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

How to get from static to dynamic electromagnetism

  • J. König
  • Physics
    European Journal of Physics
  • 2021
We demonstrate how to derive Maxwell’s equations, including Faraday’s law and Maxwell’s correction to Ampère’s law, by generalizing the description of static electromagnetism to dynamical situations.

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

The Helmholtz theorem and retarded fields

Textbooks frequently use the Helmholtz theorem to derive expressions for electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for time-dependent

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

Voigt's transformations and the beginning of the relativistic revolution

In 1887 W. Voigt published a paper on the Doppler effect, whic h marked the birth of the relativistic revolution. In his paper Voigt derived a set of spacetime transf ormations by demanding

Forty years of Galilean Electromagnetism (1973–2013)

We review Galilean Electromagnetism since the 1973 seminal paper of Jean-Marc Lévy-Leblond and Michel Le Bellac and we explain for the first time all the historical experiments of Rowland, Vasilescu

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

References

SHOWING 1-10 OF 24 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

On the electrodynamics of moving bodies at low velocities

We discuss an article by Le Bellac and Lévy-Leblond in which they have identified two Galilean limits of electromagnetism (1973 Nuovo Cimento B 14 217–33). We use their results to point out some

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

On the electrodynamics of Minkowski at low velocities

The Galilean constitutive equations for the electrodynamics of moving media are derived for the first time. They explain all the historic and modern experiments which were interpreted so far in a

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

If Maxwell had worked between Ampère and Faraday: An historical fable with a pedagogical moral

If one drops the Faraday induction term from Maxwell’s equations, they become exactly Galilei invariant. This suggests that if Maxwell had worked between Ampere and Faraday, he could have developed

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.