Solving Infinite Cylinder Homework w/ Electric Field Inside Void

[funoras]

Homework Statement

In an infinitely large evenly charged dielectric cylinder(charge density is $\rho$ ) there is an infinitely large cylindrical void. Prove that the electric field inside the void is homogenous and find its value. (picture)
http://img513.imageshack.us/img513/5747/61734727.png

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Homework Equations

The Attempt at a Solution

I don't think i can use Gauss law here. Any ideas ?

 

[marcusl]

You can calculate the field at any point (radius) in a uniformly charged cylinder using Gauss's law. Now add 2 cylinders, one big and one small, of opposite charge densities to create the hole. The field within is the sum of the fields within each cylinder.