Derivation of the Lorentz force law, the magnetic field concept and the Faraday-Lenz and magnetic Gauss laws using an invariant formulation of the Lorentz transformation

摘要

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. An important distinction between the physical meanings of the space - time and energy - momentum 4-vectors is pointed out. The formalism is shown to provide a short derivation of the Lorentz force law of classical electrodynamics, and the conventional definition of the magnetic field, in terms of spatial derivatives of the 4-vector potential, as well as the Faraday - Lenz law and the Gauss law for magnetic fields. The connection between the Gauss law for the electric field and the electrodynamic Ampere law, due to the 4-vector character of the electromagnetic potential, is also pointed out.