1000 small drops,each of radius r and charge | vedclass

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Question

(A) The potential of a small drop is given by $V_{	ext{small}} = k \frac{q}{r}$.Let $R$ be the radius of the large drop. Since the volume is conserve

Vedclass · Accepted Answer

$10^2$

Vedclass · Answer

(A) The potential of a small drop is given by $V_{	ext{small}} = k \frac{q}{r}$.Let $R$ be the radius of the large drop. Since the volume is conserved,we have $\frac{4}{3} \pi R^3 = 1000 	imes \frac{4}{3} \pi r^3$.This simplifies to $R^3 = 1000 r^3$,which gives $R = 10r$.The total charge of the large drop is $Q = 1000q$.The potential of the large drop is $V_{	ext{large}} = k \frac{Q}{R} = k \frac{1000q}{10r} = 100 \left( k \frac{q}{r} ight)$.Therefore,$V_{	ext{large}} = 100 V_{	ext{small}} = 10^2 V_{	ext{small}}$.The potential of the large drop is $10^2$ times the potential of the small drop.

$1000$ small drops,each of radius $r$ and charge $q$,coalesce to form a single large drop. How many times greater is the potential of the large drop compared to the potential of a small drop?

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