Radiation fields created by accelerated relativistic charges: A simple approach based on inertial moving charges

Abstract

An electrical circuit is considered a polygon in that it has edges and nodes. The moving (let’s say, relativistic) charges that change their velocity directions (i.e., are accelerating), radiate, and we confront this radiation with the well-known fact that DC current does not radiate at all. This method of dealing with “kinks” (i.e. sharp changes of velocity) leads us to obtain (relatively cheaply): 1) The fields of stopping charges, 2) The Biot-Savart law, and 3) The radiation field of an accelerated charge.This procedure avoids the use of retarded sources and is based on actual time or “should be actual” sources. Simple elementary arguments based on special relativity consider only inertial moving charges; the acceleration effects are implicit and obtained by consistency relations.