Maxwell's equations in the electrodynamics of moving bodies
Abstract
The electromagnetic field of a point charge moving in free space at velocity u and acceleration a is evaluated on the basis of Maxwell's equations, and an approximation of this field is made for nonrelativistic velocities. Under the hypothesis that the fields of more complex systems can be obtained by means of the superposition of the fields of the various point charges present in these systems, and under other less important hypotheses, the form of the field equations in systems with moving charge carriers is calculated. It results that Maxwell's equations seem to be valid in an inertial frame for systems in which only metallic type conductors carry considerable currents, and when only very slow body motions are involved. If moving bodies, or current in nonmetallic type conductors, are involved, other equations must be used, whose form is proposed in this paper. In such equations the extra terms not contained in Maxwell's equations represent fields depending on the square of the particle velocity, and cannot be obtained by the magnetic field, which produces only linear terms, except for the Lorentz field.
 Publication:

Nuovo Cimento B Serie
 Pub Date:
 July 1975
 DOI:
 10.1007/BF02722816
 Bibcode:
 1975NCimB..28..191V
 Keywords:

 Electrodynamics;
 Electromagnetic Fields;
 Maxwell Equation;
 Particle Motion;
 Charge Carriers;
 Field Theory (Physics);
 Inertial Reference Systems;
 Invariance;
 Lorentz Transformations;
 Particle Acceleration;
 Point Sources;
 Relativity;
 Physics (General)