Questions tagged [lienard-wiechert]
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40
questions
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2answers
64 views
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 \...
0
votes
1answer
27 views
Dirac's radiated field definition
In Dirac's 'Classical theory of radiating electrons', submitted in 1938, the electromagnetic radiated field is defined as:
$$F_\text{rad}^{\mu\nu}=F_\text{ret}^{\mu\nu}-F_\text{adv}^{\mu\nu}$$
Where $...
0
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1answer
28 views
Electromagnetic inertial reaction force?
I accelerate charged particle $A$ causing virtual photons to travel to distant charged particle $B$ which feels an electromagnetic force proportional to $A$'s acceleration (for a classical field ...
0
votes
1answer
48 views
Retarder potential strange derivation
I have an old French textbook (the author died a few years ago) that develops in quite a very very detailed way the relativist Larmor formula on more than 35 pages.
However, I've been stuck for a few ...
2
votes
2answers
172 views
Energy paradox in classical electrodynamics?
Consider two massive charged objects at rest with a large horizontal distance $d$ between them (object $1$: mass $m_1$, charge $q_1$ and object $2$: mass $m_2$, charge $q_2$).
I apply a constant ...
1
vote
1answer
43 views
Can we use the method of image charges when the source is time dependent?
Let's say we have a grounded conducting plane at $z=0$ and a charge moving above it with some position $\vec{r}_q(t)$ and velocity $\vec{v}_q(t)$. I know that in the particular case when the velocity ...
1
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0answers
32 views
Reflection and refraction by moving charge: can method of images be used?
Suppose we have a point charge moving inside the halfspace $z>0$ with a given trajectory $r(t)$. Assume that $z>0$ halfspace is Vacuum and the $z<0$ halfspace is glass or some linear ...
1
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0answers
26 views
Estimation of power of received radio signal
I would like to estimate the magnitude of a radio signal received from a transmitter by first principles:
Transmitter antenna length $L=1$ m
Transmitter antenna cross-sectional area $A=1\hbox{ cm}^2$
...
0
votes
1answer
54 views
Do the electric field and magnetic field derived from the Lienard-Wiechert potentials satisfy Gauss's law?
I've already got the electric fields and magnetic fields derived from the Lienard-Wiechert potentials:
$${\bf E}=\frac{q}{4\pi\epsilon_0}\frac{R}{(\bf R\cdot u)^3}[(c^2-v^2){\bf u}+\bf
R\times(u\...
0
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0answers
31 views
How do the time reversed retarded solutions to Maxwell's equations maintain T-symmetry?
Maxwell's equations are T-symmetrical in that they remain invariant to a change in the sign of $dt$ if the sign of $B$ and $J$ are also reversed. Hence the corresponding time reversed solution is ...
0
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2answers
174 views
Retarded potentials and special relativity?
I'm curious. . . is there a substantial difference between a classical retarded potential, such as for the electric/magnetic fields in EM, and special relativistic formulations of EM? What i'm meaning ...
0
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1answer
104 views
Where can I find a detailed derivation of Lienard-Wiechert Fields?
Wikipedia (https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential) says
"The calculation is nontrivial and requires a number of steps".
Nice but a link would be good to add ...
3
votes
1answer
127 views
Does direct interparticle action imply advanced inertial forces?
In his Nobel lecture Richard Feynman states that by varying the Schwarzschild-Tetrode-Fokker direct interparticle action
$$A=-\sum_i m_i\int\big(\mathbf{\dot X_i}\cdot\mathbf{\dot X_i}\big)^{1/2}d\...
1
vote
1answer
136 views
Physical Justification of Retarded Potentials
How did physicists interpret the physical significance of retarded potential before the advent of special relativity? , Did it account for the time taken by electromagnetic forces to propagate through ...
2
votes
2answers
110 views
What does the interaction between two charges depend on?
In our intro to electrodynamics course, we were told that the interaction between two charges depends on:
➢Magnitude of the charges
➢Separation distance between the charges
➢Velocities of the ...
1
vote
0answers
90 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 ...
8
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0answers
178 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)}{\...
2
votes
1answer
129 views
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 ...
0
votes
1answer
460 views
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 ...
0
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0answers
170 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 point ...
1
vote
1answer
732 views
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 ...
2
votes
1answer
1k views
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:
$$\varphi = \frac{q}{4\pi\epsilon_0}\int \frac{\delta\left(\mathbf{r'...
0
votes
1answer
135 views
Poynting vector from 1st term in Lienard-Wiechert field
I start with 1st (non-radiative) term from Lienard-Wiechert fields:
$$ \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{\...
10
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2answers
1k views
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') =...
1
vote
2answers
228 views
Is the Liénard-Wiechert electric field conservative?
I know that an accelerated charge should emit an e.m. field and loose energy. Therefore, the Liénard-Wiechert (L.W.) electric field of an accelerated charge should be non-conservative.
But I checked ...
2
votes
1answer
228 views
Falling charged objects: energy conservation paradox?
Imagine that we start with two oppositely charged objects on the ground, separated by a distance $d$, with charges $+q$, $-q$ and masses $m$.
We raise them both up to a height $h$.
In doing so we ...
1
vote
2answers
214 views
Energy conservation in electrodynamic system
Consider two charged particles initially at rest in the configuration below.
Let us assume the following:
Starting at time $t=0$, we apply a constant force $f$ to the the bottom particle so that it ...
0
votes
1answer
73 views
Lienard-Wiechert fields for low velocity source
I would like to use the Lienard-Wiechert E and B field expressions for a slowly moving charge where $\beta = v/c << 1$.
Is there an accepted approximate form to use?
Can one just set $\gamma = ...
6
votes
4answers
3k 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 ...
3
votes
0answers
138 views
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 ...
1
vote
3answers
1k views
Field of moving charge / Lorentz; Liénard-Wiechert
First question here. I'm really confused at the moment.
An electron moves at constant velocity, no acceleration
Wikipedia says here Lorentz:
$$\mathbf E=\frac{q}{4\pi\epsilon_0}\frac{1-v^2/c^2}{1-v^...
2
votes
2answers
470 views
Surely force on shell can't be balanced by field momentum?
Imagine a particle with charge $q$ at rest at the origin.
It is surrounded by a concentric spherical insulating shell, also at rest, with charge $Q$ and radius $R$.
At time $t=0$ I apply a constant ...
1
vote
1answer
188 views
Accelerated charge inside sphere (again!)
Sorry to go on about this scenario again but I think something is going on here.
Imagine a stationary charge $q$, with mass $m$, at the center of a stationary hollow spherical dielectric shell with ...
6
votes
1answer
312 views
Reaction-at-a-distance: Do charged plates immediately repel each other?
Imagine that we have a pair of parallel plates, $A$ and $B$, separated by some distance as in Fig. $1$ above.
At time $t_1$ we simultaneously charge both the plates. This could be done by previously ...
2
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0answers
499 views
Mathematical equivalence between Liénard-Wiechert potential and 4-potential in Rindler coordinates
I'm studying the problem of the radiation of an uniformly accelerated point charge:
$$x^{\mu}(\lambda)\to(g^{-1}\sinh g\lambda,0,0,g^{-1}\cosh g\lambda)$$
I found that when a point charge is moving ...
2
votes
1answer
758 views
Retarded time Lienard Wiechert potential
In a potential which needs to be evaluated at the retarded time, is this the time which represents the actual time the "physics" occurred? So $t_{\text{ret}}=t-\frac{r}{c}$, not just because it may be ...
3
votes
1answer
344 views
Electromagnetic inertia due to advanced radiation?
The scalar potential $\phi$ and vector potential $A$ at a distance $r$ from a charge $q$ are given approximately by
$$\phi = \frac{q}{r}$$
$$\mathbf{A} = \frac{q\mathbf v}{r}$$
where the constants ...
1
vote
3answers
2k views
Advanced Heaviside-Feynman formula implies electromagnetic inertia?
The Heaviside-Feynman formula (see Feynman Lectures vol I Ch.28, vol II Ch. 21) gives the electric and magnetic fields measured at an observation point $P$ due to an arbitrarily moving charge $q$
$$ \...
3
votes
3answers
7k 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 $...
3
votes
1answer
859 views
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 ...
