Question

1000 drops of same size are charged to a potential of 1 V each. If they coalesce to form a single drop, its potential would be :

• A. 1 V
• B. 10 V
• C. 100 V
• D. 1000 V

Answer 1

The correct option is C 100 V

Let r and q are the radius and charge of each small drop and Q and R are the radius and charge of big drop.

Thus, $\left(4/3\right)\pi R^3=1000\left(4/3\right)\pi r^3\Rightarrow R=10r$

and $Q=1000q$

here, $V_{small}=\frac{kq}{r}=1V$

and $V_{big}=\frac{kQ}{R}=\frac{k\left(1000q\right)}{10r}=100.\frac{kq}{r}=100V$