced charge $-q$ on the inner surface of the shell and $+q$ charge on the outer surface.

$V=\frac{1}{4\pi {ϵ}_0}\frac{q}{a}\times \frac{1}{2}$

$=\frac{q}{8\pi {ϵ}_{0}a}$