Q 12-02-145JEE MainJEE Main 2020 (8 Jan, Shift 2)Easy
Consider two charged metallic spheres $S_1$ and $S_2$ of radii $R_1$ and $R_2$, respectively. The electric fields $E_1$ (on $S_1$) and $E_2$ (on $S_2$) on their surfaces are such that $\dfrac{E_1}{E_2} = \dfrac{R_1}{R_2}$. Then the ratio $V_1$ (on $S_1$)$/V_2$ (on $S_2$) of the electrostatic potentials on each sphere is:
Answer: (B) $\left(\dfrac{R_1}{R_2}\right)^2$
For a charged sphere, $E = \dfrac{kQ}{R^2}$ and $V = \dfrac{kQ}{R}$ at the surface, so $V = ER$.
$$\frac{V_1}{V_2} = \frac{E_1}{E_2}\cdot\frac{R_1}{R_2} = \left(\frac{R_1}{R_2}\right)^2$$
Solution by Sreeraj P, M.Sc Physics