Relativistic electrodynamics as an extrapolation of relativistic kinematics

TL;DR

This paper derives the transformation equations for electric and magnetic fields using relativistic kinematics and fundamental laws, avoiding traditional Lorentz force transformations, thereby providing a new perspective on relativistic electrodynamics.

Contribution

It presents a novel derivation of E and B field transformations based solely on relativistic kinematics and basic laws, bypassing Lorentz force component transformations.

Findings

Derived transformation equations for E and B fields from kinematics and laws.

Connected electric and magnetic fields through relativistic addition and Lorentz transformations.

Provided an alternative approach to relativistic electrodynamics derivation.

Abstract

After having identified all the possible relationships between the electric field and the magnetic field in a given inertial reference frame we derive the transformation equations for the components of these fields. Special relativity is involved via the addition law of parallel speeds or via the Lorentz transformations for the space-time coordinates of the same event. Electricity and magnetism are involved via Gauss's and Ampere's laws. In this way we avoid the transformation equations for the Lorenz force components which are used in most derivations of the transformation equations for E and B fields.