A spherical shell with inner radius A and outer radius 3A which has a uniform charge density, i.e charge per unit volume, p0. Find difference in electric potential between the center of the shell and a point a distance 2A from the center.
The answer given is. -(p0A2)/3ε0
The Attempt at a Solution
I am completely lost as to what I'm supposed to do here. I would think you'd find the potential at 2A and subtract it from that at the center. But how exactly do you do that?
I integrated the elctric field due to a charged sphere along 2A to A. So that makes:
∫E dr= ∫(ρr)/3ε0)dr=V
[(ρr2)/6ε)] from 2A to A which does not equal the answer.
I think I'm stumped here. Any help would be greatly appreciated!