Gauss' law electrostatics problem involving charge densities

[chipotleaway]

Homework Statement

A nonconducting spherical shell has a thickness $b-a$, where b is the outer radius and a the inner radius has a volume charge density $\rho=\frac{A}{r}, r\in[a,b]$. If there is a charge +q located at the center, what must $A$ be in order for the electric field to be uniform in the shell?

The Attempt at a Solution

The electric field for any $r\in[a,b]$ must be equal to the field at $a$, whiuch is $E_1=k\frac{q}{a^2}$. The field at any point in the shell is $E_2=k(\frac{q}{r^2}+\frac{4A\pi}{3r}(r^3-a^3)\frac{1}{r^2})$. I equated the two expressions and tried to solve for A but the expression I'm getting is not in agreeance with the the solution. Is this approach correct?

Here's a diagram of the problem (right)
http://s3.amazonaws.com/answer-board-image/81404896-a1bf-4193-80c7-9d515c2eb554.jpeg

 

[vanhees71]

The approach is correct, but you should reconsider the charge inside your Gaußian surface. It's not uniform, and thus you have to really evaluate the volme integral!

 

[chipotleaway]

Got it! Thanks :p

 

[rude man]

Got it! Thanks :p

OK, and your answer is ... ?

 

[Joncat]

A non-conducting spherical shell carries a non-uniform charge density ρ=ρ0r1/r. Determine the electric field in the regions:
A) 0<r<r1
B)r1<r<r0
C)r>r0

r1 is radius to inside of shell. r0 is radius to outside of shell.