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6answers
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Do Maxwell's Equations overdetermine the electric and magnetic fields?
Maxwell's equations specify two vector and two scalar (differential) equations. That implies 8 components in the equations. But between vector fields $\vec{E}=(E_x,E_y,E_z)$ and ...
19
votes
2answers
541 views
Theoretical penetration limit for evanescent waves
Consider a problem in classical electrodynamics, when a monochromatic beam experiences total internal refraction when traveling from a medium with $n>1$ to a medium with refractive index $1$ - see ...
16
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4answers
2k views
Does a magnetic field do work on an intrinsic magnetic dipole?
When you release a magnetic dipole in a nonuniform magnetic field, it will accelerate.
I understand that for current loops (and other such macroscopic objects) the magnetic moment comes from moving ...
13
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2answers
705 views
An example which contradict to Newton's 3rd law?
Let a,b be two charged particles.
$$\vec{r}_a(0)=\vec{0}$$ $$\vec{r}_b(0)=r\hat{j}$$ $$\vec{v}_a(t)=v_a \hat{i}$$ $$\vec{v}_b(t)=v_b\hat{j}$$
In which both $v_a$ and $v_b$ $<<c$.
Then
...
13
votes
5answers
689 views
Does GR provide a maximum electric field limit?
Does GR provide a limit to the maximum electric field?
I've gotten conflicting information regarding this, and am quite confused. I will try to quote exactly when possible so as not to confuse ...
13
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3answers
1k views
What is the answer to Feynman's Disc Paradox?
[This question is Certified Higgs Free!]
Richard Feynman in Lectures on Physics Vol. II Sec. 17-4, "A paradox," describes a problem in electromagnetic induction that did not originate with him, but ...
10
votes
1answer
421 views
Explanation for speed of an electrical impulse
Our calculus book, Stewart, has a problem where they claim that for a metal cable (inner radius $r$) encased in insulation (outer radius $R$), the speed of an electrical impulse is given by
$$v = - ...
9
votes
1answer
276 views
Boundary conditions / uniqueness of the propagators / Green's functions
My question(s) concern the interpretation and uniqueness of the propagators / Green's functions for both classical and quantum fields.
It is well known that the Green's function for the Laplace ...
7
votes
2answers
458 views
Does a static electric field and the conservation of momentum give rise to a relationship between $E$, $t$, and some path $s$?
For a static electric field $E$ the conservation of energy gives rise to $$\oint E\cdot ds =0$$ Is there an analogous mathematical expression the conservation of momentum gives rise to?
6
votes
2answers
564 views
Pseudoscalar action in classical field theory
I was reading Landau and Lifschitz's "Classical Field Theory" and came across a comment that the action for electromagnetism must be a scalar, not a pseudoscalar (footnote in section 27). So I was ...
6
votes
2answers
323 views
Is it true that any system of accelerating charges will radiate?
I was recently told by a physics teacher that "any system of charges in which at least some of the charges are executing some sort of accelerated motion, will radiate and lose energy". This refers to ...
5
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3answers
536 views
Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation?
In Physical Review Letters, there was a paper recently published:
Masud Mansuripur, Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation, Phys. ...
5
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5answers
555 views
What is the Lagrangian for a relativistic charge that includes the self-force?
The usual Lagrangian for a relativistically moving charge, as found in most text books, doesn't take into account the self force from it radiating EM energy. So what is the Lagrangian for a ...
5
votes
1answer
199 views
Coulomb gauge fixing and “normalizability”
The Setup
Let Greek indices be summed over $0,1,\dots, d$ and Latin indices over $1,2,\dots, d$. Consider a vector potential $A_\mu$ on $\mathbb R^{d,1}$ defined to gauge transform as
$$
A_\mu\to ...
4
votes
1answer
281 views
Noether theorem and classical proof of electric charge conservation
How to prove conservation of electric charge using Noether's theorem according to classical (non-quantum) mechanics?
I know the proof based on using Klein–Gordon field, but that derivation use ...
4
votes
1answer
493 views
Einstein's Field equations and impulse-energy tensor
I premise that I haven't yet studied General Relativity, but in Relativistic Electrodymaics I have knowed impulse-energy tensor of Electromagnetic Field.
I know in Einstein's equations there is ...
4
votes
1answer
401 views
Force on Earth due to Sun's radiation pressure
I have been asked by my Classical Electrodynamics professor to calculate the force that the Sun exerts in the Earth's surface due to its radiation pressure supposing that all radiation is absorbed and ...
4
votes
1answer
31 views
Connections of iterative solvers for large systems of equation in Physics?
I am trying to find the domains in physics where solving large systems of equations is computationally expensive. The sparse systems are of my particular interest, where the input matrix A is in GBs ...
4
votes
1answer
274 views
Transverse current equivalence in Coulomb gauge
I have a question concerning transverse (solenoidal) current in the Coulomb gauge. This current is the one that enables the radiation, since we have a wave equation for the vector potential:
...
4
votes
1answer
131 views
On the Aharonov-Bohm effect, and the reality of the classical fields
As far as I can check, the Aharonov-Bohm effect is not -- contrary to what is claimed in the historical paper -- a demonstration that the vector potential $A$ has an intrinsic existence in quantum ...
4
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0answers
130 views
Semiclassical QED and long-range interaction
I'm interested in the (very) low energy limit of quantum electrodynamics. I've seen that taking this limit does not yield Maxwell equations, but a quantum corrected non-linear version of them.
If ...
3
votes
3answers
234 views
What does the * mean in spherical harmonics?
In Jackson's book about classical electrodynamics, this formula comes up:
$$q_{lm} = \int \mathrm d^3 x' \, Y^*_{lm}\left(\theta', \phi'\right) r'^l \rho\left(\vec x'\right)$$
What does that $^*$ ...
3
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2answers
300 views
Why do electrons around nucleus radiate light according to classical physics
As I navigate through physics stackexchange, I noticed Electron model under Maxwell's theory.
Electrons radiate light when revolving around nucleus? Why is it so obvious?
Note that I do not know ...
3
votes
1answer
134 views
Classical (or semi-classical) interpretation of photoelectric effect?
This site says that "it has recently been proven that the photoelectric effect can be interpreted classically (or at least semi-classically) in non-particle, wavelike terms". Is anyone familiar with ...
3
votes
1answer
192 views
What happens to electrons in an open circuit?
In the Physics classes, the professor did an experiment using de Van de Graaff generator, by which he held a neon tube radially outward to the V d Graaff dome, and the neon lit up. I understood that ...
3
votes
1answer
185 views
Is there a Newton's third law for the em field?
There is a momentum associated with the em field that ensures the conservation of total momentum for a system of interacting charges.
Can the same be done in an analagous way to ensure Newton's ...
3
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2answers
3k views
Graduate level Classical Electrodynamics
This is a rather broad question. But does anyone know of good video lectures for grad level classical electrodynamics?
3
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2answers
85 views
Magnetostatics of Current-Carrying wire
A question has been nagging at me about Faraday's Law as related to a wire with a constant current:
If you have a circular loop of wire with some small resistivity, connected to a battery so that it ...
2
votes
6answers
664 views
How do we visualise antenna reception of individua radiowave photons building up to a resonant AC current on the antenna?
I am a chemical/biological scientist by trade and wish to understand how quantum EM phenomena translates to our more recognizable classical world.
In particular I want to get a mechanistic picture of ...
2
votes
2answers
546 views
What is the conserved canonical momentum for a relativistically moving charge in a static Coulomb electric field?
The canonical momentum is a fundamental conserved quantity from Noether's theorem for translational invariance of the Lagrangian. Yet I'm finding it very difficult to see its derivation, or even a ...
2
votes
2answers
297 views
Magnet and energy conservation
If we consider a steel ball falling under gravity in a cup (potential well) and being stopped at the bottom by an obstacle then energy conservation implies that the gravitational potential energy has ...
2
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0answers
40 views
When can a center of mechanical momentum frame be found for an electromagnetic system?
In classical mechanics, a center of mechanical momentum frame can always be found for a system of particles interacting with one another locally. For an electromagnetic system where the charges ...
1
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1answer
186 views
Non-linear dynamics of classical hydrogen atom
I'd like to know if there have been attempts in solving the full problem of the dynamics of a classical hydrogen atom.
Taking into account Newton equations for the electron and the proton and Maxwell ...
1
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1answer
56 views
Conducting surface inside conducting surface
Let's say there's a closed conducting surface. Then by Gauss's Law the E field bound by the surface must equal the charge inside. There's no charge inside, so the E field cancels. This is a Faraday ...
1
vote
1answer
123 views
Question on 1st order Lagrangian Derivation in Faddeev-Jackiw Formalism
I'm looking at this reference (sorry it's a postscript file, but I can't find a pdf version on the web. This paper describes a similar procedure).
The topic is the Faddeev-Jackiw treatment of ...
1
vote
4answers
225 views
Interaction of matter with EM fields
For the interaction between electromagnetic fields and matter,
when do we have to include quantization of the EM field and when we can ignore it?
when do we have to include quantization of atomic ...
0
votes
1answer
80 views
Non-linear dynamics of classical hydrogen atom [duplicate]
Possible Duplicate:
Non-linear dynamics of classical hydrogen atom
I'd like to know if there have been attempts in solving the full problem of the dynamics of a classical hydrogen atom.
...
