Two metal spheres of radius R and 3R have... | Electrostatics

JEE MAIN 2025

08-04-2025 S2

Question

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

Select the correct option:

$\frac{1}{9}$

$\frac{1}{3}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

For conducting sphere, $\mathrm{V}=\frac{\sigma \mathrm{r}}{\varepsilon_0}$ After contact, $\mathrm{V}_1=\mathrm{V}_2$ $$ \begin{aligned} & \sigma_1 \mathrm{r}_1=\sigma_2 \mathrm{r}_2 \\ & \frac{\sigma_1}{\sigma_2}=\frac{\mathrm{r}_2}{\mathrm{r}_1} \\ & \frac{\sigma_1}{\sigma_2}=3 \end{aligned} $$

Question Tags

JEE Main

Physics

Easy

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