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.