Displacement current — UPSC Physics Optional CSE 2020 Paper I

For the electric field given by E=E_0e^{i\omega t}, show that the conduction current is in phase with the electric field, while the displacement current leads the electric field by \frac{\pi}{2} radians. Also, show that the displacement current in a good conductor is negligible compared to the conduction current at any frequency lower than the optical frequencies (f<10^{15}\ \mathrm{Hz}).