please answer this :

Question

Eight identical spherical raindrops are each at a potential V, relative to the potential far

away. They coalesce to make one spherical raindrop whose potential is:

A) V/8

B) V/2

C) 2V

D) 4V

E) 8V

Answer 1

One way to approach this problem is to use a textbook formula for the capacitance of an isolated sphere

C = 4 pi epsilon0 R, where R is the radius of the sphere.   Also recall that q = C V

Putting these together, an expression for the charge, q, on each of the eight droplets is seen to be

 q = 4 pi epsilon0 r V where r is the radius of the droplet.  

Switching to the raindrop, the charge will be Q = 8 q and the radius will be 2 r.

This latter because an eight fold increase in volume leads to a doubling of radius.

This means that the capacitance of the raindrop is 8 pi epsilon0 r and it will have a charge of

 32 pi epsilon0 r V

The potential of the raindrop is then the ratio of this charge to the capacitance of the raindrop.

This works out to be  (32/4) V =  4 V