Question 768: Electrostats & Capacitance

Question

' $n$ ' identical small spherical drops of water, each of radius ' $r$ ' and charged to the same potential ' v ' are combined to form a big drop. The potential of a big drop is

Accepted Answer

From conservation of volume, $\mathrm{nV}_{\mathrm{s}}=\mathrm{V}_{\mathrm{b}}$
$$ \begin{array}{ll} 	herefore & n\left(\frac{4}{3} \pi r^3ight)=\left(\frac{4}{3} \pi R^3ight) \ 	herefore & R=\left(n r^3ight)^{1 / 3} \ 	herefore & R=r(n)^{1 / 3} \end{array} $$
From conservation of charge, As each drop has potential v so:
$$ \begin{array}{ll}  & \mathrm{V}=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q}}{\mathrm{r}} \ & \mathrm{q}=\mathrm{v}\left(4 \pi \varepsilon_0ight) \mathrm{r} \ & 	ext { Total charge }=\mathrm{nq} \ 	herefore \quad & \mathrm{~V}_{	ext {big }}=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{nq}}{\mathrm{R}} \ 	herefore \quad & \mathrm{~V}_{	ext {big }}=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{nq}}{(\mathrm{n})^{1 / 3} \mathrm{r}} \ 	herefore \quad & \mathrm{~V}_{	ext {big }}=\mathrm{v}(\mathrm{n})^{2 / 3} \end{array} $$

Answer

nv

Answer

$n \sqrt{v}$

Answer

$n^{1 / 3} v$

Answer

$\mathrm{n}^{2 / 3} \mathrm{v}$

Electrostats & Capacitance

' n ' identical small spherical drops of water, each of radius ' r ' and charged to the same potential ' v ' are combined to form a big drop. The potential of a big drop is

Choose the correct answer: