A fields only version of the Lorentz Force Law: Particles replaced by their fields

@inproceedings{Butler2012AFO,
  title={A fields only version of the Lorentz Force Law: Particles replaced by their fields},
  author={Philip H Butler and Niels Gijsbertus Gresnigt and Martin B. van der Mark and Peter F. Renaud},
  year={2012}
}
We show that the Lorentz force law, F^L_1=q_1(E+v_1xB) being the charge on particle 1 interacting with the electromagnetic fields due to all other particles, can be written in a pure field form F^L_1=-\nabla_1 U^{EM}. In this expression U^{EM} is the total electromagnetic energy of the system of particle 1 and all other particles. In deriving this result we review the old but not widely known results that Maxwell's equations follow uniquely from Special Relativity, and that the Lorentz force… CONTINUE READING

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