Two metal spheres of radius R and 3R have same surface charge density σ.

Question

Two metal spheres of radius R and 3R 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.

(1) \(\frac{1}{9}\)

(2) 9

(3) \(\frac{1}{3}\)

(4) 3

Answer 1

Correct option is : (4) 3

For conducting sphere, \(V=\frac{\sigma r}{\varepsilon_{0}}\)

After contact, \(\mathrm{V}_{1}=\mathrm{V}_{2}\)

\( \sigma_{1} r_{1}=\sigma_{2} r_{2}\)

\(\frac{\sigma_{1}}{\sigma_{2}}=\frac{r_{2}}{\mathrm{r}_{1}}\)

\(\frac{\sigma_{1}}{\sigma_{2}}=3\)