Field, Force, Energy and Momentum in Classical Electrodynamics (Revised Edition)

2017 ◽  
Keyword(s):  
Classical Electrodynamics ◽  
Field Force ◽  
Energy And Momentum

Classical electrodynamics as a distribution theory. II

1958 ◽  
Vol 54 (2) ◽  
pp. 258-264 ◽  
Author(s):  
J. G. Taylor
Keyword(s):  
Electromagnetic Field ◽  
Total Energy ◽  
Distribution Theory ◽  
Classical Electrodynamics ◽  
Definition Of ◽  
Energy And Momentum

ABSTRACTIn a previous paper by the author (3) it was shown how the theory of distributions of L. Schwartz enables a mathematically consistent formalism to be given for a system composed of point charges interacting through their classical electromagnetic field. In the present paper a definition of the energy and momentum of the field lying in a space-like surface is given, and it is shown that from this four-vector it is possible to derive the usual equation of conservation of total energy and momentum.

scholarly journals Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 987
Author(s):  
Tomasz P. Stefański ◽  
Jacek Gulgowski
Keyword(s):  
Wave Propagation ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Momentum Conservation ◽  
Point Of View ◽  
Classical Electrodynamics ◽  
Classical Solutions ◽  
Systems With Memory ◽  
Energy And Momentum ◽  
With Memory

In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their properties from the point of view of classical electrodynamics, i.e., energy and momentum conservation, reciprocity, causality. Afterwards, we derive classical solutions for wave-propagation problems, assuming helical, spherical, and cylindrical symmetries of solutions. The results are supported by numerical simulations and their analysis. Discussion of relations between the TF Schrödinger equation and TF electrodynamics is included as well.

scholarly journals Implications of Gauge-Free Extended Electrodynamics

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2110
Author(s):  
Donald Reed ◽  
Lee M. Hively
Keyword(s):  
Scalar Field ◽  
Eddy Currents ◽  
Skin Effect ◽  
New Technologies ◽  
Scalar Potential ◽  
Electrical Current ◽  
Classical Electrodynamics ◽  
Magnetic Vector Potential ◽  
Novel Concept ◽  
Energy And Momentum

Recent tests measured an irrotational (curl-free) magnetic vector potential (A) that is contrary to classical electrodynamics (CED). A (irrotational) arises in extended electrodynamics (EED) that is derivable from the Stueckelberg Lagrangian. A (irrotational) implies an irrotational (gradient-driven) electrical current density, J. Consequently, EED is gauge-free and provably unique. EED predicts a scalar field that equals the quantity usually set to zero as the Lorenz gauge, making A and the scalar potential () independent and physically-measureable fields. EED predicts a scalar-longitudinal wave (SLW) that has an electric field along the direction of propagation together with the scalar field, carrying both energy and momentum. EED also predicts the scalar wave (SW) that carries energy without momentum. EED predicts that the SLW and SW are unconstrained by the skin effect, because neither wave has a magnetic field that generates dissipative eddy currents in electrical conductors. The novel concept of a “gradient-driven” current is a key feature of US Patent 9,306,527 that disclosed antennas for SLW generation and reception. Preliminary experiments have validated the SLW’s no-skin-effect constraint as a potential harbinger of new technologies, a possible explanation for poorly understood laboratory and astrophysical phenomena, and a forerunner of paradigm revolutions.

Electromagnetic fields and waves in vacuum

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Electromagnetic Field ◽  
Transmission Lines ◽  
Electromagnetic Waves ◽  
Momentum Conservation ◽  
Time Dependent ◽  
Classical Electrodynamics ◽  
Faraday’S Law ◽  
Wave Guides ◽  
Current Densities ◽  
Energy And Momentum

In previous chapters four experimental laws of electromagnetism were encountered: Gauss’s law in electrostatics, Gauss’s law in magnetism, Faraday’s law and Ampere’s law. Now, in this chapter, these laws are generalized where appropriate to include the time-dependent charge and current densities ρ‎( r, t) and J ( r, t) respectively. The result is a set of four coupled differential equations—known as Maxwell’s equations— which provide the foundation upon which the theory of classical electrodynamics is based. One of the most important aspects which emerges from Maxwell’s theory is the prediction of electromagnetic waves, and an entire spectrum of electromagnetic radiation. Some of the properties of these waves travelling in unbounded vacuum are considered, as well as their polarization states, energy and momentum conservation in the electromagnetic field and also applications to wave guides and transmission lines.

scholarly journals Relationship between Quantum Physics and Maxwell’s Equations in the Model of a Hydrogen Atom

2021 ◽  
Vol 3 (5) ◽  
pp. 29-33
Author(s):  
Y. E. Khoroshavtsev
Keyword(s):  
Hydrogen Atom ◽  
Momentum Flux ◽  
Quantum Physics ◽  
Classical Electrodynamics ◽  
Quantum Model ◽  
Quantum Energy ◽  
Magnetic Components ◽  
Electron Orbit ◽  
Energy And Momentum ◽  
New Formula

An attempt to bring together two different theories – classical electrodynamics and quantum mechanics is made. On the example of a hydrogen atom the problem of the hypothetic electron fall into a nucleus by means of the energy conservation law is examined. The essence of the present approach consists in the assumption, that the energy and momentum of an electron in quantum model are proportional to corresponding electromagnetic fluxes. In order to achieve the result, the new formula of momentum flux density not using Poynting vector was proposed. It states that the momentum flux depends not only on electric and magnetic components of the field, but also on a frequency of an electromagnetic wave. As the main result, it was demonstrated that the total including annihilation energy of an electron in Bohr’s atom model is equal to energy of a free electron mc2 without any mention of Relativity. An electromagnetic field inside an atom occurs quantized for each electron orbit. An additional consequence shows that the two fundamental definitions of quantum energy mc2 and ħω are interrelated. If ħω is admitted according to quantum physics, then mc2 follows automatically and vice versaю

Classical electrodynamics as a distribution theory

1956 ◽  
Vol 52 (1) ◽  
pp. 119-134 ◽  
Author(s):  
J. G. Taylor
Keyword(s):  
Field Intensity ◽  
Equations Of Motion ◽  
Canonical Formalism ◽  
Space Time ◽  
Continuation Methods ◽  
Classical Electrodynamics ◽  
Field Energy ◽  
Energy Tensor ◽  
The World ◽  
Energy And Momentum

ABSTRACTIn this paper a precise distribution-theoretic formalism for the description of point charges interacting through a classical electromagnetic field is given. The distribution solutions of the Maxwell equations are shown to reduce to the Lienard–Wiechert fields, which are summable over the whole of space-time. It is not possible to obtain directly a unique field intensity, on the world lines, from these distribution solutions. A brief analysis shows that analytic continuation methods also do not give a unique field intensity on the world lines. The energy tensor for the field is a distribution which can only be rigorously defined in terms of the motions of the charges. Thus only the value of the field energy or momentum residing in any finite region of space-time can be given any meaning. Equations of motion for the charges may be derived from the field energy tensor, using the principle of conservation of total energy and momentum for the system. These equations agree with those obtained previously by Dirac (2). Also any canonical formalism in which the field potentials and the particle variables enter in an equivalent manner is not possible. The difficulty of the definition of products of distributions in the stress tensor does not occur.

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