Two metal spheres of radius R and 3R have same surface charge density . If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes and , respectively. The ratio is. [2025]

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Solution

Q.
Two metal spheres of radius R and 3R have same surface charge density $σ$ . If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $σ_{1}$ and $σ_{2}$ , respectively. The ratio $\frac{σ_{1}}{σ_{2}}$ is. [2025]

1 $\frac{1}{9}$

2 9

3 $\frac{1}{3}$

4 3

Ans.
(4)

For conducting sphere, $V = \frac{σ r}{ε_{0}}$

After contact, $V_{1} = V_{2}$

$σ_{1} r_{1} = σ_{2} r_{2} \Rightarrow \frac{σ_{1}}{σ_{2}} = \frac{r_{2}}{r_{1}} = 3$

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