Finding electric potential between two concentric spheres.

[epicrux]

Homework Statement

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.

Homework Equations

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
That makes:
[(ρr²)/6ε)] from 2A to A which does not equal the answer.
I think I'm stumped here. Any help would be greatly appreciated!

 

[TSny]

Welcome to PF!

Your expression for the electric field does not look correct. E for a uniformly charged shell is different than E for a uniformly charged solid sphere.

 

[epicrux]

I was not aware of the difference. I'll look it up.

 

[TSny]

I'll look it up.

Or, apply Gauss' law to find E inside the shell.