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The paper Direct derivation of Lienard–Wiechert potentials, Maxwell’s equations and Lorentz force from Coulomb’s law by Hrvoje Dodig, purports to derive electrodynamics from Coulomb's law, without regard to special relativity, including the Lorentz force. This he does by, first, generalizing the Helmholtz decomposition:

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This seems to fly in the face of explanations of the Lorentz Force as deriving from Lorentz contraction of charged particles in motion resulting in apparent changes of density of electric charge. Does this derivation, indeed, cover the observed phenomena?

Urb
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James Bowery
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2 Answers2

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You do not need special relativity to derive electrodynamics or the lorentz force law. special relativity is derived FROM electrodynamics( ish)

jensen paull
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The whole point of that paper is not to use special relativity to derive electrodynamics from Coulomb's law. It is understood that in that paper Coulomb's law is considered an experiment (the result of the measurement), and it is remarkable that using only that information one can derive all of the electrodynamics.

Regarding the use of SR to derive electrodynamics, one should be aware that SR is valid only for objects moving with constant velocity along a straight line. That being said, the results in that paper are more general than the ones obtained by combining SR and Coulomb's law.

In conclusion, SR has nothing to do with electrodynamics.

If one is still not convinced that electrodynamics has nothing to do with SR, try to derive electromagnetic fields of the charge moving along a circular path using SR. The result would be very different than one obtained by using Lienard-Wiechert potentials.

gallieo1985
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