Problem 3.167

An inhomogeneous poorly conducting medium fills up the space between plates 1 and 2 of a parallel-plate capacitor. Its permittivity and resistivity vary from values $\varepsilon_{1}, \rho_{1}$ at plate 1 to values $\varepsilon_{2}, \rho_{2}$ at plate $2 .$ A dc voltage is applied to the capacitor through which a steady current $I$ flows from plate 1 to plate 2 . Find the total extraneous charge in the given medium.