Question

Two concentric conducting spheres of radii $R$ and $2R$ are carrying charges $Q$ and $-2Q$ respectively. If the charge on inner sphere is doubled, the potential difference between the two spheres will

• A. become two times
• B. become four times
• C. be halved
• D. remain same

Answer 1

The correct option is A become two times


From figure,

$V_A=\frac{kQ}{R}+\frac{k(-2Q)}{2R}$

$V_B=\frac{kQ}{2R}+\frac{k(-2Q)}{2R}$

So, $V_A-V_B=\frac{kQ}{2R}>0$

$\Rightarrow V_A-V_B\propto Q\text{(charge on inner sphere)}$

Also. $V_A>V_B$

Therefore, if charge on the inner sphere is doubled the potential difference between the two spheres will become two times.

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

Why this question ? Application- This question insist you to think if both shells are connected then positive charge will flow from $\text{A}$ to $\text{B}$.