Magnitude of electric field/Need answer checked

[WestTXcollegekid]

Homework Statement

A long coaxial cable consists of an inner cylindrical conductor with radius a and an outer coaxial cylinder with inner radius band outer radius c. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform positive charge per unit length λ.
Calculate the magnitude of the electric field at any point between the cylinders a distance r from the axis.
Express your answer in terms of the variables a, b, c, r, λ and constants π and ϵ0.

Homework Equations

E=(1/4πϵ0)(q/r^2)
q= λ2πr

The Attempt at a Solution

Using the equation above I got (E= λ/2ϵ0r). I just want to make sure that I'm not missing anything. I only have one attempt left at answering the question.

 

[BvU]

How did your relevant equations help you in the solution phase ? I see a lot of the problem variables not appearing in there. Please show your steps in part 3.