Problem 3.168

The space between the plates of a parallel-plate capacitor is filled up with inhomogeneous poorly conducting medium whose resistivity varies linearly in the direction perpendicular to the plates. The ratio of the maximum value of resistivity to the minimum one is equal to \(\eta\) The gap width equals \(d\). Find the volume density of the charge in the gap if a voltage \(V\) is applied to the capacitor. \(\varepsilon\) is assumed to be 1 everywhere.