The Galilean limits of Maxwell’s equations

@article{Heras2010TheGL,
  title={The Galilean limits of Maxwell’s equations},
  author={Jos{\'e} A. Heras},
  journal={American Journal of Physics},
  year={2010},
  volume={78},
  pages={1048-1055}
}
  • José A. Heras
  • Published 13 September 2010
  • Physics
  • American Journal of Physics
We show that if Maxwell’s equations are expressed in a form independent of specific units, at least three Galilean limits can be extracted. The electric and magnetic limits can be regarded as nonrelativistic limits because they are obtained using the condition |v|⪡c and restrictions on the magnitudes of the sources and fields. The third limit is called the instantaneous limit and is introduced by letting c→∞. The electric and instantaneous limits have the same form, but their interpretation is… 

Tables from this paper

Non-relativistic limits of Maxwell’s equations
In 1973, Le Bellac and Lévy-Leblond (Nuovo Cimento B 14 217–234) discovered that Maxwell’s equations possess two non-relativistic Galilei-covariant limits, corresponding to |E| ≫ c|B| (electric
Obtaining Maxwell's equations heuristically
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity
Unifying the Galilei and the Special Relativity II: the Galilei Electrodynamics
Using the concept of absolute time introduced in a previous work \cite{carvalho} we define two coordinate systems for spacetime, the Galilean and the Lorentzian systems. The relation between those
Alternative routes to the retarded potentials
Two procedures to introduce the familiar retarded potentials of Maxwell’s equations are reviewed. The first well-known procedure makes use of the Lorenz-gauge potentials of Maxwell’s equations. The
Using the Galilean Relativity Principle to Understand the Physical Basis for Magnetosphere-Ionosphere Coupling Processes
Abstract. We use the Principle of Galilean Relativity (PGR) to gain insight into the physical basis for magnetosphere-ionosphere coupling. The PGR states that the laws of physics are the same in all
Electromagnetic induction: physics, historical breakthroughs, epistemological issues and textbooks
The discovery of Electromagnetism by Ørsted (1820) initiated an “extraordinary decennium” ended by the discovery of electromagnetic induction by Faraday (1831). During this decennium, in several
ON THE AXIOMATIC STRUCTURE OF HERTZIAN ELECTRODYNAMICS
The mathematical foundation, axiomatic structure and principles of Hertzian Electrodynamics for moving bodies are reviewed. The feature of the present investigation is the introduction of a
Magnetars and Magnetic Separation of Chiral Radicals in Interstellar Space: Homochirality.
TLDR
It is asserted that, in interstellar space, a plethora of enantiomerically enriched dust clouds resulted from inter-magnetar-paramagnetic molecule force fields.
Charge Relaxation in Biological Tissues with Extremely High Permittivity
This letter presents a phenomenological model to describe charge relaxation (and the corresponding screening effect) in biological tissues, i.e., lossy dielectrics where a non-negligible conductivity
Reply to “Comments on Induction of an Electric Field in Human Bodies Moving Near MRI: An Efficient BEM Computational Procedure”
TLDR
The comment written by Cobos Sanchez provides the occasion to clarify a key point in the development of the formulation proposed in 2011 by the authors and shows that the working assumptions were properly disregarded because of insignificance on a practical side.
...
...

References

SHOWING 1-10 OF 17 REFERENCES
On some applications of Galilean electrodynamics of moving bodies
We discuss the seminal article by Le Bellac and Levy-Leblond in which they identified two Galilean limits (called “electric” and “magnetic” limits) of electromagnetism and their implications. Recent
Galilean electromagnetism
SummaryConsistent nonrelativistic electromagnetic theories are investigated by stressing the requirements of Galilean relativity. It is shown that Maxwell’s equations admit two possible
Can Maxwell’s equations be obtained from the continuity equation?
We formulate an existence theorem that states that, given localized scalar and vector time-dependent sources satisfying the continuity equation, there exist two retarded fields that satisfy a set of
Instantaneous fields in classical electrodynamics
In this paper we express the retarded fields of Maxwell's theory in terms of the instantaneous fields of a Galilei-invariant electromagnetic and we find the vector function χL whose spatial and
The covariant formulation of Maxwell's equations expressed in a form independent of specific units
The covariant formulation of Maxwell's equations can be expressed in a form independent of the usual systems of units by introducing the constants α, β and γ into these equations. Maxwell's equations
On the Galilean non-invariance of classical electromagnetism
When asked to explain the Galilean non-invariance of classical electromagnetism on the basis of pre-relativistic considerations alone, students—and sometimes their teachers too—may face an impasse.
Electromagnetics from a quasistatic perspective
Quasistatic models provide intermediate levels of electromagnetic theory in between statics and the full set of Maxwell’s equations. Quasistatics is easier than general electrodynamics and in some
Une nouvelle limite non-relativiste du groupe de Poincaré
It is shown that, for the Galilean approximation to the Poincaré group to be valid, not only do we have to consider pure Lorentz transformation with low velocities, but also great time-like
...
...