Electric field between two concentric cylinders

Question

This is a question that has been bothering for a while. I don't know if my answer is correct or not, but anyone look over it?

Both cylinders have the same length L. The first cylinder with radius R1 has a charge Q1 uniformly distributed inside the cylinder. The second cylinder is a conductor with radius R2 and charge Q2 (negative) uniformly distributed into the area between the first and second cylinder.

Find the electric field when:

a) r < R1 ; b) R1< r< R2;  c) r> R2

So, I did it like this.

a) r< R1

$∮ E.dA = E2πrL = Qi/ε₀ $

$ Qi= ρV= [Q1/(πLR1^2)]*πLr^2 $

$E= rQ1/(2πLε₀R1^2) $

b) R1< r < R2

$∮ E.dA = E2πrL = Qi/ε₀ $

$E= Q1/ (2πrLε₀)$

c) r> R2

$ E1= Q1/ (2πrLε₀) and E2= -Q2/ (2πrLε₀)$ (because Q2 is negative I put the minus in front of it)

$ Eout = E1 + E2 = Q1/ (2πrLε₀) -Q2/ (2πrLε₀) $

Comments

@Dilaton Can you verify  my answers? I really need help.

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In your present formulation there must be the edge effects. Probably you problem is about very long cylinders and the fields are calculated somewhere far from the ends. to neglect the edge effects. The the fiels only is radial.