Q 12-02-217JEE MainJEE Main 2025 (8 Apr, Shift 2)Easy
Two metal spheres of radius $R$ and $3R$ have the same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge densities on the smaller and bigger spheres become $\sigma_1$ and $\sigma_2$ respectively. The ratio $\dfrac{\sigma_1}{\sigma_2}$ is:
Answer: (D) $3$
In contact the spheres reach the same potential. For a sphere $V = \dfrac{kQ}{r} = \dfrac{\sigma r}{\varepsilon_0}$, so
$$\sigma_1R = \sigma_2(3R) \Rightarrow \frac{\sigma_1}{\sigma_2} = 3$$
Solution by Sreeraj P, M.Sc Physics