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(A) Let the radius of each small drop be $r = 2 \, cm = 0.02 \, m$ and the charge on each be $q = 10^{-9} \, C$.The potential of a small drop is $v =

Vedclass · Accepted Answer

$7.2 	imes 10^3 \, V$

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(A) Let the radius of each small drop be $r = 2 \, cm = 0.02 \, m$ and the charge on each be $q = 10^{-9} \, C$.The potential of a small drop is $v = \frac{kq}{r} = \frac{9 	imes 10^9 	imes 10^{-9}}{0.02} = \frac{9}{0.02} = 450 \, V$.When $n = 64$ drops combine to form a bigger drop of radius $R$,the volume remains constant: $\frac{4}{3}\pi R^3 = n 	imes \frac{4}{3}\pi r^3$,so $R = n^{1/3}r$.The total charge on the big drop is $Q = nq$.The potential of the big drop is $V = \frac{kQ}{R} = \frac{k(nq)}{n^{1/3}r} = n^{2/3} 	imes \frac{kq}{r} = n^{2/3}v$.Substituting the values: $V = (64)^{2/3} 	imes 450 = (4^3)^{2/3} 	imes 450 = 4^2 	imes 450 = 16 	imes 450 = 7200 \, V$.Thus,$V = 7.2 	imes 10^3 \, V$.

$A$ charge of $10^{-9} \, C$ is placed on each of the $64$ identical drops of radius $2 \, cm$. They are then combined to form a bigger drop. Find its potential.

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