Lorentz transformations for electromagnetic field vectors and the motion of charges in constant, homogeneous electromagnetic fields

Abstract

A surface in velocity space which corresponds to Lorentz transformations minimizing the magnitudes of the vectors of a given electromagnetic field is formed. The relation with Lorentz transformations which do not change the magnitudes of the given electromagnetic field is indicated. The behavior of field vectors in a system of reference bound with a charge moving in a constant and homogeneous electromagnetic field is considered. It is shown that an electric charge in a constant and homogeneous electromagnetic field with inclusion of the effect of radiation reaction moves in such a manner that in the reference frame moving with it the magnitudes of the electromagnetic field vectors decrease and their directions approach one another. The time of transition to the state in which the field vectors in the system bound with the charge are mutually parallel is determined.