A nonconducting spherical shell of inner radius R1 and outer radius R2 contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the sphere. Your answers should be in terms of ρ, R_1, R_2, r, ε_0, and π.
a) R_1 < r < R_2
b) r > R_2
∫E dA = Q_enc/ε_0
The Attempt at a Solution
For a), I tried using Gauss's law to find it and I arrived at:
E = [ρ(R_1)^3]/[3(ε_0)(r^2)]
For b), I also used Gauss's law to find:
[ρ(R_1)^3 + ρ(R_2)^3]/[3(ε_0)(r^2)]
I'm not quite sure what I'm doing wrong...