Q on Jackson. Lorentz force modification for radiation?

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Discussion Overview

The discussion revolves around the modification of the Lorentz force equation to account for radiation effects on charged particles, as mentioned in Jackson's textbook. Participants explore the implications of neglecting radiation in the standard Lorentz force equations and seek clarification on how to incorporate radiation into the equations of motion.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that Jackson states the Lorentz force equations are sufficient for describing motion in an external field while neglecting radiation effects.
  • Another participant questions whether Jackson provides a modification later in the text, indicating a lack of clarity on the topic.
  • A participant mentions that classical electromagnetism lacks a rigorous derivation for the interaction of a point charge with its own electromagnetic field.
  • It is suggested that the modification is known as the Abraham-Lorentz force, which is referenced in Jackson's later chapters discussing radiation damping.
  • One participant expresses gratitude for the reference to the Abraham-Lorentz force and the related paper.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specifics of the modification to the Lorentz force equation, and multiple viewpoints regarding the treatment of radiation effects remain present.

Contextual Notes

There is mention of a lack of rigorous derivation in classical electromagnetism regarding the interaction of a point charge with its own electromagnetic field, indicating potential limitations in understanding the topic fully.

Who May Find This Useful

This discussion may be of interest to those studying classical electromagnetism, particularly in relation to radiation effects on charged particles and modifications to the Lorentz force law.

Peeter
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Reading Jackson this morning, where it was stated that the Lorentz force equations:

[tex] \frac{dU^\alpha}{d\tau} = \frac{e}{mc} F^{\alpha\beta} U_\beta[/tex]

are sufficient to describe the motion of a charged particle in an external field, neglecting the effects of radiation.

That radiation qualifer suprised me. What is the modification of the Lorentz force equation (or Lagrangian) that correctly models radiation too?
 
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Isn't it given in Jackson book later on?
 
Bob_for_short said:
Isn't it given in Jackson book later on?

If it is I wouldn't know yet. The qualification is made in passing, and there's no hint of what to look for. Does the corrected force law have a name that I could look for in the index?
 
Jackson (or for that matter any other textbook) does not give a rigorous derivation; this was one of big problems of classical electromagnetism: How to take into account the interaction of a point charge with its ow electromagnetic field in a rigorous way?

The solution to this problem is given here:

http://arxiv.org/abs/0905.2391
 
Peeter said:
If it is I wouldn't know yet. The qualification is made in passing, and there's no hint of what to look for. Does the corrected force law have a name that I could look for in the index?

Yes, there is a name, it is the Abraham-Lorentz force. Try Wikipedia.
 
In my old 2nd edition of Jackson, the Abraham-Lorentz force is in chapter 17 which discusses radiation damping.

Jackson said:
The question now arises as to how to include the reactive effects of radiation in the equations of motion for a charged particle. [...]
 
thanks for the paper and the name.
 

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