Questions tagged [lienard-wiechert]

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28 questions
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About density charged in the Liénard - Wiechert Potential to Point Charge?

I'm reading Griffiths Ch. 10. In the 10.3.1 section, there's a proof of this integral $$\int \rho(r^\prime, t_r) \mathrm{d} \tau^\prime$$ which is not equal to the charge of the particle, but ...
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Feynman-Heaviside formula and Mach's principle

I was wondering if the Feynman-Heaviside formula for the electric field of a moving charge could be used to write down the force/reaction force between charges $q_1$ and $q_2$ in a Machian purely ...
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Electric field produced by a moving charged particle above a planar dielectric interface

The electrostatic field of a single charged particle above a planar dielectric interface is a standard example given in many books (see example 4.4 in Griffiths or https://en.wikipedia.org/wiki/...
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Lienard-Wiechert fields in D-dimentions

I tried to calculate Lienard-Wiechert fields in D-dimentions and got some expression with sums of derivatives, very ugly. Does anybody have "nice" expression for it?
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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)}{\...
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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 ...
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Confusion about Lorenz Gauge assumption in derivation of Liénard Wiechert Potentials/Fields

I have been going through Griffith's 'Introduction To Electrodynamics" 3rd Edition chapter 10 on potentials and fields and I am a little confused about the derivation of the Liénard Wiechert ...
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Lienard -Wiechert Potential Equation in Landau Vol 2

I am reading Laudau-Lifshitz The Classical Theory of Field (4th edition). In (63.2), it says In the system of reference in which the particle is at rest at time $t^\prime,$ the potential at the ...
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Retarded potentials and fields

Why can't we use retarded times to make an expression for retarded fields instead of potentials? As far as I know it doesn't work, since the solutions produced ("retarded fields") don't satisfy ...
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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 ...
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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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First question here. I'm really confused at the moment. An electron moves at constant velocity, no acceleration Wikipedia says here Lorentz: $$\mathbf E=\frac{q}{4\pi\epsilon_0}\frac{1-v^2/c^2}{1-v^... 1answer 452 views Surely force on shell can't be balanced by field momentum? Imagine a particle with charge q at rest at the origin. It is surrounded by a concentric spherical insulating shell, also at rest, with charge Q and radius R. At time t=0 I apply a constant ... 1answer 156 views Accelerated charge inside sphere (again!) Sorry to go on about this scenario again but I think something is going on here. Imagine a stationary charge q, with mass m, at the center of a stationary hollow spherical dielectric shell with ... 1answer 292 views Reaction-at-a-distance: Do charged plates immediately repel each other? Imagine that we have a pair of parallel plates, A and B, separated by some distance as in Fig. 1 above. At time t_1 we simultaneously charge both the plates. This could be done by previously ... 0answers 468 views Mathematical equivalence between Liénard-Wiechert potential and 4-potential in Rindler coordinates I'm studying the problem of the radiation of an uniformly accelerated point charge:$$x^{\mu}(\lambda)\to(g^{-1}\sinh g\lambda,0,0,g^{-1}\cosh g\lambda)$$I found that when a point charge is moving ... 1answer 639 views Retarded time Lienard Wiechert potential In a potential which needs to be evaluated at the retarded time, is this the time which represents the actual time the "physics" occurred? So t_{\text{ret}}=t-\frac{r}{c}, not just because it may be ... 1answer 325 views Electromagnetic inertia due to advanced radiation? The scalar potential \phi and vector potential A at a distance r from a charge q are given approximately by$$\phi = \frac{q}{r}\mathbf{A} = \frac{q\mathbf v}{r}$$where the constants ... 3answers 1k views Advanced Heaviside-Feynman formula implies electromagnetic inertia? The Heaviside-Feynman formula (see Feynman Lectures vol I Ch.28, vol II Ch. 21) gives the electric and magnetic fields measured at an observation point P due to an arbitrarily moving charge q$$ \...
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 \$...