Attenuation and damping of electromagnetic fields: Influence of inertia and displacement current

TL;DR

This paper investigates how inertia and displacement current influence electromagnetic field attenuation and damping in conductors, revealing that high-frequency penetration depth saturates and inertia and displacement effects oppose each other.

Contribution

It introduces a new extended Ohm's law incorporating relaxation time, providing a unified framework to analyze electromagnetic damping considering inertia and displacement current effects.

Findings

Attenuation at high frequencies depends only on relaxation time.

Inertia and displacement current effects on damping are opposite.

Penetration depth saturates at high frequencies.

Abstract

New results for attenuation and damping of electromagnetic fields in rigid conducting media are derived under the conjugate influence of inertia due to charge carriers and displacement current. Inertial effects are described by a relaxation time for the current density in the realm of an extended Ohm's law. The classical notions of poor and good conductors are rediscussed on the basis of an effective electric conductivity, depending on both wave frequency and relaxation time. It is found that the attenuation for good conductors at high frequencies depends solely on the relaxation time. This means that the penetration depth saturates to a minimum value at sufficiently high frequencies. It is also shown that the actions of inertia and displacement current on damping of magnetic fields are opposite to each other. That could explain why the classical decay time of magnetic fields scales approximately as the diffusion time. At very small length scales, the decay time could be given either by the relaxation time or by a fraction of the diffusion time, depending whether inertia or displacement current, respectively, would prevail on magnetic diffusion.