1. Tardigrade
  2. Question
  3. Physics
  4. Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S2) and E2(on S2) on their surfaces are such that E1/E2 = R1/R2. Then the ratio V1(on S1)/V2(on S2) of the electrostatic potentials on each sphere is :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Consider two charged metallic spheres $S_1$ and $S_2$ of radii $R_1$ and $R_2$, respectively. The electric fields $E_1$ (on $S_2$) and $E_2$(on $S_2$) on their surfaces are such that $E_1/E_2 = R_1/R_2.$ Then the ratio $V_1$(on $S_1$)$/V_2$(on $S_2$) of the electrostatic potentials on each sphere is :

JEE MainJEE Main 2020Electrostatic Potential and Capacitance

Solution:

$E_{1}=\frac{KQ_{1}}{R^{2}_{1}}\,E_{2}=\frac{KQ_{2}}{R^{2}_{2}}$
Given,
$\frac{E_{1}}{E_{2}}=\frac{R_{1}}{R_{2}}$
$\frac{\frac{KQ_{1}}{R^{2}_{1}}}{\frac{KQ_{2}}{R^{2}_{2}}}=\frac{R_{1}}{R_{2}}\,\Rightarrow \frac{Q_{1}}{Q_{2}}=\frac{R^{3}_{1}}{R^{3}_{3}}$
$\frac{V_{1}}{V_{2}}=\frac{KQ_{1}/ R_{1}}{KQ_{2} / R_{2}}=\frac{R^{2}_{1}}{R^{2}_{2}}$