Question

There are four concentric shells A, B, C and D of radii a, 2a, 3a and 4a respectively. Shells B and D are given charges +q and –q respectively. Shell C is now earthed. The potential difference $V_A-V_C$ is :

• A. $\frac{kq}{2a}$
• B. $\frac{kq}{3a}$
• C. $\frac{kq}{4a}$
• D. $\frac{kq}{6a}$

Answer 1

The correct option is D $\frac{kq}{6a}$

It is clear from figure, q' charge given to the earth surface and also $V_c=0$
$b=2a,c=3a,d=4a$
$V_c=\frac{kq}{3a}-\frac{kq}{4a}+\frac{k{q}^{\prime }}{3a}=0$
$q^{\prime }=-\frac{q}{4}$
Now, $V_A=\frac{kq}{2a}-\frac{kq}{4a}+\frac{k{q}^{\prime }}{3a}$
$V_A=\frac{kq}{6a}$

$V_A-V_C=\frac{kq}{6a}-0=\frac{kq}{6a}$