Q52 / 75 · JEE Main 2025 (8 Apr Shift 2) · Physics
Two metal spheres of radius $R$ and $3 R$ have same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$, respectively. The ratio $\frac{\sigma_1}{\sigma_2}$ is.
- A$\frac{1}{9}$
- B9
- C$\frac{1}{3}$
- Correct answerD3
Solution
For conducting sphere, $\mathrm{V}=\frac{\sigma \mathrm{r}}{\varepsilon_0}$
After contact, $\mathrm{V}_1=\mathrm{V}_2$
$\begin{aligned}<br/>& \sigma_1 r_1=\sigma_2 r_2 \\ & \frac{\sigma_1}{\sigma_2}=\frac{r_2}{\mathrm{r}_1} \\ & \frac{\sigma_1}{\sigma_2}=3<br/>\end{aligned}$
After contact, $\mathrm{V}_1=\mathrm{V}_2$
$\begin{aligned}<br/>& \sigma_1 r_1=\sigma_2 r_2 \\ & \frac{\sigma_1}{\sigma_2}=\frac{r_2}{\mathrm{r}_1} \\ & \frac{\sigma_1}{\sigma_2}=3<br/>\end{aligned}$
Hence, the correct answer is option: 'D'.