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## Homework Statement

Consider a long cylindrical coaxial capacitor with an inner conductor of radius a, and outer conductor of radius b, and a dielectric with a relative electric permittivity or dielectric ε(r), varying with the cylindrical radius. The capacitor is charged to the voltage V. Choose the radial dependence of ε(r) such that the energy density in the capacitor is constant.

Calculate the electric field inside the capacitor.

## Homework Equations

Energy density equation

## The Attempt at a Solution

from the energy density eq. which is defined by [itex]u = \frac{1}{2} \textbf{E} \circ \textbf{D}[/itex] we get that

1/ε(r) [itex]\propto \left| \textbf{E} \right|^{2}[/itex]

[itex]\Phi(b) - \Phi(a) = V[/itex]

Honestly I'm not quite sure which ansatz one can use. I was trying to solve it with the Gauss's law but didn't find a satisfying solution.