Question

A conducting shell $S_1$ having a charge Q is surrounded by an uncharged concentric conducting spherical shell $S_2$. Let the potential difference between $S_1$ and that $S_2$ be V. If the shell $S_2$ is now given a charge -3Q, the new potential difference between the same two shells is :

• A. 1 V
• B. 2 V
• C. 4 V
• D. -2 V

Answer 1

Answer: (A)

1 V

$S_1$ shell having energy Q is surrounded by an uncharged concentric conducting shell $S_2$.
So the potential difference between $S_1$ & $S_2$,
$V=\frac{1}{4\pi {ϵ}_0}[\frac{Q}{r_1}-\frac{Q}{r_2}]$
Now $-3Q$ charge is given to $S_2$ the $S_1$ will be the Then, potential difference , the total charge will be
$-2Q$
$V^{{}^{\prime }}=\frac{1}{4\pi {ϵ}_0}[\frac{Q}{r_1}-\frac{Q}{r_2}]$
$V^{{}^{\prime }}=1V$