On the way to understanding the electromagnetic phenomena (original) (raw)
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.
Maxwell's Equations, Electromagnetic Waves and Magnetic Charges
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.
A Brief Note on Maxwell ’ s Equations
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.
Some Variations on Maxwell's Equations
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.
Solution of Maxwell's equations
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.
Maxwell’s equation in quantum physics. Third edition.
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.
Some Applications of Electromagnetic Theory
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.
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.
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.