Question

Eight identical spherical raindrops are each at an electric potential of 8 V, relative to the potential far away. Without losing charge or volume, they coalesce to make one spherical raindrop. What is the potential of the larger raindrop?

Answer 1

Ans: 32 V

Explanation:

Let the charge of each small raindrop is q and radius r.

so, potential due to each small raindrop , V = kq/r

Now when 8 raindrops make a large raindrops , without loosing charge and volume ,

Let the radius of large raindrop is R and charge is Q.

Now , volume of large raindrop ,

Volume of each small raindrop ,

Also , the charge of large raindrop , Q = 8q

So potential due to large raindrop ,

V' = kQ/R = k(8q)/(2r) = 4×kq/r = 4V

Now potential of each small raindrop is 8 V.

So potential of larger raindrop is (4×8) V = 32 V.