A single sphere of water is created by joining 1000 of water spheres of radius r and charge (+Q).If the potential of the small and big spheres are w and v respectively, find v/w.

Question

My thoughts :
The masses of the spheres are proportional to the third power of there radius.
So

1000*(r^3)=R^3
R=10r(R-radius of the big sphere)

V=1/(4π*epsilon) (Q/r)

So v is proportional to (Q/r)

So can we simply take the charge of the big sphere as 1000Q,as it is created by 1000 small spheres being joined?

Answer 1

Yes. Consider Gauss' Law: the charge of each of those small spheres can be considered to be a charge Q at the center, even if was distributed throughout the volume.

Answer 2

So can we consider the bigger sphere has a 1000Q charge at its center?

Answer 3

yes. (of course, you have to do that only if the volumetric charge is distributed evenly), law Gauss Law.