Question

N identical drops of mercury are charged simultaneously to 10 v. When combined to form one large drop, the potential is found to be 40 v, the value of n is

Answer 1

Given that,

N identical drops of mercury are charged simultaneously to 10 V. When combined to form one large drop, the potential is found to be 40 V.

To find,

The value of N.

Solution,

Let r be the radius of smaller drops and R be the radius of one large drop.

The potential on big drop of radius R is :

$V=\dfrac{kNq}{R}$

And the potential on a drop of radius r. So,

$V'=\dfrac{kq}{r}$

N drops combines and form single drop. So,

$N\times \text{volume of smaller drop}= \text{volume of larger drop}\\\\N\times \dfrac{4}{3}\pi r^3=\dfrac{4}{3}\pi R^3$

$\\ N=(\dfrac{R}{r})^3\\\\N^{1/3}=\dfrac{R}{r}......(1)$

We have, V' = 10 V and V = 40 V

So,

$\dfrac{V}{V'}=\dfrac{kNq/R}{kq/r}\\\\\dfrac{40}{10}=\dfrac{Nr}{R}$

From equation (1) :

$4=\dfrac{N}{N^{1/3}}\\\\4=N^{2/3}\\\\N=8$

So, the value of N is 8.