Uniform E field for spherical shell.

[GwtBc]

Homework Statement

In the figure a nonconducting spherical shell of inner radius a = 2.07 cm and outer radius b = 2.51 cm has (within its thickness) a positive volume charge density ρ = A/r, where A is a constant and r is the distance from the center of the shell. In addition, a small ball of charge q = 45.8 fC is located at that center. What value should A have if the electric field in the shell (a ≤ r ≤ b) is to be uniform?

Homework Equations

$\phi = \frac{q}{\epsilon_{0}} = \oint E \cdot dA$

The Attempt at a Solution

I found the electric field due to the central charge and ρV at a radius between r (a ≤ r ≤ b), added these together (superposition) and then derived with respect to r, hoping to set the derivative to zero to find my answer, but I got $\frac{Aa^3}{r^4}- \frac{q}{2\pi r^3}$ as my expression for the derivative, (disregarding epsilon naught, the constant) and obviously I can't set this to zero and disregard r. Not sure where to go from here.

 

[GwtBc]

Ok, I can't use Gauss' law without integration cause charge density isn't constant, have to integrate to find charge first. So derp, I got it now.