On the way to understanding the electromagnetic phenomena (original) (raw)

New Solutions of Maxwell's Equations

Mathematics in Computer Comp. MiC, Israel, 2024

New solutions of Maxwell's equations are proposed for a vacuum, for a wire with direct and alternating current, for a capacitor, for a sphere, etc. It is preliminarily noted that the proof of the uniqueness of the known solution is based on the law of conservation of energy, which is not observed (for instantaneous values) in the known solution. Proposed solutions • does not contradict the law of conservation of energy at any moment in time, i.e. it establishes the constancy of the density of the electromagnetic energy flow over time, • reveals the phase shift between electrical and magnetic intensities, • explains the existence of a flow of energy along the wire equal to the power consumed, etc. Detailed evidence is provided for the interested reader. Experimental confirmation of the theory is considered. Explanations are offered for experiments that have not yet been substantiated. Technical applications of the obtained solution are considered.

The Second Solution of Maxwell's Equations

viXra, 2016

A new solution of Maxwell equations for vacuum is presented. First it must be noted that the proof of the solution's uniqueness is based on the Law of energy conservation which is not observed (for instantaneous values) in the known solution. The presented solution does not violate the Law of energy conservation. Besides, in this solution the electrical and magnetic components of intensity are shifted in phase. A detailed proof is given for interested readers.

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.