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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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Advanced fields are absorbed by the charges and retarded fields are emitted. From Wikibooks, open books for an open world. Ah, Jackson sections I have corrected the section reference.

Thus, the charged particle is “smeared” out! So why is my argument wrong? This second term is connected with electromagnetic radiation.

Thanks, but that doesn’t really explain why Feynman’s approach gives the right result while the method seems wrong to me. Is the continuity of the cloud, somehow crucial for the proof? There is 1 pending change awaiting review.

As to why this we may apply this reasoning to the case of discrete point charges, Feynman provides: Electromagnetic radiation leinard the form of waves can be obtained from these potentials.

As I said, I’m not going to try to defend Feynman’s derivation. Multiplying electric parameters of both problems by arbitrary real constants produces a coherent interaction of light with matter which generalizes Einstein’s theory A. The first of these is the static electric or magnetic field term that depends only on the distance to the moving charge, and does not depend on the retarded time at all, if the velocity of the source is constant.


So, there’s no contradiction: The retarded time is not guaranteed to exist in general. This is true over any distance separating objects. Part of a series of articles about Electromagnetism Electricity Magnetism Electrostatics.

Lineard, introducing the fluctuations of the zero point field produces Willis E.

Liénard–Wiechert potential

Thus, electromagnetic radiation described by the second term always appears to come from the direction of the position of the emitting charge at the retarded time.

Hmmm, I think I may have misinterpreted your question somewhat. To compute energy, it is necessary to use the absolute fields which includes the zero point field; otherwise, an error appears, for instance in photon counting. This trick allows Maxwell’s equations to become linear in matter. 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.

To see why, consider the following situation with discrete charges:. None of her papers can be found on the internet. Post as a guest Name. Even though we are considering a point particle, the formula is still wrong, since the correction factor doesn’t depend on geometric size! These are the Lienard-Wiechert Potentials for a moving charge.

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

I think I need more time than I’ve got right now, to avoid making another ptoential. 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.


It is important to take into account the zero point field discovered by Planck M. David Chester 1 1. Feynman highlights this when he says the equation preceding Home Questions Tags Users Unanswered.

Electrodynamics/Lienard-Wiechert Potentials

I don’t think the increase in potential due to the moving charge leading to an “overcounting” IS in disagreement with Feynman’s result.

From Wikipedia, the free encyclopedia. At least, that’s how it seems to me The reason is very subtle: What matters is if it gives a correct solution to Maxwell’s equations and Feynman’s derivation does. Consider, in the “primed” coordinates, a stationary discrete charge at the origin. This is not an effect of length contraction; this is rather more similar to the Doppler shift.

We will use the formulas developed in the previous section to find the potentials and the fields. I will patch it today or tomorrow.