Question

Consider a solid neutral conducting sphere of radius 2R having a concentric cavity of radius R. Points A , D and B are at distances $3R,\frac{3R}{2}$ and $\frac{R}{2}$from centre C respectively. $S_1$ & $S_2$ are inner and outer surface of the hollow sphere. If we place a point charge $q_0$ at C then choose the correct statement :

• A. Induced charge on $S_1$ is $-q_0$
• B. Electric field at D is not zero
• C. Potential at D is zero
• D. induced charge on $S_2$ is $-q_0/2$

Answer 1

Answer: (A)

Induced charge on $S_1$ is $-q_0$

As per the given problem charge $q_0$ is placed at C, the potential due to this charge at points A, B and D are
$V_A=\frac{k{q}_0}{9R^2}$
$V_D=\frac{4k{q}_0}{9R^2}$
$V_B=\frac{4k{q}_0}{R^2}$
Hence,
$V_A-V_B=\frac{k{q}_0}{9R^2}-\frac{4k{q}_0}{R^2}$
$V_A-V_B=-\frac{35k{q}_0}{9R^2}$
Negative potential difference indicates that Induced charge on S1 is $-q_0$ or when S2 is grounded S1 will acquire negative charge $-q_0$.