%0 Journal Article
%T Derivation of the Lorentz Force Law, the Magnetic Field Concept and the Faraday-Lenz Law using an Invariant Formulation of the Lorentz Transformation
%A J. H. Field
%J Physics
%D 2004
%I arXiv
%R 10.1088/0031-8949/73/6/018
%X 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.
%U http://arxiv.org/abs/physics/0409103v2