Derivation of the Lorentz Force Law, the Magnetic Field Concept and the Faraday-Lenz Law using an Invariant Formulation of the Lorentz Transformation

This communication is devoted to a brief historical framework and to a comprehensive critical discussion concerning foundational issues of Electrodynamics. Attention is especially focused on the events which, about the end of XIX century, led to the notion of Lorentz force, still today ubiquitous in literature on Electrodynamics. Is this a noteworthy instance of a rule which, generated by an improper simplification of Maxwell-JJ Thomson formulation, is in fact physically unte...

The Lorentz Transformations are derived without any linearity assumptions and without assuming that y and z coordinates transform in a Galilean manner. Status of the invariance of the speed of light is reduced from a foundation of the Special Theory of Relativity to just a property which allows to determine a value of the physical constant. While high level of rigour is maintained, this paper should be accessible to a second year university physics student.

The standard classic special relativistic transformation of the electromagnetic (EM) field under proper Lorentz transformations is revisited. As to the pure Lorentz-boosts, popular treatments on EM transformation contemplate ideal geometries generating special static charge and steady current distributions and in conjunction, invoke parallel and perpendicular (to the boost-velocity) components of the fields so engendered; the outcomes subsequently being suitably generalized. ...

Two results support the idea that the scalar and vector potentials in the Lorenz gauge can be considered to be physical quantities: (i) they separately satisfy the properties of causality and propagation at the speed of light and not imply spurious terms and (ii) they can naturally be written in a manifestly covariant form. In this paper we introduce expressions for the Lorenz-gauge potentials at the present time in terms of electric and magnetic fields at the retarded time. ...

In this paper we present the formulation of relativistic electrodynamics (independent of the reference frame and of the chosen system of coordinates in it) that uses the Faraday bivector field F. This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames or, when some basis is introduced, every quan...

Lorentz Transformations of Special Relativity are derived from two postulates: the first is the Principle of Relativity, while the postulate of invariance of the velocity of light, used in usual derivations, is replaced by a law of lectro-magneto-statics and invariance of electrical charge. Our derivation does not require the assumption of regularity conditions of the Transformations, such as linearity and continuity required by other derivations. The level of the needed math...

The statement that Maxwell's electrodynamics in vacuum is already covariant under Lorentz transformations is commonplace in the literature. We analyse the actual meaning of that statement and demonstrate that Maxwell's equations are perfectly fit to be Lorentz-covariant; they become Lorentz-covariant if we construct to be so, by postulating certain transformation properties of field functions. In Aristotelian terms, the covariance is a plain potentiality, but not necessarily ...

We will display the fundamental structure of classical electrodynamics. Starting from the axioms of (1) electric charge conservation, (2) the existence of a Lorentz force density, and (3) magnetic flux conservation, we will derive Maxwell's equations. They are expressed in terms of the field strengths $(E,{\cal B})$, the excitations $({\cal D},H)$, and the sources $(\rho,j)$. This fundamental set of four microphysical equations has to be supplemented by somewhat less general ...

There is actually a mistake in this paper, but it is still a nice try worth a read. It is (not quite) proved that within the framework of Special Relativity, a force exerted on a \emph{classical particle} by a field must be of the form $\yv{E}+\yv{v}\times\yv{B}$, the Lorentz force form. The proof makes use of an action principle in which the action is the sum of a free particle part, and an interaction part.

This article contains a digest of the theory of electromagnetism and a review of the transformation between inertial frames, especially under low speed limits. The covariant nature of the Maxwell's equations is explained using the conventional language. We show that even under low speed limits, the relativistic effects should not be neglected to get a self-consistent theory of the electromagnetic fields, unless the intrinsic dynamics of these fields has been omitted completel...