Problem 3.163

The gap between the plates of a parallel-plate capacitor is filled up with an inhomogeneous poorly conducting medium whose conductivity varies linearly in the direction perpendicular to the plates from \(\sigma_{1}=1.0 \mathrm{pS} / \mathrm{m}\) to \(\sigma_{2}=2.0 \mathrm{pS} / \mathrm{m} .\) Each plate has an area \(S=230 \mathrm{~cm}^{2},\) and the separation between the plates is \(d\) \(=2.0 \mathrm{~mm} .\) Find the current flowing through the capacitor due to a voltage \(V=300 \mathrm{~V}\).