Question

There are two concentric spherical shells of radii $r$ and $2r$. Initially a charge $Q$ is given to the inner shell and both the switches are open. If switch $S_1$, is closed and then opened, charge on the outer shell will be

• A. $Q$
• B. $\frac{Q}{2}$
• C. $-Q$
• D. $\frac{-Q}{2}$

Answer 1

The correct option is C $-Q$

When $S_1$ is closed, the shell must have potential equal to the potential of the Earth, i.e $zero$. So Earth will supply some charge (say $x$) to the shell to make its potential equal to $zero$.

Take a point on the outer shell and calculate it's potential due to the sphere and shell and make it $zero$, it'll give $x$:

$V_A=0$

$V_{duetosphere}+V_{duetoshell}=0$

$\frac{KQ}{2r}+\frac{Kx}{2r}=0$

$\Rightarrow x=-Q$