Evidence for Maxwell’s equations, fields, force laws and alternative theories of classical electrodynamics

@article{Tran2018EvidenceFM,
  title={Evidence for Maxwell’s equations, fields, force laws and alternative theories of classical electrodynamics},
  author={Max M. Tran},
  journal={European Journal of Physics},
  year={2018},
  volume={39}
}
  • M. Tran
  • Published 15 October 2018
  • Physics
  • European Journal of Physics
The set of equations known today as Maxwell’s equations along with a few constitutive equations lie at the heart of classical electromagnetism. A common misconception held by many is that Maxwell’s equations are essential, and that classical electromagnetic theory is settled science and is no longer an active field of investigations. We will review the four Maxwell’s equations and related equations, their supporting experimental evidence, the field concept, and the Lorentz and Ritz force laws… 
Electromagnetism from 5D gravity: beyond the Maxwell equations
Ever with the work of Kaluza, it has been known that 4D Einstein- and Maxwell-type equations emerge from the equations for 5D gravity, in Ricci-flat space-times having a space-like Killing vector. We
Electric fields on a two-dimensional spherical surface
Previous works have addressed the effects of geometry on Maxwell’s equations. Global solutions have been found for radiation solutions, electro-magnetic fields with no charges. For electro-magnetic
Gauge-Underdetermination and Shades of Locality in the Aharonov–Bohm Effect
I address the view that the classical electromagnetic potentials are shown by the Aharonov–Bohm effect to be physically real (which I dub: ‘the potentials view’). I give a historico-philosophical

References

SHOWING 1-10 OF 50 REFERENCES
The mass of the photon
Because classical Maxwellian electromagnetism has been one of the cornerstones of physics during the past century, experimental tests of its foundations are always of considerable interest. Within
VIII. A dynamical theory of the electromagnetic field
  • J. Maxwell
  • Physics
    Philosophical Transactions of the Royal Society of London
  • 1865
(1) The most obvious mechanical phenomenon in electrical and magnetical experiments is the mutual action by which bodies in certain states set each other in motion while still at a sensible distance
The fundamentals of electromagnetic theory revisited
  • J. W. Arthur
  • Education
    IEEE Antennas and Propagation Magazine
  • 2008
This tutorial paper deals with several aspects of basic electromagnetic theory that appear to be insufficiently appreciated a century and one-half after Maxwell published his well-known equations,
Evaluation of Electron Beam Deflections across a Solenoid Using Weber-Ritz and Maxwell-Lorentz Electrodynamics
The deflection of charged particle beams by electric and/or magnetic fields is invariably based on the field centred approach associated with Maxwell-Lorentz and incorporated into the Lorentz force
Can Maxwell’s equations be obtained from the continuity equation?
We formulate an existence theorem that states that, given localized scalar and vector time-dependent sources satisfying the continuity equation, there exist two retarded fields that satisfy a set of
Investigating Electron Beam Deflections by a Long Straight Wire Carrying a Constant Current using Direct Action, Emission-based and Field Theory Approaches of Electrodynamics
Results are presented for the transverse de ection of an electron beam by a long, straight wire carrying direct current. The experimental de ections are compared with three calculation methods based
An Elementary View of Maxwell's Displacement Current
  • J. W. Arthur
  • Physics
    IEEE Antennas and Propagation Magazine
  • 2009
Maxwell's displacement current is addressed in the most basic of terms, starting from Coulomb's law. The aim of this approach is to shed new light on some questions that have dogged the concept, and
Has the Lorentz-covariant electromagnetic force law been directly tested experimentally?
So far, no convincing experimental evidence for the Lorentz-covariant electromagnetic force law has been reported. This paper utilizes an available experiment, which is often claimed as one of the
The Helmholtz theorem and retarded fields
Textbooks frequently use the Helmholtz theorem to derive expressions for electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for time-dependent
A Very Accurate Test of Coulomb's Law of Force Between Charges
The exponent 2 in Coulomb's inverse square law of force between charges in empty space has been found experimentally to be correct to within 1 part in ${10}^{9}$. The wellknown electrostatic
...
...