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Derivation of the Lorentz Force Law, the Magnetic Field Concept and the Faraday-Lenz Law using an Invariant Formulation of the Lorentz Transformation

J. H. Field
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Abstract

It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. This formalism, making essential use of the 4-vector electromagnetic potential concept, provides a short derivation of the Lorentz force law of classical electrodynamics, the conventional definition of the magnetic field, in terms of spatial derivatives of the 4--vector potential and the Faraday-Lenz Law. An important distinction between the physical meanings of the space-time and energy-momentum 4--vectors is pointed out.

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J. H. Field. 2005-08-19. Derivation of the Lorentz Force Law, the Magnetic Field Concept and the Faraday-Lenz Law using an Invariant Formulation of the Lorentz Transformation. https://doi.org/10.1088/0031-8949%2F73%2F6%2F018

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