Inter-charge forces in relativistic classical electrodynamics: electromagnetic induction in different reference frames

We show that invariance of the electric charge and relativistic kinematics lead to the transformation equations for electric field intensity and the magnetic induction.

In this article, it is pointed out that Faraday induction can be treated from an untraditional, particle-based point of view. The electromagnetic fields of Faraday induction can be calculated explicitly from approximate point-charge fields derived from the Li\'enard-Wiechert expressions or from the Darwin Lagrangian. Thus the electric fields of electrostatics, the magnetic fields of magnetostatics, and the electric fields of Faraday induction can all be regarded as arising fr...

It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. The formalism is shown to provide a short derivation, in which the 4--vector electromagnetic potential plays a crucial role, of the Lorentz force law of classical electrodynamics, and the conventional definition of the magnetic field in terms spatial derivatives of the 4--vector potential. The time component of the re...

A new approach to classical electrodynamics is presented, showing that it can be regarded as a particular case of the most general relativistic force field. In particular, at first it is shown that the structure of the Lorentz force comes directly from the structure of the three-force transformation law, and that E and B fields can be defined, which in general will depend not only on the space-time coordinate, but also on the velocity of the body acted upon. Then it is proved...

The Lorentz law of force is the fifth pillar of classical electrodynamics, the other four being Maxwell's macroscopic equations. The Lorentz law is the universal expression of the force exerted by electromagnetic fields on a volume containing a distribution of electrical charges and currents. If electric and magnetic dipoles also happen to be present in a material medium, they are traditionally treated by expressing the corresponding polarization and magnetization distributio...

We analyze the transformation properties of Faraday law in an empty space and its relationship with Maxwell equations. In our analysis we express the Faraday law via the four-potential of electromagnetic field and the field of four-velocity, defined on a circuit under its deforming motion. The obtained equations show one more facet of the physical meaning of electromagnetic potentials, where the motional and transformer parts of the flux rule are incorporated into a common ph...

The Coulomb force, established in the rest frame of a source-charge $Q$, when transformed to a new frame moving with a velocity $\vec{V}$ has a form $\vec{F}= q\vec{{E}} + q\vec{v} \times \vec{{B}}$, where $\vec{{E}}=\vec{E}'_\parallel + \gamma\vec{E}'_\perp $ and $\vec{{B}}= \vec{\frac{V}{c^2}} \times \vec{{E}}$ and $\vec{E}'$ is the electric field in the rest frame of the source. The quantities $\vec{E}$ and $\vec{B}$ are then manifestly interdependent. We prove that they a...

Although relativistic electrodynamics is more than 100 year old, there is one neglected topic in its presentation and application: relativistic transformations of electromagnetic integrals. Whereas in theoretical and applied electrodynamics electric and magnetic fields are mainly expressed in terms of integrals over charge and current distributions, relativistic transformations are traditionally applied to point charges and elementary currents. The purpose of this paper is to...

In this paper it is shown that the real cause of the apparent electrodynamic paradox discussed by Jackson [J. D. Jackson, Am. J. Phys. 72, 1484 (2004)] is the use of three-dimensional (3D) quantities E, B, F, L, N, .. . When 4D geometric quantities are used then there is no paradox and the principle of relativity is naturally satisfied.

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...