Problem 3.347

The space between two concentric metallic spheres is filled up with a uniform poorly conducting medium of resistivity \(\rho\) and permittivity \(\varepsilon .\) At the moment \(t=0\) the inside sphere obtains a certain charge. Find: (a) the relation between the vectors of displacement current density and conduction current density at an arbitrary point of the medium at the same moment of time; (b) the displacement current across an arbitrary closed surface wholly located in the medium and enclosing the internal sphere, if at the given moment of time the charge of that sphere is equal to \(q\).