Generalization of the Biot–Savart law to Maxwell’s equations using special relativity

1992 ◽  
Vol 60 (1) ◽  
pp. 35-38 ◽  
Author(s):  
Dwight E. Neuenschwander ◽  
Brian N. Turner
Keyword(s):  
Special Relativity ◽  
Maxwell’S Equations ◽  
Maxwell's Equations

scholarly journals Determination of Photon and Elementary Particles Rest Masses Using Maxwell’s Equations and Generalized Potential Dependent Special Relativity

2020 ◽  
Vol 12 (08) ◽  
pp. 588-598
Author(s):  
Abeer Mohammed Khairy Ahmed ◽  
Mashair Ahmed Mohammed Yousif ◽  
Zainab Mustapha Kurawa ◽  
Zoalnoon Ahmed Abeid Allah Saad ◽  
Suhair Salih Makawy ◽  
...  
Keyword(s):  
Special Relativity ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Elementary Particles ◽  
Generalized Potential

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.

Sumudu Applications to Maxwell's Equations

PIERS Online ◽  
2009 ◽  
Vol 5 (4) ◽  
pp. 355-360 ◽  
Author(s):  
Fethi Bin Muhammad Belgacem
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations

Maxwell’s Equations versus Newton’s Third Law

2018 ◽  
Author(s):  
Glyn Kennell ◽  
Richard Evitts
Keyword(s):  
Electric Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Simulated Data ◽  
Numerical Data ◽  
Transport Equations ◽  
Concentration Gradients ◽  
Third Law

The presented simulated data compares concentration gradients and electric fields with experimental and numerical data of others. This data is simulated for cases involving liquid junctions and electrolytic transport. The objective of presenting this data is to support a model and theory. This theory demonstrates the incompatibility between conventional electrostatics inherent in Maxwell's equations with conventional transport equations. <br>

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