## LIENARD WIECHERT POTENTIAL PDF

might suggest that the retarded scalar potential for a moving point charge is {also } .. Thus, we have obtained the so-called Liénard-Wiechert retarded potentials. Lecture 27 – Liénard-Wiechert potentials and fields – following derivations in. Lecture When we previously considered solutions to the. The Lienard-Wiechert potentials are classical equations that allow you to compute the fields due to a moving point charge in the Lorenz Gauge Condition.

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Feynman’s proof utilizes a geometrical and fundamental integration argument. I like it, except this bit:. What makes me potentkal somehow is that in c we are counting in some of the charge we counted at b.

It wichert to me that it is this extra counting which makes the potential to be larger than expected, and I am uncomfortable with it. To see why, consider the following situation with discrete charges:. Here, the yellow line represents the light cone the observer being, of course at its apexand the blue dots, the places where the observer “sees” each of the constituent charges.

However, it is clear that if the charge cloud was small enough, or if we were far enough, the potential would be just the potential for a point charge of charge equal to the total charge of the cloud, as no charge is “overcounted” something which is also due to the cloud’s speed being less than c.

So why is my argument wrong? Is the continuity of the cloud, somehow crucial for the proof? I won’t try to defend Feynman’s derivation, which seems strangely non-relativistic. A similar argument is used by Schwartz in his “Principles of Electro-Dynamics”.

The argument proceeds in two steps: Consider, in the “primed” coordinates, a stationary discrete charge at the origin. Actually, Feynman performs this same calculation in Section As I said, I’m not going to try to defend Feynman’s derivation. Ah, Jackson sections Now to evaluate that delta function, we use the rule: Note the appearance of the “stretching” or “over-counting” factor.

So, there’s no contradiction: The “over-counting” that concerned you in Feynman’s development is just an approximation to the exact behavior of the light-cone delta-function, reducing to it in the limit.

I don’t think the increase in potential due to the moving charge leading to an “overcounting” IS in disagreement with Feynman’s result. When you say “it is clear that if the charge cloud was small enough, or if we were far enough, the potential would be just the potential for a point charge of charge equal to the total charge of the cloud” you’ve also implicitly made the assumption that the charge is moving slowly enough that it’s distribution may be integrated over at a single time co-ordinate.

Feynman highlights this when he says the equation preceding So think the way to think of it, is that the terms in the denominator for the potential act as an “enhancement factor” to the charge because of the integration over it’s history where the same spatial element of the charge may contribute over a period of time to the potential felt at any given moment to the observer. According to CK Whitney in multiple papers starting inthe Lienard-Wiechert potential of electrodynamics does not exhibit conservation of electric charge, similar to what the author of this question points out.

None of her papers can be found on the internet. She points out that the Lienard-Wiechert potentials are a solution to Maxwell’s equations, but do not satisfy the appropriate boundary conditions for highly-relativistic sources. According to her, this is due to a Jacobian factor missed, as many physicists do not apply a rigorous treatment of distribution theory and work with the Dirac delta function.

Jackson refutes Chubykalo’s argument by claiming that Lienard-Wiechert potentials are indeed a solution of Maxwell’s equations, but Chubykalo did not state the issue as precisely as Whitney, which is related to boundary conditions rather than solutions to the differential equations. Before Field or Chubykalo, Harold Aspden seemed to suggest that instantaneous fields were only needed if the internal structure of hadrons was different than leptons, which I think might be true in Einstein-Cartan theory.

Aspden has worked on various aspects of aether theories, and Whitney is also against notions of Einsteinian relativity, which led to their work being largely disregarded by the physics community at large. Jackson also points out that other gauges in classical electrodynamics lead to instantaneous dynamics, but is not needed in the Lorenz gauge. Whitney’s solution is geometrically simpler than Lienard and Wiechert, and resolves the issue pointed out by the author.

My thesis briefly discusses aspects of Whitney’s argument and cites many relevant references for further study. By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

### Electrodynamics/Lienard-Wiechert Potentials – Wikibooks, open books for an open world

Home Questions Tags Wiecheft Unanswered. I like it, except this bit: To see why, consider the following situation with discrete charges: You’re not the only one who’s noticed this double counting: What matters is if it gives a correct solution to Maxwell’s equations wicehert Feynman’s derivation does. Art Brown 4, 1 18 Thanks, but that doesn’t really explain why Feynman’s approach gives the right result while the method seems wrong to me.

Btw, a minor thing, but I think that your 4-current should have an extra factor of c Jackson agrees with me. I will patch it today or tomorrow. I think I need more time than I’ve got right now, to avoid making another goof. Thanks again for the catch. I have corrected the section reference.

## Liénard–Wiechert potential

At least, that’s how it seems to me I said ” It seems to me that it is this extra counting which makes the potential to be larger than expected”, so I agree with what you say in the first paragraph.

The rest, you seem to just be repeating the results, but not really address my argument. Hmmm, I think I may have misinterpreted your question somewhat. As to why this we may apply this reasoning to the case of discrete point charges, Feynman provides: David Chester 1 1.

## Electrodynamics/Lienard-Wiechert Potentials

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