Equations of Electrodynamics

Maxwell’s equations are valid only for a stationary observation point, therefore, to adequately describe real processes so far we have had to move to a moving reference frame. This paper presents the equations of electrodynamics for the moving observation point, it is shown that plane and spherical electromagnetic waves are their solutions, while the spherical wave propagates only outward, which cannot be said about Maxwell’s equations. The fields of uniformly moving charges are also solutions of the equations. Now there is no need to move to a moving reference frame, to use four-dimensional space and covariant form of equations. The question of finding a universal form of the equations that allows a solution in the form of the field of an arbitrarily moving charge remains open. This raises the question of the existence of a two-parameter group of transformations of electromagnetic fields along with the known one-parameter group has been posed. The phenomena derived from the equations, which make an additional contribution to the phase overrun in the Aharonov-Bohm effect are considered. The equation of motion of a charged particle in an electromagnetic field without simplifying approximations is considered, which allows us to take into account the radiation effects. It is shown that the fields in a moving observation point depend on its velocity and acceleration. In particular, although in a constant uniform electric field a force qE acts on a motionless charged particle, but on the same motionless but not fixed particle the force 4/3qE acts already, because it has a nonzero acceleration and the electric field at this point is larger. As the speed increases, the field decreases, and when it reaches the speed of light, when the particle stops accelerating, the force again becomes equal to qE The principle of operation of an unconventional alternator in a constant electric field and its corresponding engine, as well as new types of direct and impulse current generators, predicted by the equations, are described.

The atomic structure of chemical elements in the theory of compressible oscillating ether

Previously, the basic laws and equations of electrodynamics, atomic nuclei, elementary particles theory and gravitation theory were derived from the equations of compressible oscillating ether. In this work, the theory of atomic structure for all chemical elements is constructed. A formula for the values of the energy levels of the electrons of an atom, which are the values of the energies of binding of electrons with the nucleus of an atom in the ground unexcited state, is derived from the equations of the ether. Based on experimental data on the ionization energies of atoms and ions, it is shown that the sequence of values of the energy levels of electrons has jumps, exactly corresponding to the periods of the table of chemical elements. It is concluded that it is precisely these jumps, and not quantum-mechanical rules, prohibitions and postulates that determine the periodicity of the properties of chemical elements. Ethereal correction of the table of chemical elements is presented which returns it to the form proposed by D.I. Mendeleev.

Equations of Electrodynamics

The equations of electrodynamics are presented, it is shown that plane and spherical electromagnetic waves are their solutions, while the spherical wave propagates only outward. Fields of uniformly moving charges are also solutions of equations. The question of finding a universal form of equations admitting a solution in the form of a field of an arbitrarily moving charge remains open. The question is raised about the existence of a two-parameter group of transformations of electromagnetic fields along with the well-known one-parameter group. The equation of motion of a charged particle in an electromagnetic field is considered without simplifying approximations. The principle of operation of an unconventional alternator in a constant electric field and a corresponding engine, as well as new types of generators of direct and impulse current, are described.

Integral representations in boundary-value problems on calculation of devices of microwave and EHF bands

In the electrodynamic calculation of microwave (EHF) devices using methods that lead to algorithms in an open form, strict integral relations (representations) are very useful: Lorentz lemma, reciprocity theorem, orthogonality condition for eigenwaves, etc. of the results obtained, their convergence improves, and in some cases the calculation of characteristics that cannot be calculated without the indicated representations. Integral representations are a record of the equations of electrodynamics (in any unified form) and their solutions in one or another generalized form, linking in general the electromagnetic fields in electrodynamic structures described by boundary value problems. Integral views are used to control the results obtained; insome cases, they allow obtaining analytical solutions; lead to self-consistent problems that take into account the reverse effect of the radiation field on the primary sources; allow obtaining a priori information about the spectrum of possible solutions; solve associated problems as specific problems of arousal. Consideration of the phenomenon of complex resonance in this work shows that integral representations make it possible to establish a connection between non-self-adjointness and self-consistency of boundary value problems.

Scattering of electromagnetic waves by a discrete octahedron from resonant spheres

A solution is given to the problem of scattering of electromagnetic waves by a discrete convex polyhedron – an octahedron of resonant magnetodielectric spheres based on a complex rhombic crystal lattice. Here we consider a case equivalent to the X-ray optics of crystals, when α / λ՛<<1 and can be α / λg ~ 1; d, h, l / λ՛ ~ 1, where α is the radius of the spheres; λ՛, λg are the lengths of the scattered wave outside and inside the spheres; d, h, l are constant lattices. The solution of the problem is obtained based on the Fredholm integral equations of electrodynamics of the second kind with nonlocal boundary conditions. The expressions found in this work for a metacrystal in the form of an octahedron can be used to study the fields scattered by the crystal in the Fresnel and Fraunhofer zones, as well as to study its internal field. The relations obtained in this work can find application in the study of the scattering of waves of various kinds by convex polyhedrons, the creation on their basis of new types of limited metacrystals, including nanocrystals with resonance properties, and in the study of their behavior in various external media. As well as in the development of methods for modeling electromagnetic phenomena that can occur in real crystals in resonance regions in the optical and X-ray wavelength ranges.

Maxwell Equations for Material Systems, Version 2

The Maxwell equations of electrodynamics describe electrical and magnetic forces with great accuracy in the vacuum of space. But the equations of electrodynamics applied to material systems are usually written in a way that obscures their accuracy. The usual formulation of the Maxwell equations includes a dielectric constant as a single real number that grossly over-approximates the actual properties of matter, particularly liquid matter so important in applications of electrodynamics to biology and chemistry. We rewrite two Maxwell equations here to make clear the precision of the Maxwell equations in the presence or absence of matter. We discuss and derive two well known corollaries that are as universal and precise as the Maxwell equations themselves: (1) a continuity equation that relates charge and flux and (2) a conservation equation in which total current never accumulates at all. The total current is the right hand side of the Ampere-Maxwell law. Total current is perfectly incompressible. It is conserved exactly, everywhere and at every time, independent of the microphysics of charge conduction. The total current combines the flux of charges and the ethereal current. The ethereal current \varepsilon_{o\ }\sfrac{\partial\mathbf{E}}{\partial t}\ exists everywhere, including the interior of atoms, because it is a property of space, not matter. The ethereal current exists, and thus flows, in a vacuum devoid of mass. The ethereal current is a consequence of the relativistic (Lorentz) invariance of charge. Charge does not change even if it moves at speeds approaching the velocity of light. Total current has properties quite distinct from flux of mass because of the ethereal current. Most strikingly, in the one dimensional unbranched systems of electronic circuits and biological ion channels, the total current is independent of location, even if the flux of charges varies a great deal. Indeed, the Maxwell equations&mdash;and thus conservation of total current&mdash;act as a perfect low pass spatial filter, converting the infinite variation of (the Brownian model of) thermal motion of charges to the zero variation of the total current.

Maxwell Equations for Material Systems, Version 1

The Maxwell equations of electrodynamics describe electrical and magnetic forces with great accuracy in the vacuum of space. But the equations of electrodynamics applied to material systems are usually written in a way that obscures their accuracy. The usual formulation of the Maxwell equations includes a dielectric constant as a single real number that grossly over-approximates the actual properties of matter, particularly liquid matter so important in applications of electrodynamics to biology and chemistry. We rewrite two Maxwell equations here to make clear the precision of the Maxwell equations in the presence or absence of matter. We discuss and derive two well known corollaries that are as universal and precise as the Maxwell equations themselves: (1) a continuity equation that relates charge and flux and (2) a conservation equation in which total current never accumulates at all. The total current is the right hand side of the Ampere-Maxwell law. Total current is perfectly incompressible. It is conserved exactly, everywhere and at every time, independent of the microphysics of charge conduction. The total current combines the flux of charges and the ethereal current. The ethereal current \varepsilon_{o\ }\sfrac{\partial\mathbf{E}}{\partial t}\ exists everywhere, including the interior of atoms, because it is a property of space, not matter. The ethereal current exists, and thus flows, in a vacuum devoid of mass. The ethereal current is a consequence of the relativistic (Lorentz) invariance of charge. Charge does not change even if it moves at speeds approaching the velocity of light. Total current has properties quite distinct from flux of mass because of the ethereal current. Most strikingly, in the one dimensional unbranched systems of electronic circuits and biological ion channels, the total current is independent of location, even if the flux of charges varies a great deal. Indeed, the Maxwell equations&mdash;and thus conservation of total current&mdash;act as a perfect low pass spatial filter, converting the infinite variation of (the Brownian model of) thermal motion of charges to the zero variation of the total current.