Question

Two concentric conducting spheres are of radii $r_1$ and $r_2$. The outer sphere is given a charge $q$. The charge $q^{\prime }$ on the inner sphere will be (inner sphere is grounded):-

• A. $q$
• B. $-q$
• C. $-q\frac{r_1}{r_2}$
• D. Zero

Answer 1

The correct option is C $-q\frac{r_1}{r_2}$


Let charge $q^{\prime }$ is flown from the ground to $S_1$ to make net potential at $S_1$ is zero.

$V_{S_1}=V_{ground}=0$

So, net potential at the surface of $S_1$ will be

$\Rightarrow \left(V_{S_1}\right)=\frac{k{q}^{\prime }}{r_1}+\frac{kq}{r_2}=0$

$\Rightarrow q^{\prime }=-q\frac{r_1}{r_2}$

Hence, option $\left(c\right)$ is correct.