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 $(k=\frac{1}{4\pi {\epsilon }_0})$

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

Answer 1

Answer: (D)

$V_C=\frac{kq}{3a}+\frac{k{q}^{\prime }}{3a}-\frac{kq}{4a}=0$
$\frac{kq}{12a}=\frac{k{q}^{\prime }}{3a}$
$q^{\prime }=\frac{-q}{4}$
$V_A=\frac{kq}{2a}-\frac{\frac{kq}{4}}{3a}-\frac{kq}{4a}$

$V_A=\frac{kq}{2a}-\frac{\frac{kq}{4}}{3a}-\frac{kq}{4a}$

$V_A=\frac{kq}{4a}-\frac{kq}{12a}$
$V_A=\frac{kq}{6a}$
$V_A-V_C=\frac{kq}{6a}$