Find an electric field around a hollow insulating sphere.

[hockey]

Homework Statement

An insulating hollow sphere has inner radius a and outer radius b. Within the insulating material the volume charge density is given by ρ(r)=\alpha/r,where \alpha is a positive constant. What is the magnitude of the electric field at a distance r from the center of the shell, where a<r<b?
Express your answer in terms of the variables α, a, r, and electric constant ϵ0.

Homework Equations

E*4\pir^2 = Q * volume

The Attempt at a Solution

Substituting and integrating with the above formula, I came out with (α/3\epsilon0)(r-((a^3)/(r^2)). I cannot tell if the error is with my math, or with the formula I began this process with.

 

[BvU]

Hello sport, and welcome to PF.
Apparently you conclude that your answer is in error. How do you know ?
You show your answer, but I can't reconstruct what you do to get there...
Please post some intermediary steps...