Electric Field Of A Cable

1. The problem statement, all variables and given/known data
A long coaxial cable of length L consists of a cylindrical metal sheath of radius b surrounding a conducting wire with outer radius a. The sheath and wire are given the same charge per length +Q/L. Find the electric field in terms of distance r from the central axis of the wire in the regions 0 < r < a, a < r < b, and r > b.

2. Relevant equations
Gauss’ Law ∫EdA = Qino

3. The attempt at a solution
I am not really sure how to do this problem but I think I have an idea. I have to find the electric field in terms of distance r of three different regions 0 < r < a, a < r < b, and r > b. Since the cable and metal sheath have the same charge per length, wouldn’t they both have the same charge and cancel out? Could someone explain how I can find the Gaussian surface for the first region?

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