n identical droplets are charged to V volt ea | vedclass

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(A) Let $r$ be the radius of each small droplet and $R$ be the radius of the large drop formed by coalescing $n$ droplets.Since the volume remains con

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$n^{2/3} V$

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(A) Let $r$ be the radius of each small droplet and $R$ be the radius of the large drop formed by coalescing $n$ droplets.Since the volume remains conserved:$n 	imes \frac{4}{3} \pi r^3 = \frac{4}{3} \pi R^3$$R^3 = n r^3 \implies R = r n^{1/3}$Each small droplet has a charge $q = C_0 V = (4 \pi \varepsilon_0 r) V$.The total charge on the large drop is $Q = n q = n (4 \pi \varepsilon_0 r) V$.The potential of the large drop is $V' = \frac{Q}{4 \pi \varepsilon_0 R}$.Substituting the values of $Q$ and $R$:$V' = \frac{n (4 \pi \varepsilon_0 r) V}{4 \pi \varepsilon_0 (r n^{1/3})}$$V' = n 	imes \frac{1}{n^{1/3}} V = n^{2/3} V$.

$n$ identical droplets are charged to $V$ volt each. If they coalesce to form a single drop, then its potential will be

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