a solid sphere of radius r is uniformly charged. At what distance from its surface is electrostatic potential half of the potential at the centre.

A) r

B) r/2

c) r/3

d) 2r

nothing is given in the question about whether sphere is conducting or insulating.rates for correct answer+explanation.

Potential inside the sphere = kQr/R^2, Potential outside the sphere = kQ/d... as as the centre of sphere r = R, potential = kQ/R, so half of that potential will be at 2R from the sphere... You have to assume the sphere is insulating material inside... otherwise potential inside is 0 and that is not an option...

I think that the sphere is metallic/conducting with some insulating material inside bcoz if it is a solid conducting sphere,potential at center will be 0 and question will have no meaning.

Potential at center of metallic sphere which has some insulating material inside is same as that on surface as electric field inside is 0

So going by that answer is 2r from center and r from surface of sphere where V(s)=kq/r

where k is as known. 

In case the sphere is an insulating solid uniformly charged one, the potential at its centre is    3kQ/2r

                                                                 (d - distance from centre)                         and outside it is       kQ/d

kQ/ d = (1/2) 3kQ/ 2r

d = 4r/ 3

distance from surface = r/ 3

and i did not know, how is potential at centre of a solid conducting sphere = 0 ? please answer..

Hi

Potential at any point inside a spherical conductor/insulator is not zero. But it is same as that on the surface. since it is mentioned that sphere has uniform charge distribution of charge,(like nucleus of an atom).  The answer given by Ludic is correct. If it is hollow sphere/solid which has charge on its surface, then the answer given by  Abhisekh will be correct. Cheers