N small drops of same size are charged to V volts each. If they coalesce to form a signal large drop

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1. Electric Charges and Fields

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$n$ small drops of same size are charged to $V$ $volts$ each. If they coalesce to form a signal large drop, then its potential will be

A

$V/n$

B

$Vn$

C

$Vn^{1/3}$

D

$Vn^{2/3}$

Solution

Potential of each drop

$=V=\frac{k q}{R} \Rightarrow q=\frac{V R}{k}$

If $n$ drops coalse, $Q=n q=n \frac{V R}{k}$

Radius $\mathrm{R}^{\prime}=\mathrm{n}^{1 / 3} \mathrm{R}$

The potential of new drop

$=\frac{n k V R}{k n^{1 / 3} R}=V n^{2 / 3}$

Standard 12

Physics

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