Solutions for self-consistent systems in electromagnetism, where field equations are coupled with particle motion, are challenging but have been addressed in recent literature. Key references include "Classical Charged Particles" by Fritz Rohrlich, which provides a comprehensive overview, and a shorter article by D. J. Griffiths et al. that discusses the applicability of classical electrodynamics. The discussion also highlights a classical work by P. A. M. Dirac, known for its clarity and depth. These resources collectively illustrate the complexities of energy conservation in these systems. The topic remains an active area of research in classical electrodynamics.
