Questions tagged [lienard-wiechert]
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Derivation of Liénard-Wiechert Potential in quasi-rest reference frame
In electrodynamics, using the Maxwell equation:
$\partial_{\mu}F^{\mu\nu}=\frac{4\pi}{c}J^{\nu}$, together with the Lorentz gauge: $\partial^{\mu}A_{\mu}=0$, we can derive the equation for vector ...
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Where did I misunderstand Lienard-Wiechert?
Here's my problem.
Intensity of radiation follows an inverse square law with distance.
https://byjus.com/physics/inverse-square-law/
Electromagnetic fields can be derived from the Lienard Wiechert ...
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Is there anything special about sinusoidal EM waves? How does the strength of a purely sinusoidal EM wave vary with distance from the source?
In this atoms and sporks video, the narrator mentions that not all Electromagnetic (EM) waves have to be sinusoidal. In fact, he gives a nice animation of such a case at 16:42.
He talks about a ...
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Do the Lienard Wiechert Potentials satisfy the wave equation?
The Lienard Wiechert potential (leaving out the vector potential for simplicity),
$$\left.\phi(\vec{r},t)=\frac{e}{4\pi\epsilon_0R\,(1-\hat{n}\cdot\vec{\beta})} \right|_{t'=t_{\rm ret}},$$
where the ...
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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 \...
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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 $...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $A=1\hbox{ cm}^2$
...
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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:
$${\bf E}=\frac{q}{4\pi\epsilon_0}\frac{R}{(\bf R\cdot u)^3}[(c^2-v^2){\bf u}+\bf
R\times(u\...
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Retarded potentials and special relativity?
I'm curious. . . is there a substantial difference between a classical retarded potential, such as for the electric/magnetic fields in EM, and special relativistic formulations of EM? What i'm meaning ...
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Where can I find a detailed derivation of Lienard-Wiechert Fields?
Wikipedia (https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential) says
"The calculation is nontrivial and requires a number of steps".
Nice but a link would be good to add ...
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Does direct interparticle action imply advanced inertial forces?
In his Nobel lecture Richard Feynman states that by varying the Schwarzschild-Tetrode-Fokker direct interparticle action
$$A=-\sum_i m_i\int\big(\mathbf{\dot X_i}\cdot\mathbf{\dot X_i}\big)^{1/2}d\...
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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 ...
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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 ...
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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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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 point ...
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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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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:
$$\varphi = \frac{q}{4\pi\epsilon_0}\int \frac{\delta\left(\mathbf{r'...
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Poynting vector from 1st term in Lienard-Wiechert field
I start with 1st (non-radiative) term from Lienard-Wiechert fields:
$$ \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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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') =...
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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 ...
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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 ...
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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 ...
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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 = ...
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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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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:
$$\mathbf E=\frac{q}{4\pi\epsilon_0}\frac{1-v^2/c^2}{1-v^...
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Surely force on shell can't be balanced by field momentum?
Imagine a particle with charge $q$ at rest at the origin.
It is surrounded by a concentric spherical insulating shell, also at rest, with charge $Q$ and radius $R$.
At time $t=0$ I apply a constant ...
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Accelerated charge inside sphere (again!)
Sorry to go on about this scenario again but I think something is going on here.
Imagine a stationary charge $q$, with mass $m$, at the center of a stationary hollow spherical dielectric shell with ...
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Reaction-at-a-distance: Do charged plates immediately repel each other?
Imagine that we have a pair of parallel plates, $A$ and $B$, separated by some distance as in Fig. $1$ above.
At time $t_1$ we simultaneously charge both the plates. This could be done by previously ...
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Mathematical equivalence between Liénard-Wiechert potential and 4-potential in Rindler coordinates
I'm studying the problem of the radiation of an uniformly accelerated point charge:
$$x^{\mu}(\lambda)\to(g^{-1}\sinh g\lambda,0,0,g^{-1}\cosh g\lambda)$$
I found that when a point charge is moving ...
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Retarded time Lienard Wiechert potential
In a potential which needs to be evaluated at the retarded time, is this the time which represents the actual time the "physics" occurred? So $t_{\text{ret}}=t-\frac{r}{c}$, not just because it may be ...
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Electromagnetic inertia due to advanced radiation?
The scalar potential $\phi$ and vector potential $A$ at a distance $r$ from a charge $q$ are given approximately by
$$\phi = \frac{q}{r}$$
$$\mathbf{A} = \frac{q\mathbf v}{r}$$
where the constants ...
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Advanced Heaviside-Feynman formula implies electromagnetic inertia?
The Heaviside-Feynman formula (see Feynman Lectures vol I Ch.28, vol II Ch. 21) gives the electric and magnetic fields measured at an observation point $P$ due to an arbitrarily moving charge $q$
$$ \...
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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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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 ...
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