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(B) Let the charge on each small drop be $q$. The potential of a small drop is given by $V = \frac{1}{4\pi\epsilon_0} \frac{q}{r}$.When $N$ small drop

Vedclass · Accepted Answer

$N^{2/3}V$

Vedclass · Answer

(B) Let the charge on each small drop be $q$. The potential of a small drop is given by $V = \frac{1}{4\pi\epsilon_0} \frac{q}{r}$.When $N$ small drops coalesce to form a large drop of radius $R$,the volume remains conserved: $\frac{4}{3}\pi R^3 = N 	imes \frac{4}{3}\pi r^3$,which gives $R = N^{1/3}r$.The total charge on the large drop is $Q = Nq$.The potential of the large drop is $V_{big} = \frac{1}{4\pi\epsilon_0} \frac{Q}{R} = \frac{1}{4\pi\epsilon_0} \frac{Nq}{N^{1/3}r}$.Substituting $V = \frac{1}{4\pi\epsilon_0} \frac{q}{r}$,we get $V_{big} = N^{1 - 1/3} V = N^{2/3}V$.

$N$ small drops,each of radius $r$,are charged to a potential $V$. If they coalesce to form a single large drop,what is the potential of the large drop?

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