Self consistent maxwells equations

[HomogenousCow]

Are there any articles on solutions for simple self consistent systems in EM, as in when the field equations are coupled with the motion of the particles, I would like to explicitly see the energy conservation in those systems.

 

[vanhees71]

There are! In fact, it's a very difficult problem, only solved very recently. The classical text on this with the newest results is

Fritz Rohrlich, Classical Charged Particles, 3rd Edition, World Scientific (2007)

A much shorter article, containing a thorough discussion of all the problems and how it's solved within the applicability range of classical electrodynamics is

D. J. Griffiths, T. C. Proctor, Darrell F. Schroeder, Abraham-Lorentz vs. Landau-Lifgarbagez, Am J. Phys 78, 391 (2010)
http://dx.doi.org/10.1119/1.3269900

A classical article, very nicely written, as anything by PAM Dirac is

P. A. M. Dirac, Proc. R. Soc. London, Ser. A 167, 148 (1938)
http://dx.doi.org/10.1098/rspa.1938.0124