Physics – Mathematical Physics
Scientific paper
2011-05-17
Physics
Mathematical Physics
67 pages, 3 figures, XXV International Workshop on Differential Geometric Methods in Theoretical Mechanics Levico Terme (Trent
Scientific paper
The Faraday-Ampere laws of electro-magnetic induction are formulated in terms of plain and twisted differential forms, taking in due account the body motion in terms of Lie time-derivatives. Covariance of Lie derivatives with respect to arbitrary relative motions, and Galilei invariance of the electro-magnetic fields, imply Galilei invariance of the induction laws, contrary to most claims in literature. A noteworthy outcome of the theory is the conclusion that the so called Lorentz force on a charged particle is not an additional law of electromagnetism, but rather, when corrected by a factor one-half, a contribution to the electric field evaluated, according to Faraday law, by an observer testing a translating charged body crossing a region of uniform magnetic field. The formulation of the laws of electromagnetism in the four dimensional classical space-time, by stating the observer-dependent splitting for bodies in motions, provides a proof of Galilei invariance of all the electric and magnetic fields involved in the analysis.
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