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38
votes
8answers
3k views

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 ...
6
votes
1answer
1k 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 ...
25
votes
6answers
6k 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 ...
39
votes
1answer
30k views

How does this “simple” electric train work?

In this YouTube video, a dry cell battery, a wound copper wire and a few magnets (see image below) are being used to create what can be described as "train". It looks fascinating but how does this ...
7
votes
2answers
7k views

Video lectures on graduate level Classical Electrodynamics

This is a rather broad question. Does anyone know of good video lectures for graduate level classical electrodynamics?
10
votes
7answers
4k views

Recommended books for undergraduate electrodynamics

What books are recommended for an advanced undergraduate course in electrodynamics?
3
votes
1answer
120 views

Induced magnetic field produces electric field and vice versa forever!

So here are the two of Maxwell's laws that I am interested in: So we have the simple circuit (from google): So, before the system goes into steady-state we know that charge slowly accumulates on ...
8
votes
2answers
418 views

What is the mechanism by which magnetic fields do work?

I've seen some conflicted answers to this question in texts and on the web, in the case of a dipole, for example. Do magnetic fields do work directly, or is it their induced electric fields that do ...
14
votes
5answers
879 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 ...
6
votes
5answers
1k 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 ...
2
votes
2answers
227 views

Magnetic field due to a charge having uniform velocity

Faraday's law states that "Any change in electric field induces a magnetic field and vice versa". I don't see exactly where these fields are induced, but I assume that these fields are induced at each ...
13
votes
3answers
931 views

Is classical electromagnetism a dead research field?

Is classical electromagnetism a dead research field? Are there any phenomena within classical electromagnetism that we have no explanation for?
4
votes
3answers
938 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
408 views

electric field of unpolarized light after reflect?

Reflection and transmission (Fresnel equation) of polarized light are treated in many optics or electromagnetism books. If $E_s$ and $E_p$ is incident electric field with s-polarization and ...
2
votes
3answers
274 views

Why do surfaces act like barriers for electrons?

Say you have a conductor, filled with free electrons. The nuclei have a weak pull on the valence electrons so they are moving around in the conductor. But the electrons don't leave the solid. If you ...
16
votes
2answers
429 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 ...
9
votes
1answer
559 views

Recovering all of Maxwell's equations from the variational principle

Whether you can get the first couple of Maxwell equations from a variational principle? In the second volume of the Landau theoretical physics said that it is impossible.
8
votes
3answers
2k views

Maxwells Equation from Electromagnetic Lagrangian

In Heaviside-Lorentz units the Maxwell's equations are: $$\nabla \cdot \vec{E} = \rho $$ $$ \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} = \vec{J}$$ $$ \nabla \times \vec{E} + ...
8
votes
3answers
896 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. ...
7
votes
2answers
742 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?
10
votes
2answers
675 views

Trouble understanding the Bohr model of the atom

In this article it says: The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits") at a certain discrete set of distances from the nucleus. ...
1
vote
3answers
322 views

The propagation of electric field

In case of a charged particle which is travelling at a uniform velocity, the electric field due to it at a given point doesn't change instantaneously . The reason for this delay in change of electric ...
1
vote
2answers
270 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 ...
20
votes
3answers
4k 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 ...
13
votes
4answers
840 views

Can we measure an electromagnetic field?

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 ...
13
votes
2answers
503 views

The problem of self-force on point charges

Allow me to preface this by stating that I am a high school student interested in physics and self-studying using a variety of resources, both on- and off-line, primarily GSU's HyperPhysics website, ...
10
votes
3answers
244 views

Is the electromagnetic mass real?

In his Lectures on Physics vol II Ch.28-2 Feynman calculates the field momentum of a moving charged sphere with charge $q$, radius $a$ and velocity $\mathbf{v}$. He finds that the total momentum in ...
13
votes
2answers
1k 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 ...
7
votes
4answers
651 views

Why does electric field intensity $E$ can be uniquely determined by its divergence and curl? [duplicate]

My question is, the number of following equations $$\nabla\cdot E=\frac{\rho}{\varepsilon}$$ $$\nabla\times E=-\frac{\partial B}{\partial t}$$ is 4 while the number of unknown variables ...
5
votes
1answer
413 views

Is there a Hamiltonian for the (classical) electromagnetic field? If so, how can it be derived from the Lagrangian?

The classical Lagrangian for the electromagnetic field is $$\mathcal{L} = -\frac{1}{4\mu_0} F^{\mu \nu} F_{\mu \nu} - J^\mu A_\mu.$$ Is there also a Hamiltonian? If so, how to derive it? I know how ...
5
votes
0answers
216 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
2answers
208 views

Why is there no induced electric field in the experiment (Faraday's Law)

Below are three circuit diagrams for each of Faraday's experiments that allowed Faraday to come up with Faraday's Law. In Griffiths' Introduction to Electrodynamics Griffiths states (on page 302 of ...
3
votes
2answers
179 views

Problem with Maxwell's theory

What exactly is the problem with classical Maxwell theory and the blowing up of energy at $r=0$? Does it have any other problems on the classical level?
2
votes
1answer
106 views

Current, Current density

edit: Hi I'm trying to find the magnetic field generated by a time dependent oscillating current in the quasistatic case ($|z|,r <<c\omega$) where r is the perpendicular distance from the ...
2
votes
5answers
618 views

Is the canonical momentum conserved when a particle moves in magnetic field?

Here is a question about the canonical momentum that I had asked some days ago, but I still have one point that I am not understand. Considering a particle moves in a magnetic field with charge $q$ ...
1
vote
4answers
191 views

A question about canonical momentum and arbitrariness for potential in magnetism

The following question confuses me: There exists magnetic field $B_z =- \beta x$ where $x > 0$, and a particle is incident from origin point $(0,0)$ with pisitive charge $q$, mass $m$, and ...
6
votes
2answers
893 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 ...
4
votes
1answer
197 views

How does light pass through rough glass?

Light incident on a rough surface will be diffuse after passing it. Angular intensity depends on the grinding of the glass surface. I'm trying to find information about the scattering indicatrix of ...
4
votes
2answers
419 views

When studying electrodynamics do we assume Maxwell's Equations or derive them?

This question is because something made me confused. I always thought that the idea behind electrodynamics was to postulate some things, like Coulomb's law in electrostatics and so on, and then ...
3
votes
1answer
244 views

Missing terms in Hamiltonian after Legendre transformation of Lagrangian

Short question Given any Lagrangian density of fields one could possibly conceive, is it the case that after one has performed a Legendre transformation, if the Hamiltonian is then expressed in terms ...
2
votes
2answers
892 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 ...
1
vote
1answer
45 views

Signs in derivation of capacitor discharge differential equation

In deriving the discharge current for a capacitor I have seen two different approaches: By Kirchhoff's law we have: $$ \begin{align} 0 &= I R + \frac{Q}{C}\\ \implies 0 &= \dot I R + ...
1
vote
1answer
312 views

What's the reason behind calling cathode rays tube by the name cathode?

I do believe that maybe due to the accumulation of negative electron on the metal surface so we called it cathode. But the thing is that we have studied that regardless of the polarity, the cathode ...
0
votes
0answers
39 views

Interaction between charged particles as seen from two inertial frames of references

Let us consider two charged particles travelling at a uniform velocity, V, as seen from a frame of reference A . Now let us consider a frame of reference, B, which is also travelling at a uniform ...
0
votes
0answers
57 views

Electric and Magnetic Field Created by Moving Electron

From a classical perspective, what are the electric and magnetic fields created by a single electron, initially located at the origin and moving along the $x$ axis with velocity $v \ll c$? I'm ...
0
votes
0answers
136 views

Field inside a conductor?

If the above image is a cross section of a conductor, the field at the point shown is not zero. So the field inside a conductor is not zero at all points. You could argue that the electrons would ...