An infinitely long, cylindrical, insulating shell of inner radius a and outer radius b has a uniform volume charge density. A line of uniform linear charge density is placed along the axis of the shell.

Determine the electric field in the following regions. (Choose a Gaussian cylinder of radius r and length L. Use any variable or symbol stated above along with the following as necessary: ke.)

(a) r < a
(b) a < r < b
(c) r > b