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 $V=300 \mathrm{~V}$.