Question

Two concentric spherical conducting shells of radii $R$ and $2R$ carry charges $Q$ and $2Q$ respectively. Change in electric potential on the outer shell when both are connected by a conducting wire is $\left(\text{k} = \frac{1}{4 \left(\pi ε\right)_{0}}\right)$

• A. zero
• B. $\frac{3 \text{kQ}}{2 \text{R}}$
• C. $\frac{\text{kQ}}{\text{R}}$
• D. $\frac{2 \text{kQ}}{\text{R}}$

Answer 1

Answer: (A)

When two concentric shells are connected by a wire the whole charge on inner shell is transferred to the outer shell.
Potential of the outer shell
$\left(\text{V}\right)_{\text{i}} = \frac{\text{kQ}}{2 \text{R}} + \frac{\text{k} \left(2 \text{Q}\right)}{2 \text{R}}$
$\text{V}_{\text{i}} = \frac{3 \text{kQ}}{2 \text{R}}$
$\left(\text{V}\right)_{\text{f}} = \frac{\text{k} \left(3 \text{Q}\right)}{2 \text{R}}$
$∴ \, \, \, \Delta \text{V} = \text{V}_{\text{f}} - \text{V}_{\text{i}} = 0$