Classical Physics

   

Maxwell Field Equation Tutorial: Its Causal Lorentz-Covariant Solution in Integral Form

Authors: Steven Kenneth Kauffmann

This tutorial sets out the detailed steps which produce the causal solution in integral form of the Maxwell field equation set, the causal solution being the one which vanishes in the absence of the source charge-current density, including during the time prior to that source being switched on. After warming up by obtaining the causal solution in integral form for the static source and field case, the Lorentz-covariant antisymmetric electromagnetic field tensor is defined, and the Maxwell field equation set is converted to its Lorentz-covariant form, whose formal causal solution is obtained in nine lines, but whose Green's function initially is ill-defined, a subtle issue whose ultimate causal resolution prompts a substantial effusion of ink. The integral solution which emerges can be exhibited either as manifestly Lorentz covariant or as very closely related to the static-case solution, except for systematic causal time retardation. Although direct solution for the electromagnetic field tensor is emphasized, the algebraically less involved four-vector intermediary potential approach is outlined in parallel.

Comments: 5 Pages.

Download: PDF

Submission history

[v1] 2019-03-06 14:04:44

Unique-IP document downloads: 0 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus