Inhomogeneous Dielectric Question

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The discussion revolves around finding the electric field between two coaxial conducting cylinders filled with an inhomogeneous dielectric. The user initially considers using Gauss's Law and the relationship D = εE to analyze the electric field. They express uncertainty about how to perform the necessary integral to demonstrate that the electric field can be made invariant. Ultimately, the user concludes that the problem is simpler than initially thought and believes they have found a solution. The focus is on the appropriate choice of the dielectric constant's radial variation to achieve a position-independent electric field.
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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!
 
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This was way easier than I made it out to be. I think I found the solution.
 
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