A distance d separates the infinitesimally thin and circular plates of a capacitor. The plates have radius R >> d and instantaneous charges ±Q(t) as they are slowly discharged by connection to a large resistor (not shown below). Use the non-uniform surface charge distribution of a perfectly conducting circular plate and model the actual current distribution on the right (left) plate using a single surface current density K_R (K_L).

(a) Integrate the continuity equation to find K_L(ρ, t) and K_R(ρ, t).
(b) Use the Amp`ere-Maxwell law to find the magnetic field on both sides of both plates whenρ (c) Show that the fields in (b) satisfy the matching conditions with the current densities in (a).

-Q Q K KR -d- R I