On the way to understanding the electromagnetic phenomena

The development of Maxwell's equations which govern the behavior of electromagnetic fields was one of the significant feet of achievements in the nineteenth century physics. It gives the complete unification of the electricity and the magnetism, and also it implies light as electromagnetic waves. Remarkably enough, it leads to a series of new ideas including the concept of the possibility of magnetic charges in nature. In this review article, we have discussed different stages of the basic formulations towards the development of the classical Maxwell equations, electromagnetic waves and idea of Dirac monopole.

2016

The combined mathematical representation of Gauss’ laws of electricity and magnetism, Ampere’s circuital law, and Faraday’s law is known as ”Maxwell’s Equations”. It is one of the important milestones in the human history and was championed by the great Scottish Scientist James Clerk Maxwell in 19th Century (1860 -1871). In this note, we will quickly discuss about the important terms used in Maxwell’s Equations, their role in understanding electromagnetism and its versatile applications.

Eprint Arxiv Physics 0610020, 2006

In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work-a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schrooinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems-{)ne describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out a priori by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity. It is a pleasure to dedicate this paper to Gerard Emch, whose skeptical perspective helps motivate those who know him to the pursuit of deeper scientific understandings.

Computer Physics Communications, 1992

A numerical approach for the solution of Maxwell's equations is presented. Based on a finite difference Yee lattice the method transforms each of the four Maxwell equations into an equivalent matrix expression that can be subsequently treated by matrix mathematics and suitable numerical methods for solving matrix problems. The algorithm, although derived from integral equations, can be consideredto be a special case of finite difference formalisms. A large variety of two-and three-dimensional field problems can be solved by computer programs based on this approach: electrostatics and magnetostatics, low-frequency eddy currents in solid and laminated iron cores, high-frequency modes in resonators, waves on dielectric or metallic waveguides, transient fields of antennas and waveguide transitions, transient fields of free-moving bunches of charged particles etc.

Mathematics in Computer Comp., Israel, 2021

Quantum physics differs from classical physics in the methods of study, and both of them consider the methods of the opposite side unacceptable for themselves. The author proposes the solution of some problems that are the privilege of quantum physics, using the methods of classical physics. At the same time, the author does not introduce any new postulates, but uses one and only tool, which is recognized by both physicists - the Maxwell system of equations. Strong interactions, atomic model, elementary particles, vacuum structure, electric charge, static electric field, electric current are considered etc.

In this work we summarize the electromagnetic theory (E.M.T) and its applications precisely on receiving and transmitting antennas, electromagnetic resonance image (MRI) as well as microwaves oven.

Electromagnetic Field Theory Fundamentals

arXiv (Cornell University), 2020

A procedure for solving the Maxwell equations in vacuum, under the additional requirement that both scalar invariants are equal to zero, is presented. Such a field is usually called a null electromagnetic field. Based on the complex Euler potentials that appear as arbitrary functions in the general solution, a vector potential for the null electromagnetic field is defined. This potential is called natural vector potential of the null electromagnetic field. An attempt is made to make the most of knowing the general solution. The properties of the field and the potential are studied without fixing a specific family of solutions. A equality, which is similar to the Dirac gauge condition, is found to be true for both null field and Lienard-Wiechert field. It turns out that the natural potential is a substantially complex vector, which is equivalent to two real potentials. A modification of the coupling term in the Dirac equation is proposed, that makes the equation work with both real potentials. A solution, that corresponds to the Volkov's solution for a Dirac particle in a linearly polarized plane electromagnetic wave, is found. The solution found is directly compared to Volkov's solution under the same conditions.

Proyecciones (Antofagasta), 2007

This work explores what other mathematical possibilities were available to Maxwell for formulating his electromagnetic field model, by characterizing the family of mathematical models induced by the analytical equations describing electromagnetic phenomena prevailing at that time. The need for this research stems from the article "Inertial Relativity-A Functional Analysis Review", recently published in "Proyecciones", which claims and demonstrates the existence of an axiomatic conflict between the special and general theories of relativity on one side, and functional analysis on the other, making the reformulation of the relativistic theories, mandatory. As will be shown herein, such reformulation calls for a revision of Maxwell's electromagnetic field model. The conclusion is reached that-given the set of equations considered by Maxwell-not a unique, but an infinite number of mathematically correct reformulations to Ampère's law exists, resulting in an equally abundant number of potential models for the electromagnetic phenomena (including Maxwell's). Further experimentation is required in order to determine which is the physically correct model. 5. Gauss' equation in its differential form is assumed valid for timeinvariant and time-varying fields 10. 6. Faraday's equation in its differential form is assumed valid for timeinvariant and time-varying fields 11. 7. Ampère's original equation in its differential form is assumed valid for time-invariant fields 12. 8. Biot-Savart's equation is assumed valid for time-invariant fields 13. 6 Gave rise to Eqn. (F) in [5], Eqn. (G) in [8]. 7 Defined in Par. (60), gave rise to Eqn. (B) in [5], Eqn. (L) in [8]. 8 Gave rise to Eqn. (E) in [5], Eqn. (F) in [8]. 9 Gave rise to Eqn. (H) in [5]. Gave rise to Eqn. (G) in [5], Eqn. (J) in [8]. Gave rise, jointly with Eqn. (B), to Eqn. (D) in [5], Eqn. (B) in [8]. Coherent with prevailing model for time-invariant fields. Coherent with prevailing model for time-invariant fields. Evolves into Ampère's law.

Journal of Mathematical Analysis and Applications, 1985

Let us summarize the main results. The wave solution for the Generalized Maxwell equations led us to the concept of the wave created by a moving electron as an essentially three-dimensional torsional oscillation. This oscillation takes place in longitudinal (along speed) and transverse (perpendicular) directions. This oscillation defines a traveling wave with amplitudes in longitudinal and transverse directions that are connected. Therefore, suppression of oscillation in one direction leads to suppression of oscillation in the other direction. In addition to this two-dimensional oscillation, the electron’s wave oscillates in the third dimension creating a standing wave independent with respect to time and the electron’s own movement, in contrast to the above mentioned-traveling wave. This standing wave defines the electron’s charge and Coulomb interaction force with other charges. Therefore the Coulomb force turns to be a long range one, in contrast to the Lorentz force, which is defined by a traveling wave that moves with electron’s velocity. One can say this in another way. The wave creating Coulomb force exists I ether from time immemorial. But the generalized Lorentz force is generated by movement and disappears with it. A positron possesses a similar standing wave with opposite sign. In an electron-positron collision, the standing waves are mutually annihilated, which means charge annihilation. These waves can appear only being “repulsed” by each other. Therefore electric charges appear only in couples: positive and negative ones. A certain visual notion about the electron as a massive torus rotating in equatorial and meridional planes is proposed. Charge magnitude is defined by the electron’s mass and the angular velocity of its equatorial rotation. If it constitutes right hand screw with meridional angle velocity, one gets charge of one sign, and of opposite sign in the opposite case. This screw also defines the sign of the above-mentioned standing wave.

Foundations of Physics Letters, 2006

The quantities E and B are then manifestly interdependent. We prove that they are determined by Maxwell's equations, so they represent the electric and magnetic fields in the new frame and the force F is the well known from experiments Lorentz force. In this way Maxwell's equations may be discovered theoretically for this particular situation of uniformly moving sources. The general solutions of the discovered Maxwell's equations lead us to fields produced by accelerating sources.

European Journal of Physics, 2004

Expressions for Maxwell's equations independent of the unit system are presented and compared with those given in Jackson's book. Both the cases of electromagnetism in vacuum and in a medium are considered through the introduction of two sets of proportional constants: the set of empirical constants and that of 'conventional constants'. The latter set is needed to account for the different conventions adopted in different unit systems for the definitions of various electromagnetic quantities in the presence of a medium.

It is shown that Maxwell's equations (Lorentz's gauge) have two independent branches. The first branch describes the wave phenomena. It is established that there are virtual charges. These charges have no inertia. They radiate waves. The new proof of a Poynting's theorem is given. The second branch describes the quasi-static phenomena. The solution of the problem of electromagnetic mass is given. The theory of interaction of two charges is described. It is shown that the laws of electrodynamics fit well within the framework of Classical Mechanics. Hypotheses are absent. PASC: 40

European Journal of Physics

The original "theoretical discovery" of electromagnetic waves by Maxwell is analyzed and presented in modern notations. In light of Maxwell's well-known prophetic dedication to the concept of the vector potential, it is interesting to reveal his derivation of the wave equation for this potential without the application of any gauge condition. This is to contrast with typical approaches students learn from standard textbooks for the derivation of the wave equation in various forms. It is in our opinion that intuition and insight, rather than logical deduction, must have played a more significant role in Maxwell's original discovery, as is not uncommon with discoveries made by the pioneers in science.