Charge Distribution....?

Question

A thick insulating cylindrical shell with inner radius a, and outer radius b has
charge distributed throughout its volume with a uniform charge density ρ. Find the
electric field in three regions, (a) rb. (Ignore the ends of the
cylinder)

Answer 1

You need to apply Gauss's law in all the cases.
Let epsilon_0 to be written as e_0.
(a) E = 0 for r < a (since no charge is inside)
(b) |E|*2πr*(e_0) = π(r^2 - a^2)ρ
Thus: |E| = (r^2 - a^2)ρ/ (2r*(e_0))
(c) |E|*2πr*(e_0) = π(b^2 - a^2)ρ
Thus: |E| = (b^2 - a^2)ρ/ (2r*(e_0))