Question

A solid conducting sphere having a charge $Q$ is surrounded by an uncharged concentric conducting spherical shell. Let the potential difference between the surface of the solid sphere and the outer surface of the shell be $V.$ If the shell is now given a charge $-3Q,$ the new potential difference between the same two surfaces is:

• A. $V$
• B. $2V$
• C. $4V$
• D. $-2V$

Answer 1

The correct option is A $V$

Initial case:


Given that

$V_{S_1}-V_{S_2}=V$

Using formula of electric potential of sphere and shell

$\Rightarrow \frac{kQ}{a}-\frac{kQ}{b}=V..........\left(1\right)$


Final case:


$V_{S_1}^{\prime }=\frac{kQ}{a}-\frac{3kQ}{b}$

$V_{S_2}^{\prime }=\frac{kQ}{b}-\frac{3kQ}{b}$

So $V_{S_1}^{\prime }-V_{S_2}^{\prime }=(\frac{kQ}{a}-\frac{3kQ}{b})-(\frac{kQ}{b}-\frac{3kQ}{b})$

From eq. $\left(1\right)$

$\Rightarrow V_{S_1}^{\prime }-V_{S_2}^{\prime }=\frac{kQ}{a}-\frac{kQ}{b}=V$

Hence, option $\left(a\right)$ is correct.

Why this question:- Concept of potential on various spherical surface for a given charge.