Question

Three concentric conducting spherical shells are arranged as shown in figure. The middle and outermost shells are earthed. The innermost sphere is given a charge $q_{0}$, what are the charges in the middle and the outermost sphere respectively?

• A. $q_{0}$ and $-q_{0}$
• B. $-q_{0}$ and zero
• C. zero and $q_{0}$
• D. $-q_{0}$ and $+q_{0}$.

Answer 1

Answer: (B)

Since the middle and outermost shells are earthed, therefore their potential on their surfaces will be zero. Let the charges on the middle and outermost shells be $q_{1}$ and $q_{2}$ respectively. Then
$V_{A} =\frac{q_{0}}{2 a}+\frac{q_{1}}{2 a}+\frac{q_{2}}{3 a}=0$
and $ V_{B} =\frac{q_{0}}{3 a}+\frac{q_{1}}{3 a}+\frac{q_{2}}{3 a}=0$
These imply
$3 q_{0}+3 q_{1}+2 q_{2}=0, q_{0}+q_{1}+q_{2}=0$
$\therefore q_{1}=-q_{0} ; q_{2}=0$