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Questions tagged [lienard-wiechert]

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0
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1answer
90 views

Poynting vector from 1st term in Lienard-Wiechert field

I start with 1st (non-radiative) term from Lienard-Wiechert fields: $$ \vec{E} = q (1-v^2) \frac{\vec{R_{t'}} - \vec{v}R_{t'}}{(R_{t'} - \vec{v}\vec{R_{t'}})^3} $$ $$ \vec{H} = - q (1-v^2) \frac{\...
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0answers
143 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)}{\...
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0answers
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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 ...
2
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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 ...
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0answers
33 views

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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0answers
50 views

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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0answers
25 views

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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0answers
28 views

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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0answers
134 views

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 ...