Eigenvectors of the Faraday tensor of a point charge in arbitrary motion

2001 ◽  
Vol 79 (1) ◽  
pp. 75-80 ◽  
Author(s):  
J L López-Bonilla ◽  
V Gaftoi ◽  
G Ovando
Keyword(s):  
Electromagnetic Field ◽  
Eigenvalue Problem ◽  
Point Charge ◽  
Faraday Tensor

We study the eigenvalue problem of the Faraday tensor associated with the Liénard–Wiechert electromagnetic field. We find all the eigenvectors (null and nonnull ones) that do not appear explicitly in the literature. PACS Nos.: 03.50De, 02.10Sp, 41.20-q

scholarly journals WITHOUT A CONFLICT MODEL OF ELECTRON

2019 ◽  
pp. 16-20
Author(s):  
Vasil Tchaban
Keyword(s):  
Elementary Particle ◽  
Black Hole ◽  
Electromagnetic Field ◽  
Charge Density ◽  
Point Charge ◽  
Quark Distribution ◽  
Electromagnetic Mass ◽  
White Hole ◽  
Universal Formula ◽  
Conflict Model

The model of electron is offered with quark distribution of charge density and ”white hole” (on similarity of ”black hole” in gravitation) in a center. Such structure abolishes the crisis of electromagnetic mass, calculated on universal formula and on the impulse of the electromagnetic field. A model in order to please a classic electrodynamics keeps monolithic nature of elementary particle, and in order to please a quantum allows the separate charged zones to interpret as separate quarks. Coming from harmony of spheres of the separate charged zones, a white hole can be interpreted as white (neutral) quark conditionally in addition to three coloured. As after the electric radius re = 1.185246·10−15 m of white hole the laws of electricity do not operate, then the crisis of point charge is removed at the same time too, because of must be: r ≥ re.

Electromagnetism and special relativity

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Electromagnetic Field ◽  
Special Relativity ◽  
Point Charge ◽  
Reference Frames ◽  
Classical Electrodynamics ◽  
Covariant Form ◽  
Field Tensor ◽  
Electromagnetic Field Tensor ◽  
Preferred Reference Frame ◽  
Physical Quantities

In 1905, when Einstein published his theory of special relativity, Maxwell’s work was already about forty years old. It is therefore both remarkable and ironic (recalling the old arguments about the aether being the ‘preferred’ reference frame for describing wave propagation) that classical electrodynamics turned out to be a relativistically correct theory. In this chapter, a range of questions in electromagnetism are considered as they relate to special relativity. In Questions 12.1–12.4 the behaviour of various physical quantities under Lorentz transformation is considered. This leads to the important concept of an invariant. Several of these are encountered, and used frequently throughout this chapter. Other topics considered include the transformationof E- and B-fields between inertial reference frames, the validity of Gauss’s law for an arbitrarily moving point charge (demonstrated numerically), the electromagnetic field tensor, Maxwell’s equations in covariant form and Larmor’s formula for a relativistic charge.

scholarly journals A class of solitons in Maxwell-scalar and Einstein–Maxwell-scalar models

2020 ◽  
Vol 80 (1) ◽  
Author(s):  
Carlos A. R. Herdeiro ◽  
João M. S. Oliveira ◽  
Eugen Radu
Keyword(s):  
Electromagnetic Field ◽  
Scalar Field ◽  
Quantum Gravity ◽  
Exact Solutions ◽  
Point Charge ◽  
Coulomb Field ◽  
Specific Class ◽  
Minimal Coupling ◽  
Flat Spacetime ◽  
Physical Quantities

AbstractRecently, no-go theorems for the existence of solitonic solutions in Einstein–Maxwell-scalar (EMS) models have been established (Herdeiro and Oliveira in Class Quantum Gravity 36(10):105015, 2019). Here we discuss how these theorems can be circumvented by a specific class of non-minimal coupling functions between a real, canonical scalar field and the electromagnetic field. When the non-minimal coupling function diverges in a specific way near the location of a point charge, it regularises all physical quantities yielding an everywhere regular, localised lump of energy. Such solutions are possible even in flat spacetime Maxwell-scalar models, wherein the model is fully integrable in the spherical sector, and exact solutions can be obtained, yielding an explicit mechanism to de-singularise the Coulomb field. Considering their gravitational backreaction, the corresponding (numerical) EMS solitons provide a simple example of self-gravitating, localised energy lumps.

Field of a Uniformly Moving Charge in an Anisotropic Dispersive Medium

1973 ◽  
Vol 28 (6) ◽  
pp. 907-910
Author(s):  
S. Datta Majumdar ◽  
G. P. Sastry
Keyword(s):  
Electromagnetic Field ◽  
Fourier Transform ◽  
Point Charge ◽  
Rest Frame ◽  
Dispersive Medium ◽  
Scalar Potential ◽  
Fourier Integral ◽  
The Third ◽  
Dispersion Formula ◽  
The Fourier Transform

The electromagnetic field of a point charge moving uniformly in a uniaxial dispersive medium is studied in the rest frame of the charge. It is shown that the Fourier integral for the scalar potential breaks up into three integrals, two of which are formally identical to the isotropic integral and yield the ordinary and extraordinary cones. Using the convolution theorem of the Fourier transform, the third integral is reduced to an integral over the isotropic field. Dispersion is explicitly introduced into the problem and the isotropic field is evaluated on the basis of a simplified dispersion formula. The effect of dispersion on the field cone is studied as a function of the cut-off frequency.

scholarly journals The Field Of A Step–Like Accelerated Point Charge: Liénard–Wiechert Potentials And Čerenkov Shock Waves Revisited

2015 ◽  
Vol 66 (6) ◽  
pp. 317-322
Author(s):  
L’ubomír Šumichrast
Keyword(s):  
Electromagnetic Field ◽  
Shock Waves ◽  
Vector Potential ◽  
Point Charge ◽  
Solvable Problems

Abstract Scalar and vector potential as well as the electromagnetic field of a moving point charge is a nice example how the application of symbolic functions (distributions) in electromagnetics makes it easier to obtain and interpret solutions of otherwise hardly solvable problems.

scholarly journals Second Gradient Electromagnetostatics: Electric Point Charge, Electrostatic and Magnetostatic Dipoles

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1104 ◽  
Author(s):  
Markus Lazar ◽  
Jakob Leck
Keyword(s):  
Field Theory ◽  
Electromagnetic Field ◽  
Point Charge ◽  
Constitutive Relations ◽  
Higher Order ◽  
Gradient Field ◽  
Theoretical Point ◽  
Second Gradient ◽  
Maxwell Electrodynamics ◽  
Constitutive Parameters

In this paper, we study the theory of second gradient electromagnetostatics as the static version of second gradient electrodynamics. The theory of second gradient electrodynamics is a linear generalization of higher order of classical Maxwell electrodynamics whose Lagrangian is both Lorentz and U ( 1 ) -gauge invariant. Second gradient electromagnetostatics is a gradient field theory with up to second-order derivatives of the electromagnetic field strengths in the Lagrangian. Moreover, it possesses a weak nonlocality in space and gives a regularization based on higher-order partial differential equations. From the group theoretical point of view, in second gradient electromagnetostatics the (isotropic) constitutive relations involve an invariant scalar differential operator of fourth order in addition to scalar constitutive parameters. We investigate the classical static problems of an electric point charge, and electric and magnetic dipoles in the framework of second gradient electromagnetostatics, and we show that all the electromagnetic fields (potential, field strength, interaction energy, interaction force) are singularity-free, unlike the corresponding solutions in the classical Maxwell electromagnetism and in the Bopp–Podolsky theory. The theory of second gradient electromagnetostatics delivers a singularity-free electromagnetic field theory with weak spatial nonlocality.

Geometry of Electrostatic Fields

2018 ◽  
Vol 6 (1) ◽  
pp. 10-19 ◽  
Author(s):  
О. Графский ◽  
O. Grafskiy ◽  
Ю. Пономарчук ◽  
Yu. Ponomarchuk ◽  
А. Холодилов ◽  
...  
Keyword(s):  
Electromagnetic Field ◽  
Fourth Order ◽  
Electrostatic Field ◽  
Point Charge ◽  
Positive Charge ◽  
Double Points ◽  
Electrostatic Fields ◽  
Special Cases ◽  
Lines Of Force

Electrostatic fields have been most fully studied as special cases of electromagnetic field. They are created by a set of charged bodies that are considered immovable in relation to the observer and unchanged in time [1–3; 19; 20; 27]. Since any field is characterized by basic quantities, then such quantities for electrostatic fields are strength E and potential ϕ. Therefore, geometrically, such fields are characterized by a combination of force and equipotential lines. These fields were considered in the thesis of N.P. Anikeeva [1]. In particular, the author notes that in the case of dissimilar equal charges "... families of force and equipotential lines make up two orthogonal bundles of circles" [1, p. 59]. However, it is necessary to clarify that each "force" circle gj represents by itself not one but two lines of force, which emanate from a positive charge and terminate on a negative one. A similar review on the work [1] can be done with respect to the picture of two equal positive charges’ electrostatic field. Here the author considers a family ui of equipotential lines, which are Cassini ovals. It is truly said that these ovals belong to the fourth-order bicircular curves of genre 1 (have two double imaginary points, which are cyclic). But these ovals’ family includes one curve of zero genre — the Bernoulli lemniscate; it has three double points (two of them are the same cyclic ones, and one is real, which coincides with the origin of coordinates). In addition, it has been noted that "... the lines of current are equilateral hyperbolas gj» [1, p. 63]. However, clarification is also required here. The lines of force exit from each point charge and each line has two opposite directions. One such line of "double direction" forms only one branch of an equilateral hyperbola. A similar set of branches of equilateral hyperbolas also emanates from the second charge.

Electromagnetic field lines of a point charge moving arbitrarily in vacuum

1986 ◽  
Vol 29 (11) ◽  
pp. 1053-1057 ◽  
Author(s):  
S G Arutyunyan
Keyword(s):  
Electromagnetic Field ◽  
Point Charge ◽  
Field Lines

Operator theory for solving the eigenvalue problem of electromagnetic field

2002 ◽  
Author(s):  
Ren Xiaoyu ◽  
Ma Jifu ◽  
Zhang Liyang ◽  
Song Wenmiao
Keyword(s):  
Electromagnetic Field ◽  
Eigenvalue Problem ◽  
Operator Theory
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