Question

Two concentric shell R and 2R, charges $q_A$ and $q_B$ and potential 2V and $\frac{3V}{2}$ respectively. Now shell B is earthed and finally charges on shell A and B are $q_A$ and $q_B$ respectively. Then

• A. Potential difference between A and B will increase
• B. Potential difference between A and B will decrease
• C. Potential difference between A and B will not change
• D. From given data potential difference between A and B is zero.

Answer 1

The correct option is C

Potential difference between A and B will not change

Before earthing:
$\begin{array}{c}{V}_A=\frac{k{q}_A}{R}+\frac{k{q}_B}{2R}=2V\\ V_B=\frac{k{q}_A}{R}+\frac{k{q}_B}{2R}=\frac{3V}{2}\end{array}\}$ $\Rightarrow q_A=\frac{VR}{k}{q}_B=\frac{2VR}{k}$
After earthing: $q_A^1=q_A$ and $q_B^1=-q_A$
potential difference between A and B $=\frac{V}{2}$