Question

'n' small spherical drops of same size which are charged to 'V' volt each coalesce to form a single big drop. The potential of the big drop is ______.

Options

• \[\frac {V}{n}\]

• n . V

• n^1/3 . V

• n^2/3 . V

Answer 1

'n' small spherical drops of same size which are charged to 'V' volt each coalesce to form a single big drop. The potential of the big drop is n^2/3 . V.

Explanation:

V = \[\frac{1}{4\pi\varepsilon_{0}}\frac{\mathrm{q}}{\mathrm{r}}\]

V' = \[\frac{1}{4\pi\varepsilon_{0}}\frac{\mathrm{q^{\prime}}}{\mathrm{r^{\prime}}}\] = \[\frac{1}{4\pi\varepsilon_{0}}\frac{\mathrm{nq}}{\mathrm{n}^{1/3}\mathrm{r}}\]   (\[\because\]q' = nq, r' = n^1/3r)

V' = Vn^2/3