If 27 charged water droplets, each of radius | vedclass

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(D) Let $n = 27$ be the number of small droplets.Let $r = 10^{-3} \,m$ be the radius of each small droplet.Let $q = 10^{-12} \,C$ be the charge on eac

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$81$

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(D) Let $n = 27$ be the number of small droplets.Let $r = 10^{-3} \,m$ be the radius of each small droplet.Let $q = 10^{-12} \,C$ be the charge on each small droplet.The volume of the big drop is equal to the sum of the volumes of the $27$ small droplets: $\frac{4}{3} \pi R^3 = 27 	imes \frac{4}{3} \pi r^3$.Thus, $R^3 = 27 r^3$, which implies $R = 3r = 3 	imes 10^{-3} \,m$.The total charge on the big drop is $Q = n 	imes q = 27 	imes 10^{-12} \,C$.The potential of the big drop is given by $V = \frac{kQ}{R}$, where $k = 9 	imes 10^9 \,N \cdot m^2/C^2$.Substituting the values: $V = \frac{9 	imes 10^9 	imes 27 	imes 10^{-12}}{3 	imes 10^{-3}}$.$V = \frac{9 	imes 27 	imes 10^{-3}}{3 	imes 10^{-3}} = 3 	imes 27 = 81 \,V$.

If $27$ charged water droplets, each of radius $10^{-3} \,m$ and charge $10^{-12} \,C$ coalesce to form a single big spherical drop, then the potential of the big drop is (in $\,V$)

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