Maxwell's Equations, Electromagnetic Waves and Magnetic Charges (original) (raw)

Introduction to Electromagnetism According to Maxwell

Generis Publishing

Introduction to Maxwell's initial electromagnetics theory with deeper analysis leading to the establishment at the subatomic level of clear mechanics of electromagnetic photons emission and absorption and of electron stabilization in atoms. The resulting discovery of the adiabatic nature of the energy induced in all elementary charged particles, related to Maxwell's first equation, tends to confirm the conclusion that Einstein reached towards the end of his life that gravitation seems to follow the pattern of electromagnetism. Complement to the previously published monograph describing the electromagnetic mechanics of elementary particles.

On Maxwell’s discovery of electromagnetic waves and the gauge condition

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.

On some properties of the electromagnetic field and its interaction with a charged particle

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.

The Lorentz-Dirac Equation and the Physical Meaning of the Maxwell's Fields

1995

Classical Electrodynamics is not a consistent theory because of its field inadequate behaviour in the vicinity of their sources. Its problems with the electron equation of motion and with non-integrable singularity of the electron self field and of its stress tensor are well known. These inconsistencies are eliminated if the discrete and localized (classical photons) character of the electromagnetic interaction is anticipatively recognized already in a classical context. This is possible, in a manifestly covariant way, with a new model of spacetime structure, shown in a previous paper 1^{1}1, that invalidates the Lorentz-Dirac equation. For a point classical electron there is no field singularity, no causality violation and no conflict with energy conservation in the electron equation of motion. The electromagnetic field must be re-interpreted in terms of average flux of classical photons. Implications of a singularity-free formalism to field theory are discussed.

Concepts for a Theory of the Electromagnetic Field

The object of this contribution is twofold. On one hand, it rises some general questions concerning the definition of the electromagnetic field and its intrinsic properties, and it proposes concepts and ways to answer them. On the other hand, and as an illustration of this analysis, a set of quadratic equations for the electromagnetic field is presented, richer in pure radiation solutions than the usual Maxwell equations, and showing a striking property relating geometrical optics to all the other Maxwell solutions.

On the Origins of Electromagnetism

The origin of electromagnetism has been a recurring question since the discovery of electricity. In the 19th century, Maxwell unified electricity and magnetism into a single electrodynamic theory described by Maxwell's equations. This was followed by the discovery of the electrodynamic force on a moving charge by Lorentz. Later, Einstein demonstrated that magnetism and the Lorentz force can be considered a relativistic effect. However, despite these important theories, there is at present no physical theory that identifies the single fundamental cause of all known classical electromagnetism. In an attempt to identify this single fundamental cause, this paper shows that classical electromagnetism can be considered as effect of scalar waves emanating from charges. It is shown in this paper that Coulomb's law, Maxwell's equations, the magnetic and electric field, the Lorentz force, and the Lienard-Wiechert potentials, can all be derived only from this single hypothesis that...

On the foundational equations of the classical theory of electrodynamics

Resonance, 2013

A close examination of the Maxwell-Lorentz theory of electrodynamics reveals that polarization and magnetization of material media need not be treated as local averages over small volumes -volumes that nevertheless contain a large number of electric and/or magnetic dipoles. Indeed, Maxwell's macroscopic equations are exact and self-consistent mathematical relations between electromagnetic fields and their sources, which consist of free charge, free current, polarization, and magnetization. When necessary, the discrete nature of the constituents of matter and the granularity of material media can be handled with the aid of special functions, such as Dirac's delta-function. The energy of the electromagnetic field and the exchange of this energy with material media are treated with a single postulate that establishes the Poynting vector S = E ×H as the rate of flow of electromagnetic energy under all circumstances. Similarly, the linear and angular momentum densities of the fields are simple functions of the Poynting vector that can be unambiguously evaluated at all points in space and time, irrespective of the type of material media, if any, that might reside at various locations. Finally, we examine the Einstein-Laub force-and torque-density equations, and point out the consistency of these equations with the preceding postulates, with the conservation laws, and with the special theory of relativity. The set of postulates thus obtained constitutes a foundation for the classical theory of electrodynamics.

Comment on “Massive electrodynamics and the magnetic monopoles”

Physical Review D, 2021

In this paper we correct previous work on magnetic charge plus a photon mass. We show that contrary to previous claims this system has a very simple, closed form solution which is the Dirac string potential multiplied by a exponential decaying part. Interesting features of this solution are discussed namely: (i) the Dirac string becomes a real feature of the solution; (ii) the breaking of gauge symmetry via the photon mass leads to a breaking of the rotational symmetry of the monopole's magnetic field; (iii) the Dirac quantization condition is potentially altered.