Q65 / 75 · JEE Main 2020 (08 Jan Shift 2) · Physics

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 $\frac{E_{1}}{E_{2}} = \frac{R_{1}}{R_{2}} .$ Then the ratio $V_{1}$ (on $S_{1}$ ) $/$ $V_{2}$ (on $S_{2}$ ) of the electrostatic potentials on each sphere is:

Solution

Given,

\frac{E_{1}}{E_{2}} = \frac{R_{1}}{R_{2}}

Then ratio of potential would be,

\frac{V_{1}}{V_{2}} = \frac{E_{1} R_{1}}{E_{2} R_{2}} = \frac{R_{1}}{R_{2}} \times \frac{R_{1}}{R_{2}} = {(\frac{R_{1}}{R_{2}})}^{2}

Hence, the correct answer is option: 'B'.