Average Lorentz self-force from electric field lines

摘要

We generalize the derivation of electromagnetic fields of a charged particle moving with a constant acceleration Singal (2011 Am. J. Phys. 79 1036) to a variable acceleration (piecewise constants) over a small finite time interval using Coulomb's law, relativistic transformations of electromagnetic fields and Thomson's construction Thomson (1904 Electricity and Matter (New York: Charles Scribners) ch 3). We derive the average Lorentz self-force for a charged particle in arbitrary non-relativistic motion via averaging the fields at retarded time.