Derivation of the Lorentz Force Law and the Magnetic Field Concept using an Invariant Formulation of the Lorentz Transformation

J. H. Field

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Derivation of the Lorentz Force Law and the Magnetic Field Concept 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. The formalism is shown to provide a short derivation, in which the 4--vector electromagnetic potential plays a crucial role, of the Lorentz force law of classical electrodynamics, and the conventional definition of the magnetic field in terms spatial derivatives of the 4--vector potential. The time component of the relativistic generalisation of the Lorentz force law is discussed. An important physical distinction between the space-time and energy-momentum 4--vectors is also pointed out.

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J. H. Field. 2003-07-28. Derivation of the Lorentz Force Law and the Magnetic Field Concept using an Invariant Formulation of the Lorentz Transformation. https://arxiv.org/abs/physics/0307133

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