Frequency Dependence of the Displacement Current Density

Abstract

In Maxwell's equations, the electric field can be expressed as the sum of the Coulombic field associated with the electric charge and the induced field associated with the time variation of the magnetic field from Faraday's law. The same holds true for the displacement current densities, which are the time-derivatives of the respective electric fields. In the case of an AC current of constant amplitude, the amplitude of the displacement current density associated with the Coulombic field is independent of the frequency. In contrast, the displacement current density associated with the induced field is very small at low frequencies, increasing initially as the square of the frequency, and ultimately becomes of the same order of magnitude as that of the Coulombic field.