Inhomogeneous Dielectric Question

[jackd3]

Homework Statement

The space between two long coaxial conducting cylinders is filled with an inhomogeneous dielectric. Show that the E field can be made independent of position between the cylinders by an appropriate choice for the radial variation of the dielectric constant.

Homework Equations

I thought about starting with the "Gauss's Law" for dielectrics

where $$D=\epsilon E$$ is substituted for the electric field.

The Attempt at a Solution

My first approach was to try and calculate the electric field between the two cylinders by choosing an arbitrary Gaussian surface inside the dielectric material. But I'm not sure how to carry out that integral for this problem if I have to show the E field is invariant and I can't assume it.

Any tips or hints would be great, thanks!

 

[jackd3]

This was way easier than I made it out to be. I think I found the solution.