How to derive Lienard-Wiechert potential from Maxwell's equation?

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Discussion Overview

The discussion revolves around the derivation of the Lienard-Wiechert potentials from Maxwell's equations. Participants are seeking rigorous methods and various sources for this derivation, exploring different texts and approaches.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant references the Feynman Lectures on Physics but criticizes the derivation as not rigorous due to its reliance on a special case.
  • Another participant mentions Jackson's derivation in chapter 14, noting the necessity of understanding relativistic formalism and retarded Green's functions to follow the derivation.
  • A participant expresses a lack of familiarity with the manipulations involved in Jackson's approach and seeks additional derivations.
  • Griffiths' "Electrodynamics" is suggested by a participant as having a self-contained and intuitive derivation in chapter 10, despite the participant's personal reservations about Griffiths' work.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single rigorous derivation method, as multiple sources and approaches are discussed, indicating a variety of opinions and preferences.

Contextual Notes

Some participants express uncertainty regarding their familiarity with the necessary mathematical tools and concepts, which may limit their ability to engage with the derivations discussed.

kof9595995
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I've seen one derivation on Feynman Lectures on Physics, but the derivation is not really rigorous(he took a very special case for the derivation),I googled about the topic and couldn't find a satisfactory one. So can anybody give me a rigorous one?
Thanks in advance
 
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Jackson derives it in 6 equations at the start of chapter 14, but you need to be familiar with the relativistic formalism (current and potential as four-vectors) and retarded Green's functions. If you are familiar with these, than the LW potentials follow from:

\mathbf{A} = \frac{4\pi}{c} \int d^4x' G(x-x') \mathbf{J}(x')

\mathbf{J}(x') = \int d\tau \mathbf{v}(\tau) \delta^4(x' - r(\tau))

where r is the trajectory (four-vector), and v is the four-velocity. All you do is sub the second eq into the first and crank it out to derive the LW potentials.
 
Thanks.But I'm not quite familiar with the manipulation of those, I'll give a shot.
And are there any other derivations avaliable?
 
I'm not a big fan of Griffiths, but his "Electrodynamics" text has a pretty good derivation of it in chapter 10 - self contained and quite intuitive.


-----
Assaf
http://www.physicallyincorrect.com"
 
Last edited by a moderator:
ozymandias said:
I'm not a big fan of Griffiths, but his "Electrodynamics" text has a pretty good derivation of it in chapter 10 - self contained and quite intuitive.


-----
Assaf
http://www.physicallyincorrect.com"
Thanks, I will have a look at it.
 
Last edited by a moderator:

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