Each of the N small drops has a radius r and | vedclass

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Question

(A) Let the radius of the small drop be $r$ and the charge on each small drop be $q$. The potential of a small drop is given by $V = \frac{1}{4\pi \ep

Vedclass · Accepted Answer

$N^{2/3}V$

Vedclass · Answer

(A) Let the radius of the small drop be $r$ and the charge on each small drop be $q$. The potential of a small drop is given by $V = \frac{1}{4\pi \epsilon_0} \frac{q}{r}$.Thus,$q = 4\pi \epsilon_0 r V$.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 $Q = Nq = N(4\pi \epsilon_0 r V)$.The potential of the large drop is $V_{large} = \frac{1}{4\pi \epsilon_0} \frac{Q}{R} = \frac{1}{4\pi \epsilon_0} \frac{Nq}{N^{1/3}r} = N^{2/3} \left( \frac{1}{4\pi \epsilon_0} \frac{q}{r} ight) = N^{2/3}V$.

Each of the $N$ small drops has a radius $r$ and is charged to a potential $V$. If these drops coalesce to form a single large drop,what is the potential of the large drop?

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