Q 12-02-013NEETNEET 2021Top questionEasy
Two charged spherical conductors of radius $R_1$ and $R_2$ are connected by a wire. Then the ratio of surface charge densities of the spheres ($\sigma_1/\sigma_2$) is :
Answer: (C) $\dfrac{R_2}{R_1}$
Connected conductors reach the same potential:
$$\frac{q_1}{4\pi\epsilon_0R_1} = \frac{q_2}{4\pi\epsilon_0R_2} \;\Rightarrow\; \frac{q_1}{q_2} = \frac{R_1}{R_2}$$
$$\frac{\sigma_1}{\sigma_2} = \frac{q_1/4\pi R_1^2}{q_2/4\pi R_2^2} = \frac{R_1}{R_2}\cdot\frac{R_2^2}{R_1^2} = \frac{R_2}{R_1}$$
Solution by Sreeraj P, M.Sc Physics