Self consistent maxwells equations

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SUMMARY

This discussion focuses on self-consistent systems in electromagnetic (EM) theory, particularly the coupling of field equations with particle motion. Key resources include "Classical Charged Particles, 3rd Edition" by Fritz Rohrlich, which addresses the complexities of this topic, and the article by D. J. Griffiths et al., which discusses solutions within classical electrodynamics. Additionally, P. A. M. Dirac's classic work provides foundational insights into the subject. These references highlight the recent advancements in understanding energy conservation in these systems.

PREREQUISITES
  • Understanding of classical electrodynamics
  • Familiarity with the concepts of self-consistent systems
  • Knowledge of particle dynamics in electromagnetic fields
  • Basic grasp of energy conservation principles in physics
NEXT STEPS
  • Read "Classical Charged Particles, 3rd Edition" by Fritz Rohrlich
  • Study the article "Abraham-Lorentz vs. Landau-Lifgarbagez" by D. J. Griffiths et al.
  • Explore P. A. M. Dirac's 1938 paper on electromagnetic theory
  • Investigate recent advancements in self-consistent EM systems
USEFUL FOR

Physicists, researchers in electromagnetism, and students studying advanced topics in classical electrodynamics will benefit from this discussion.

HomogenousCow
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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.
 
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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
 

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