Q 12-02-083JEE MainJEE Main 2023 (30 Jan, Shift 1)Medium
Two isolated metallic solid spheres of radii $R$ and $2R$ are charged such that both have same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $\sigma'$, the ratio $\dfrac{\sigma'}{\sigma}$ is
Answer: (D) $\dfrac56$
Initial charges: $4\pi R^2\sigma$ and $16\pi R^2\sigma$; total $20\pi R^2\sigma$.
After connection the potentials are equal, $\dfrac{Q_1}{R}=\dfrac{Q_2}{2R}$, so $Q_2=2Q_1=\dfrac23\times20\pi R^2\sigma=\dfrac{40}{3}\pi R^2\sigma$.
$$\sigma'=\frac{Q_2}{4\pi(2R)^2}=\frac{40\pi R^2\sigma}{3\times16\pi R^2}=\frac56\sigma$$
Solution by Sreeraj P, M.Sc Physics