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

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  • Hrvoje Dodig

    (Department of Electrical and Information Technology, Faculty of Maritime Studies, University of Split, 21000 Split, Croatia
    Current address: Faculty of Maritime Studies, University of Split, Rud¯era Boškovic´a 37, 21000 Split, Croatia.)

Abstract

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.

Suggested Citation

  • Hrvoje Dodig, 2021. "Direct Derivation of Liénard–Wiechert Potentials, Maxwell’s Equations and Lorentz Force from Coulomb’s Law," Mathematics, MDPI, vol. 9(3), pages 1-28, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:237-:d:486871
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    Cited by:

    1. Hrvoje Dodig, 2024. "The Wave Equation for a Moving Source and a Moving Receiver," Mathematics, MDPI, vol. 12(14), pages 1-17, July.

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