Derivation of Maxwell's Equations and the Boundary Conditions from Coulomb's Law

1962 ◽  
Vol 30 (11) ◽  
pp. 788-795
Author(s):  
T. A. Green
Keyword(s):  
Boundary Conditions ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Coulomb’S Law ◽  
Coulomb's Law

scholarly journals Direct Derivation of Liénard–Wiechert Potentials, Maxwell’s Equations and Lorentz Force from Coulomb’s Law

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 237
Author(s):  
Hrvoje Dodig
Keyword(s):  
Energy Conservation ◽  
Special Relativity ◽  
Lorentz Force ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Conservation Principle ◽  
Coulomb’S Law ◽  
The Moment ◽  
Coulomb's Law ◽  
Energy Conservation Principle

In this paper, the solution to long standing problem of deriving Maxwell’s equations and Lorentz force from first principles, i.e., from Coulomb’s law, is presented. This problem was studied by many authors throughout history but it was never satisfactorily solved, and it was never solved for charges in arbitrary motion. In this paper, relativistically correct Liénard–Wiechert potentials for charges in arbitrary motion and Maxwell equations are both derived directly from Coulomb’s law by careful mathematical analysis of the moment just before the charge in motion stops. In the second part of this paper, the electrodynamic energy conservation principle is derived directly from Coulomb’s law by using similar approach. From this energy conservation principle the Lorentz force is derived. To make these derivations possible, the generalized Helmholtz theorem was derived along with two novel vector identities. The special relativity was not used in our derivations, and the results show that electromagnetism as a whole is not the consequence of special relativity, but it is rather the consequence of time retardation.

scholarly journals New perspectives for photoelectric phenomena

2016 ◽  
Vol 55 (4) ◽  
Author(s):  
Igor Lashkevych ◽  
Oleg Yu. Titov ◽  
Yuri G. Gurevich
Keyword(s):  
Solar Cells ◽  
Boundary Conditions ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Transport Phenomena ◽  
Space Charges ◽  
Recombination Processes ◽  
New Formulation ◽  
Physical Phenomena

The functioning of the solar cells (and photoelectric phenomena in general) relies on the photo-generation of carriers in p–n junctions and their subsequent recombination in the quasi-neutral regions. A number of basic issues concerning the physics of the operation of solar cells still remain obscure. This paper reports on some unsolved basic problems, namely: a model of the recombination processes that does not contradict Maxwell’s equations; boundary conditions; the role played by space charges in the transport phenomena, and the formation of quasi-neutral regions under the presence of nonequilibrium photo-generated carriers. In this work, a new formulation of the theory that explains the underlying physical phenomena involved in the generation of a photo-e.m.f. is presented.

scholarly journals Eigenvalues for Maxwell’s equations with dissipative boundary conditions

2016 ◽  
Vol 99 (1-2) ◽  
pp. 105-124 ◽  
Author(s):  
Ferruccio Colombini ◽  
Vesselin Petkov ◽  
Jeffrey Rauch
Keyword(s):  
Boundary Conditions ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Dissipative Boundary
Sign in / Sign up

Export Citation Format

Share Document