First slide

Electrostatic potential

Question

Twenty seven identical drops of mercury are charged simultaneously to the same potential of 10 units, Assuming the drops are made to combine to form one large drop, then its potential is

Moderate

A

45 units
B

135 units
C

270 units
D

90 units

Solution

Let r be the radius sf small drop and R, the radius of big drop. Then $\frac{4}{3} {πR}^{3} = (27) \frac{4}{3} {πr}^{3} or R = 3 r$
Charge on bigger drop = 27 q
$\begin{array}{l} V = \frac{1}{4 {πε}_{n}} \times \frac{27 q}{3 r} = 9 [\frac{1}{4 {πε}_{0}} \times \frac{q}{r}] \\ = 9 \times 10 = 90 units . \end{array}$

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