Implications of Galilean Electromagnetism in Numerical Modeling
Keywords:
Implications of Galilean Electromagnetism in Numerical ModelingAbstract
The purpose of this article is to present a wider frame to treat the quasi-static limit of Maxwell’s equations. We discuss the fact that there exists not one but indeed two dual Galilean limits, the electric and the magnetic one. We start by a re-examination of the gauge conditions and their compatibility with Lorentz and Galilean covariance. By means of a dimensional analysis on fields and potentials we first emphasize the correct scaling yielding the equations in the two limits. With this particular point of view, the gauge conditions of classical electromagnetism are continuity equations whose range of validity depend on the relativistic or Galilean nature of the underlying phenomenon and have little to do with mathematical closure assumptions taken without physical motivations. We then present the analysis of the quasi-static models in terms of characteristic times and visualize their domains of validity in a suitable diagram. We conclude by few words on the Galilean electrodynamics for moving media, underlying the transformation laws for fields and potentials which are valid in the different limits.
Downloads
References
M. Le Bellac and J.-M. Lévy-Leblond,
“Galilean Electromagnetism,” Il Nuovo Cimento, vol. 14, pp. 217-233, 1973.
J. R. Melcher and H. A. Haus, Electromagnetic Fields and Energy, Prentice Hall,
M. de Montigny and G. Rousseaux, “On
Some Applications of Galilean Electrodynamics of Moving Bodies,” Am. J. Phys.,
vol. 75, pp. 984-992, 2007.
G. I. Barenblatt, Scaling, Cambridge University Press, 2003.
E. Guyon, J.-P. Hulin, L. Petit and C. D.
Mitescu, Physical Hydrodynamics, Oxford
University Press, 2001.
T. Steinmetz, S. Kurz and M. Clemens,
“Domains of Validity of Quasistatic and
Quasistationary Field Approximations,”
COMPEL, vol. 30, no. 4, pp. 1237-1247,
O. D. Jefimenko, “A Neglected Topic
in Relativistic Electrodynamics: Transformation of Electromagnetic Integrals”,
arXiv:physics/0509159v1, pp. 1-9, 2005.
J. A. Heras, “The c Equivalence Principle
and the Correct Form of Writing Maxwell’s
Equations,” European Journal of Physics,
vol. 31, pp. 1177-1185, 2010.
J. A. Stratton, Electromagnetic Theory,
McGraw-Hill, New York, 1941.
G. Benderskaya, Numerical Methods for
Transient Field-Circuit Coupled Simulations Based on the Finite Integration Technique and a Mixed Circuit Formulation,
PhD, 2007.
H. Goldstein, Classical Mechanics, 2nd ed.,
Addison-Wesley Reading, MA, 1981.
A. Einstein and J. Laub, 1908, articles available at http://einstein-annalen.
mpiwg-berlin.mpg.de/home.
H. Ammari, A. Buffa and J.-C. Nédélec, “A
Justification of Eddy Currents Model for the
Maxwell Equations,” SIAM J. Appl. Math.,
vol. 60, no. 5, pp. 1805-1823, 2000.
