Questions tagged [lienard-wiechert]

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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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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 ...
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1answer
50 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 ...
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2answers
175 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 ...
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1answer
47 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 ...
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0answers
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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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27 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 $A=1\hbox{ cm}^2$ ...
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1answer
58 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\...
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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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1answer
112 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 ...
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1answer
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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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1answer
142 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 ...
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2answers
112 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 ...
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93 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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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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1answer
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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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1answer
464 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 ...
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172 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 ...
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1answer
741 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 ...
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1answer
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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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1answer
138 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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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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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 ...
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215 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 ...
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1answer
75 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 = ...
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4answers
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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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3answers
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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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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 ...
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1answer
189 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 ...
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1answer
313 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 ...
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0answers
501 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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1answer
763 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 ...
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1answer
345 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 ...
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3answers
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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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3answers
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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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1answer
863 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 ...