Questions tagged [lienard-wiechert]
46 questions
12
votes
2 answers
From Liénard-Wiechert to Feynman potential expression
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') = \frac{q}{4\pi\epsilon_0} \frac{1}{r'} $,
where $…
Jodocus
- 255
8
votes
0 answers
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)}{\epsilon_0},\ \mathrm{and} &…
Sean E. Lake
- 22,927
6
votes
1 answer
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 sending a light signal to a charging apparatus at…
John Eastmond
- 6,111
6
votes
3 answers
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 $t_1$ and $t_r$ are related…
Ana S. H.
- 1,403
5
votes
1 answer
Deriving the Lienard-Wiechert Potentials
Let $\mathbf{w}(t)$ be the trajectory of a moving charge. Let the observation event be $(\mathbf{r},t)$.
The scalar potential is:
$$\varphi = \frac{q}{4\pi\epsilon_0}\int \frac{\delta\left(\mathbf{r'} - \mathbf{w}\left(t - \frac{|\mathbf{r} -…
Si Chen
- 425
5
votes
5 answers
Feynman's proof for Liénard-Wiechert's potential of a moving charge
Feynman's proof utilizes a geometrical and fundamental integration argument. I like it, except this bit:
What makes me unconfortable somehow is that in (c) we are counting in some of the charge we counted at (b). It seems to me that it is this…
guillefix
- 1,748
3
votes
1 answer
Electromagnetic inertia due to advanced radiation?
The scalar potential $\phi$ and vector potential $A$ at a distance $r$ from a charge $q$ are given approximately by
$$\phi = \frac{q}{r}$$
$$\mathbf{A} = \frac{q\mathbf v}{r}$$
where the constants have been suppressed.
The corresponding electric and…
John Eastmond
- 6,111
3
votes
1 answer
Does direct interparticle action imply advanced inertial forces?
In his Nobel lecture Richard Feynman states that by varying the Schwarzschild-Tetrode-Fokker direct interparticle action
$$A=-\sum_i m_i\int\big(\mathbf{\dot X_i}\cdot\mathbf{\dot X_i}\big)^{1/2}d\alpha_i+\frac{1}{2}\sum_{i\ne…
John Eastmond
- 6,111
3
votes
1 answer
why is advanced radiation absent?
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 observed so far only the retarded emission…
lurscher
- 14,933
3
votes
2 answers
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 Maxwell's equations, but I would like a more physical…
Stathis Artis
- 510
3
votes
0 answers
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 the divergence of the lienard wiechert fields to…
user55782
- 31
2
votes
2 answers
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 horizontal acceleration $\mathbf{a}$ to the…
John Eastmond
- 6,111
2
votes
0 answers
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 along the $z$ axis with a constant acceleration…
Ana S. H.
- 1,403
2
votes
2 answers
Gauge invariant Green's function for electrodynamics
Varying the electromagnetic action
\begin{equation}
S=-m c \int d s\left(\dot{z}^{2}\right)^{\frac{1}{2}}-\frac{e}{c} \int d s A_{\mu} \dot{z}^{\mu}-\frac{1}{16 \pi c} \int d^{4} x F_{\mu \nu} F^{\mu \nu}
\end{equation}
we get the two equations of…
NicAG
- 498
2
votes
2 answers
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 that you are receiving a signal at light speed…
shilov
- 295
- 2
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