Question

In the figure, A, B, C and D are four concentric spheres of radius $a,2a,3a$ and $4a$ and contain charges $+3q,+6q,-9q$ and $+12q$ respectively. In the beginning, switches $S_1$ and $S_2$ are open. After earthing the sphere C, $\Delta q_1$ amount of charge flows from the sphere C to the earth. If the sphere B is also earthed, then $\Delta q_2$ amount of charge flows from the sphere B to the earth. Then,

• A. The value of $\Delta q_1$ is $9q$
• B. The value of $\Delta q_2$ is $6q$
• C. The value of $\Delta q_1$ is $6q$
• D. The value of $\Delta q_2$ is $9q$

Answer 1

Answer: (A), (D)

The correct options are
A The value of $\Delta q_1$ is $9q$
D The value of $\Delta q_2$ is $9q$

(a) If C is grounded


Total electric potential on the surface of C must be zero (conductor).
$\frac{1}{4\pi {\in }_0}[\frac{3q}{3a}+\frac{6q}{3a}+\frac{q_1}{3a}+\frac{12q}{4a}]=0$
$\Rightarrow q_1=-18q$
Hence, amount of charge which flows from C
$|\Delta q_1|=9q$

(b) If both B and C are grounded,




In this case, net potential on the surfaces of B and C each must be zero.
$\frac{1}{4\pi {\in }_0}[\frac{3q}{3a}+\frac{q_2}{3a}+\frac{q_3}{3a}+\frac{12q}{4a}]=0$
$\frac{1}{4\pi {\in }_0}[\frac{3q}{2a}+\frac{q_2}{2a}+\frac{q_3}{3a}+\frac{12q}{4a}]=0$

Solving the two equations,
$q_2=-3q$
$|\Delta q_2|=9q$