Q108 / 150 · MHT CET 2025 (27 Apr Shift 2) · Physics

Two conducting spheres of radii ' $r_1$ ' and ' $r_2$ ' are equally charged. The ratio of their potentials is (potential of $r_1$ to potential $r_2$ )

  • Correct answer
    A
    $\frac{r_1^2}{r_2^2}$
  • B
    $\frac{r_2^2}{r_1^2}$
  • C
    $\frac{r_1}{r_2}$
  • D
    $\frac{r_2}{r_1}$

Solution

The potential of a conducting sphere with charge $Q$ and radius $r$ is $V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r}$.

After charging disconnected identical spheres to equal potential and reconnecting them, both spheres share the same charge $Q$.

The ratio of the potentials becomes $\frac{V_1}{V_2} = \frac{\frac{Q}{r_1}}{\frac{Q}{r_2}} = \frac{r_2}{r_1}$.

The correct choice is D.

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

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