Question

Consider a thin conducting spherical shell of radius $R$ having charge $Q$. A point charge $q$ is placed at a distance $R/3$ from the center of the shell and another point charge $2q$ is placed at a distance $3R$ from the center of the shell. If the shell is grounded, find the charge flown through the grounding wire.

• A. $Q+q$
• B. $Q+3q$
• C. $Q+\frac{2}{3}q$
• D. $Q+\frac{5}{3}q$

Answer 1

Answer: (B)

$Q+3q$

The inner surface has $-q$ due to $+q$ at $\frac{R}{3}$ and outer surface has $-2q$ due to $-2q$ at $3R$

Therefore, let charge flown out $=Q+q+2q$

$=Q+3q$

Hence, the answer is $Q+3q.$