Abstract
This chapter explores the study of varying fields in the presence of arbitrarily moving charges. Because of the linearity of the field equations, the actual field will be the sum of the fields produced by all such elements. The charge de in a given volume element is a function of the time. The electric field of the Lienard–Wiechert potentials consists of two parts of different type. The first term depends only on the velocity of the particle (and not on its acceleration) and varies at large distances like 1/R 2 . The second term depends on the acceleration, and for large R it varies like 1/R. As for the first term, because it is independent of the acceleration, it must correspond to the field produced by a uniformly moving charge. For systems consisting of particles with the same charge-to-mass ratio, the appearance of radiation is put off to the fifth approximation in v/c ; in such a case, there is a Lagrangian to terms of fourth order in v/c .
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