Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop. [2021]

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Solution

Q.
Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop. [2021]

1 1980 V

2 660 V

3 1320 V

4 1520 V

Ans.
(1)

Here : $n = 27$

Potential, $V = 220$ $V$

Potential at the surface of a solid charged sphere

$V = \frac{1}{4 π ε_{0}} \frac{q}{r}$

$\frac{4}{3} π r^{3} \times n = \frac{4}{3} π r'^{3} or r' = r n^{1 / 3}$ ...(i)

Potential of bigger drop,

$V_{n} = \frac{1}{4 π ε_{0}} \cdot \frac{n q}{r'}$

$V_{n} = \frac{1}{4 π ε_{0}} \frac{n q}{r n^{1 / 3}} (using (i))$

$∴$ $V_{n} = V n^{2 / 3}$ ...(ii)

Putting the values of $n$ and $V$ in equation (ii), we get:

$V_{n} = 220 \times {(27)}^{2 / 3} or V_{n} = 1980$ $V$

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