Questions tagged [lienard-wiechert]
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About Feynman and Heaviside electric and magnetic field [on hold]
How to calculate the magnetic field from the given expression of the electric field?
$$ \vec{E}= \frac{q}{4 \pi \epsilon_0} \left( \left[\frac{\hat{R}}{R^2}\right] _{ret}+ \frac{[R]_{ret}}{c} \frac{\...
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About density charged in the Liénard - Wiechert Potential to Point Charge?
I'm reading Griffiths Ch. 10. In the 10.3.1 section, there's a proof of this integral
$$ \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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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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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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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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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
98 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 ...
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1answer
312 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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129 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 ...
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1answer
526 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
702 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'...
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1answer
89 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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2answers
751 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') =...
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2answers
186 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 ...
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1answer
214 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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2answers
206 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
63 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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3answers
2k 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 ...
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0answers
102 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 ...
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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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1answer
452 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
156 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
291 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
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 ...
2
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1answer
632 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
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1answer
325 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
1k 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 $q$
$$ \...
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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 $...
3
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1answer
778 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 ...
