Questions tagged [lienard-wiechert]

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When studying the potential of an uniformly moving charge in vacuum, Feynman proposes to apply a Lorentz transformation on the Coulomb potential, which reads in the rest frame $\phi'(\mathbf r',t') =... 0answers 147 views Has the Helmholtz decomposition of the$\mathbf{E}$field from the Liénard–Wiechert potentials been worked out? If you look at Maxwell's equations for$\mathbf{E}(\mathbf{x},t)they split neatly into two categories. They are: \begin{align} \nabla\cdot\mathbf{E}(\mathbf{x},t)&=\frac{\rho(\mathbf{x},t)}{\... 3answers 2k views Feynman's proof for Liénard-Wiechert's potential of a moving charge Feynman's proof utilizes a geometrical and fundamental integration argument. I like it, except this bit: What makes me unconfortable somehow is that in (c) we are counting in some of the charge we ... 1answer 293 views Reaction-at-a-distance: Do charged plates immediately repel each other? Imagine that we have a pair of parallel plates,A$and$B$, separated by some distance as in Fig.$1$above. At time$t_1$we simultaneously charge both the plates. This could be done by previously ... 3answers 5k views What is the physical meaning of retarded time? Consider this figure Now, when I measure a field produced by the charge$e$at the point$\mathbf r$, at the time$t=t_1$, it means that the charge sent the signal field at the time$t=t_r$, where$...
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The scalar potential $\phi$ and vector potential $A$ at a distance $r$ from a charge $q$ are given approximately by $$\phi = \frac{q}{r}$$ $$\mathbf{A} = \frac{q\mathbf v}{r}$$ where the constants ...
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the Lienard-Wiechert green functions have future and past null cones of radiation. Maxwell equations allow for a continuous range of mixtures between the retarded and advanced components, but we have ...
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How can I calculate the divergence of the lienard wiechert eletric field?

I was reading Introduction to Eletrodynamics by Griffiths and I see that´s nothing there about to prove the gauss law for charges in arbitrary motion and non constant velocity . So I try to calculate ...
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Liénard-Wiechert Fields for a static particle

Note: There was already a similar question to mine, but it did not actually answer my question: Retarded time Lienard Wiechert potential When considering the Liénard-Wiechert fields, which are the ...