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39
votes
1answer
31k 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 ...
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 ...
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 ...
20
votes
3answers
5k 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 ...
20
votes
2answers
1k 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 ...
17
votes
4answers
2k views

Can two electrons get ever so close as to touch each other?

My friend and I were studying for our EM test when we started to think about what happens to the electric field near an infinite line of charge. $$E = \frac{\lambda}{2\pi\rho\epsilon_{0}}$$ As 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 ...
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 ...
14
votes
1answer
759 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 ...
13
votes
3answers
933 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?
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 ...
13
votes
2answers
505 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, ...
13
votes
4answers
841 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
1answer
530 views

Physical Interpretation of EM Field Lagrangian

Using differential forms and their picture interpretations, I wonder if it's possible to give a nice geometric & physical motivation for the form of the Electromagnetic Lagrangian density? The ...
10
votes
7answers
4k views

Recommended books for undergraduate electrodynamics

What books are recommended for an advanced undergraduate course in electrodynamics?
10
votes
2answers
677 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. ...
10
votes
3answers
245 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 ...
10
votes
1answer
571 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
560 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
2answers
423 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 ...
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. ...
8
votes
2answers
555 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 ...
7
votes
2answers
1k views

Why are EM waves transverse?

I was reading Griffiths' Introduction to Electrodynamics, specifically the section on plane waves. I can see that if we want a transverse wave traveling in the $z$ direction that we are only going to ...
7
votes
2answers
333 views

Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics

How do I definitively show that there are only two propagating degrees of freedom in the Lorenz Gauge $\partial_\mu A^\mu=0$ in classical electrodynamics. I need an clear argument that involves the ...
7
votes
4answers
653 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 ...
7
votes
3answers
899 views

Maxwell's Stress Tensor

What really is the Maxwell Stress Tensor? I understand that it's derived from $$\mathbf {F} = \int _V ( \mathbf E + \mathbf v \times \mathbf B )\rho \ d \tau$$ Griffiths describes this as "total EM ...
7
votes
2answers
746 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?
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?
6
votes
2answers
895 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
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 ...
6
votes
3answers
792 views

How do I calculate electric fields due to currents of magnetic dipoles?

Short version of my question: Do dipole currents cause fields? I think currents of aligned magnetic dipoles cause an electric field, but I don't know how to calculate this field except in the ...
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 ...
6
votes
1answer
108 views

Why can the Lorenz gauge condition always be fullfilled?

Why is the Lorenz gauge condition always possible for classical electromagnetic fields? So far I can only understand the following: If we perform a gauge transformation $A\mapsto ...
6
votes
3answers
97 views

Why isn't it obvious that a particle doesn't interact with its own field, classically?

The Wheeler-Feynman absorber theory or any other theory that tries to avoid the notion of field as an independent degree of freedom has always been concerned about infinite self energy of a charged ...
5
votes
2answers
364 views

Evidence for electrodynamics in curved spacetime

Field theories in curved spacetime is usually formulated by integrating their Lagrangian over the curved spacetime. For example, for electrodynamics, we have the action $$ S = \int d^4x \left( ...
5
votes
2answers
419 views

What is the difference between surface plasmon and surface plasmon polariton?

I'm trying to understand this reading article linked below and I still don't know how to explain this simply, without need to derive everything mathematically. Can someone just write here how do SP's ...
5
votes
1answer
421 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
4answers
222 views

Method of calculating eddy currents of a conductor, is this correct?

I have a conductor with volume $V$, passing a magnetic field($B$) with velocity($v$): I'm trying to calculate the Eddy currents to figure out the magnitude of the drag force($F_d$) generated the ...
5
votes
2answers
144 views

Charge vs Charge Density in classical electrodynamics

What is assumed to be a more fundamental physical quantity in classical electrodynamics. The charge density as a scalar field or the physical entity charge.
5
votes
1answer
297 views

Chern-Simons Energy-Momentum Tensor

I'm assuming the following statement is true. I'm not finding any reference which shows that explicitly. Statement: Chern-Simons term is a topological one and does not contribute to the ...
5
votes
1answer
656 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 ...
5
votes
1answer
137 views

Time reversal in classical electrodynamics

It is known that classical electrodynamics is time reversal invariant if one assumes that the transformation laws under such operation are $$\mathbf E(t,\mathbf x)\mapsto\mathbf E(-t,\mathbf x)$$ ...
5
votes
2answers
426 views

Electrostatics/ magnetostatics: why is $\int_\text{all space} d\vec r \; \nabla \cdot(\vec A \times \vec B)$ equal to 0?

I'm reading electrodynamics notes and come across that: $$\int_\text{all space} d\vec r \; \nabla \cdot(\vec A \times \vec B)=0$$ in case of magnetostatics and: $$\int_\text{all space} d\vec r \; ...
5
votes
1answer
100 views

Classical EM neglects electron recoil?

Imagine two electrons $A$ and $B$ at rest. Electron $B$ is at a vertical distance $r$ above electron $A$. Let us assume that the electrons are constrained to move on horizontal rails. At time $t=0$ ...
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 ...
4
votes
6answers
742 views

Is electromagnetic vector field a sum of E and B?

I have a hard time to fully understand (classical) electromagnetic field theory with respect to Helmholtz's decomposition. Let me start from Helmholtz's theorem: Any vector field of class ...
4
votes
2answers
386 views

Aharonov–Bohm effect on a non-contractible manifold

The Aharonov–Bohm effect shows the vector potential $\mathbf{A}$ is more fundamental than magnetic flux density $\mathbf{B}$. However, vector potential is introduced by $$ \nabla \times \mathbf{A} = ...
4
votes
3answers
942 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 ...
4
votes
2answers
421 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 ...