Self consistent maxwells equations

In summary, There are several articles available on solutions for simple self consistent systems in EM, particularly in cases where the field equations are coupled with the motion of particles. One such article is "Classical Charged Particles" by Fritz Rohrlich, which was published in 2007. Another, shorter article that discusses this problem in depth within the realm of classical electrodynamics is "Abraham-Lorentz vs. Landau-Lifgarbagez" by D. J. Griffiths, T. C. Proctor, and Darrell F. Schroeder, published in 2010. Finally, a well-written article on this topic is "Proc. R. Soc. London, Ser. A" by P.
  • #1
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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  • #2
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
 

FAQ: Self consistent maxwells equations

What are self consistent Maxwell's equations?

Self consistent Maxwell's equations are a set of four equations that describe the behavior of electric and magnetic fields in space. They are fundamental to the study of electromagnetism and are used to understand and predict the behavior of electromagnetic waves, including light.

Why are self consistent Maxwell's equations important?

Self consistent Maxwell's equations are important because they provide a fundamental framework for understanding the behavior of electric and magnetic fields. They have been extensively tested and have been found to accurately describe the behavior of electromagnetic waves in a variety of situations. They are also used in many different fields, including engineering, physics, and telecommunications.

What are the four equations in self consistent Maxwell's equations?

The four equations in self consistent Maxwell's equations are Gauss's law, Gauss's law for magnetism, Faraday's law, and Ampere's law. These equations describe the relationships between electric and magnetic fields, as well as how these fields interact with charged particles.

How are self consistent Maxwell's equations derived?

Self consistent Maxwell's equations are derived from the fundamental principles of electromagnetism, including Coulomb's law, the Biot-Savart law, and the Lorentz force law. They were first described by James Clerk Maxwell in the 1860s and have been refined and expanded upon by subsequent scientists.

What are some applications of self consistent Maxwell's equations?

Self consistent Maxwell's equations have a wide range of applications, including in the design and engineering of electronic devices, the study of optics and light, and the development of telecommunications technology. They are also used in fields such as medical imaging, remote sensing, and materials science.

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