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
$V_A=\frac{q_0}{2a}+\frac{q_1}{2a}+\frac{q_2}{3a}=0$
and $V_B=\frac{q_0}{3a}+\frac{q_1}{3a}+\frac{q_2}{3a}=0$
These imply
$3q_0+3q_1+2q_2=0,q_0+q_1+q_2=0$
$\therefore q_1=-q_0;q_2=0$