Question

A thin spherical conducting shell has radius $R$ and charge $q$. Another charge $Q$ is placed at the centre of the shell. The electric potential at a point $P$ at a distance $0.5d$ from the centre of the shell is :

• A. $\frac{2(q+Q)}{4\pi {ϵ}_{0}R}$
• B. $\frac{2(Q-q)}{4\pi {ϵ}_{0}R}$
• C. $\frac{2Q+q}{4\pi {ϵ}_{0}R}$
• D. $\frac{2Q}{4\pi {ϵ}_{0}R}$

Answer 1

The correct option is C $\frac{2Q+q}{4\pi {ϵ}_{0}R}$

$r=\frac{R}{2}$

Potential at any point inside a shell is given by $\frac{q}{4\pi {ϵ}_{o}R}$

$V=V_{chargeQ}+V_{shell}$

$⟹V=\frac{1}{4\pi {ϵ}_o}(\frac{Q}{r}+\frac{q}{R})$

$⟹V=\frac{1}{4\pi {ϵ}_o}(\frac{2Q}{R}+\frac{q}{R})$

$⟹V=\frac{2Q+q}{4\pi {ϵ}_{o}R}$

Answer-(C)