A thin wire carries constant current I into one plate of a charging capacitor, and another thin wire carries constant current l out of the other plate. The capacitor plates are disks of radius a and separation w « a (so edge effects can safely be neglected). The region between the plates has $\epsilon ~ \epsilon_0$, $\mu ~ \mu_0$, but does have a non-negligible, constant conductivity $\sigma$.
Note: The capacitor is not an ideal capacitor, since the material between the plates is not a perfect insulator.
(a) Supposing that the charges are uniformly distributed on the plates, find a differential equation for the charge Q(t) on the plates, and solve it for Q(t), taking Q(O) = O.
(b) Find the electric and magnetic fields in the gap. Approximate the electric field as just that due to the charged plates. When computing the magnetic field,
include all sourcing contributions.