Question 795: Electrostats & Capacitance

Question

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

Accepted Answer

To find the potential of a single large drop formed by the coalescence of '$n$' small drops, each initially charged to '$V$' volts, we use the formula for the potential of a charged sphere:
$ V = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r} $
For the combined drop, the potential $ V' $ is:
$ V' = \frac{1}{4 \pi \varepsilon_0} \frac{q'}{r'} $
Given:
Total charge when combined $ q' = n 	imes q $
New radius $ r' = n^{1/3} 	imes r $ (since volume is conserved and $ V_{	ext{initial}} = n 	imes V_{	ext{final}} $ leads to the cubed root relationship)
Substituting these into the potential formula:
$ V' = \frac{1}{4 \pi \varepsilon_0} \frac{nq}{n^{1/3}r} $
This simplifies to:
$ V' = n^{2/3} 	imes \frac{1}{4 \pi \varepsilon_0} \frac{q}{r} $
Since $ \frac{1}{4 \pi \varepsilon_0} \frac{q}{r} = V $:
$ V' = V 	imes n^{2/3} $
Thus, the potential of the large drop is $ V 	imes n^{2/3} $.

Answer

$\mathrm{Vn}^{\frac{1}{3}}$

Answer

$\mathrm{Vn}^{\frac{2}{3}}$

Answer

$\mathrm{V n}$

Answer

$\mathrm{Vn}^{-1}$

Electrostats & Capacitance

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

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