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Introduction
Abstract
Consider Maxwell’s equations for a medium at rest with scalar constants for the permeability µ permittivity ϵ and conductivity σ. Furthermore, we have the electric and magnetic field strengths E and H, electric charge and current density ρ e and g e as well as electric and magnetic flux densities D and B. Using the International System of units we get:
... Later on H. Harmuth noticed that even though magnetic charges have not been discovered yet there are many physical problems where one may consider dipole magnetic currents rather than monopole ones to make Maxwell's equations symmetric. In particular, this model has been applied to describe interstellar propagation of electromagnetic signals [10] and propagation of signals in non-conducting media with electric and magnetic dipole currents [11]. This short paper is devoted to another physical justification of Harmuth's modification of Maxwell's equations applicable to adequate description of electromagnetic properties of conducting media. ...
... Normally, the related losses should be much less compared to the losses associated with the electric Ohm's law and therefore in many cases they may be ignored. However, this is not the case when studying the propagation of step-like (or rectangular pulse) signals through lossy media, in particular over extremely long distances since small effects will be accumulated during the long distance of propagation, and sooner or later they will make an appreciable contribution to the solution [10]. For the above reasons, Maxwell's equations with an added term for magnetic current density should be considered as one of the possible modifications of Maxwell's equations, but because of the exceptional importance of the particular case of lossy media the term Modified Maxwell's equations may be applied and reasonably used. ...
... Since in our case we have very fast variation of the EM signal fields those methods are not applicable anymore. In order to solve the problem of signal propagation through conducting media one has to modify Maxwell equations using both electric and magnetic dipole current densities [10]. This implies description of the medium in the frame of a microscopic approach using the representation of an atom as a combination of electric and magnetic dipoles. ...
Dissipation of electromagnetic energy in conducting media takes place not only because of its absorption due to acceleration of charged particles by the electric field and their inelastic collisions with atoms, but also due to interaction of the wave's magnetic field with magnetic and electric dipole currents induced by those collisions in the atoms. The simplest way to describe this phenomenon is to use Ohm's law for magnetic dipole current as H. Harmuth suggested in his Modified Maxwell's equations.
... Later on Henning F. Harmuth noticed that even though magnetic charges have not been discovered yet, there are many physical problems where one may consider dipole magnetic currents rather than monopole ones to make Maxwell equations symmetric. In particular, this model has been applied to describe interstellar propagation of electromagnetic signals [10] and propagation of signals in non-conducting media with electric and magnetic dipole currents [11]. It is typical for human beings to create a cult figure or idolize somebody in an area of their mental activity , and to follow his or her doctrine after that. ...
... I am grateful to Henning F. Harmuth for cooperation, consultations and hospitality when I was visiting him in Washington, DC and Destin, Florida. My special thanks to him for inviting me to work on the book [10], which was very instructive and informative for me. I also would like to thank Dr. Gerry Kaiser who gave me as a gift an excellent book by Bruce Hunt " The Maxwellians " (when attending the NRT-2003 Conference in Kharkov): not having this book I would not be able to write the " Historical Parallels " section. ...
Considerable nontrivial contributions that have been done by Henning F. Harmuth to electromagnetic signal theory and UWB radar and Communication systems are briefly described in the paper. An interesting historical analogy in scientific life of Henning Harmuth and Oliver Heaviside is traced.
... The four, are relation between electric field E with conductive current J and electric displacement D. And the relation between magnetic field H with magnetic induction B and magnetic polarization M. In this section we apply the theorems and properties of preceding section to solve Maxwell's equations describing planar transverse electromagnetic wave (TEMP) propagating in lossy medium. The Laplace transform method and mathematical models were used to solve Maxwell's partial differential equations in [12, 13, 14, 17, 18, 20, 25]. Other than Laplace transform, F. B. M. Belgacem applied the new Sumudu transform [21, 22] to the Maxwell's equation in [8]. ...
... Now expanding cos γ √ sz γ √ s of equation (4.10) and performing inverse Natural transform operation, the transient magnetic field H y (z,t) solution [12, 13] of Maxwell's equations (3.3) and (3.4) with the initial conditions (4.2), (4.3) and boundary condition (4.4) is obtained. This will be our future work. ...
The Natural transform is applied to Maxwell’s Equations describing transient electromagnetic planar waves propagating in lossy medium (TEMP), in order to obtain its electric and magnetic fields solutions. To achieve this task, many of the basic Natural transform properties are initially
investigated, and then pragmatically used.
It is shown that if the Lorentz condition is discarded, the Maxwell–Heaviside field equations become the Lehnert equations, indicating the presence of charge density and current density in the vacuum. The Lehnert equations are a subset of the O(3) Yang–Mills field equations. Charge and current density in the vacuum are defined straightforwardly in terms of the vector potential and scalar potential, and are conceptually similar to Maxwell's displacement current, which also occurs in the classical vacuum. A demonstration is made of the existence of a time dependent classical vacuum polarization which appears if the Lorentz condition is discarded. Vacuum charge and current appear phenomenologically in the Lehnert equations but fundamentally in the O(3) Yang–Mills theory of classical electrodynamics. The latter also allows for the possibility of the existence of vacuum topological magnetic charge density and topological magnetic current density. Both O(3) and Lehnert equations are superior to the Maxwell–Heaviside equations in being able to describe phenomena not amenable to the latter. In theory, devices can be made to extract the energy associated with vacuum charge and current.
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