Question

Two conducting, concentric, hollow spheres $A$ and $B$ have radii $a$ and $b$ respectively, with $A$ inside $B$. Their common potential is $V . A$ is now given some charge such that its potential becomes zero. The potential of $B$ will now be

• A. 0
• B. $V\left(1-\frac{a}{b}\right)$
• C. $\left(\frac{V}{a b}\right)$
• D. $V \frac{(b-a)}{(b+a)}$

Answer 1

Answer: (B)

Let initial charge on $B$ be $Q$.
Then, $V=k Q / b$.
There is no initial charge on $A$, as $A$ and $B$ are at the same potential.
Let $q$ charge be now given to $A$. Potential of $A$ now is
$k \frac{q}{a}+k \frac{Q}{b}=0$ or $q=-\frac{Q a}{b} \dots$(i)
Potential of $B$ now is
$k\left(\frac{Q+q}{b}\right)=\frac{k}{b}\left[Q-\frac{Q a}{b}\right]$
$=k \frac{Q}{b}\left(1-\frac{a}{b}\right)=V\left(1-\frac{a}{b}\right)$ (Using (i))