Chapter 29, Problem 29.64P

CP CALC A capacitor has two parallel plates with area A separated by a distance d. The space between plates is filled with a material having dielectric constant K. The material is not a perfect insulator but has resistivity ρ. The capacitor is initially charged with charge of magnitude Q₀ on each plate that gradually discharges by conduction through the dielectric. (a) Calculate the conduction current density j_C(t) in the dielectric. (b) Show that at any instant the displacement current density in the dielectric is equal in magnitude to the conduction current density but opposite in direction, so the total current density is zero at every instant.