Q 12-02-118JEE MainJEE Main 2022 (25 Jul, Shift 2)Medium
The capacitance of an isolated conducting sphere of radius $R_1$ becomes $n$ times when it is enclosed by a concentric conducting sphere of radius $R_2$ connected to earth. The ratio of their radii $\left(\dfrac{R_2}{R_1}\right)$ is:
Answer: (A) $\dfrac{n}{n-1}$
Spherical capacitor: $C' = \dfrac{4\pi\varepsilon_0R_1R_2}{R_2 - R_1} = n(4\pi\varepsilon_0R_1)$.
$$\frac{R_2}{R_2 - R_1} = n\ \Rightarrow\ R_2(n-1) = nR_1\ \Rightarrow\ \frac{R_2}{R_1} = \frac{n}{n-1}$$
Solution by Sreeraj P, M.Sc Physics