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5
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1answer
613 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: ...
5
votes
1answer
104 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
2answers
176 views

Far field diffraction of EM waves: what does the zero frequency signify?

If you have a system of independently radiating electrons/point-charges, the far field distribution of the EM waves can be approximated by the Fraunhoffer diffraction integral, or simply by the ...
4
votes
6answers
851 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
407 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
4answers
284 views

When does the concept of electric field in classical electrodynamics fail, and QED is needed?

It is really hard to find reference to when the traditional concept of electric wave, especially TEM wave, fails, and needs to be replaced by quantum electrodynamics. So when does the concept fail? ...
4
votes
3answers
1k 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
505 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 ...
4
votes
2answers
1k views

What is the time component of velocity of a light ray?

If we have a light ray $x^\mu$ with velocity $c$, what is $c^0$ (the time component)?
4
votes
1answer
424 views

Does a magnetic field decrease or increase entropy?

My question is just the title: Does a magnetic field decrease or increase the entropy of a system? For example if we apply a magnetic filed to a substance, is the entropy decreased or increased?
4
votes
2answers
763 views

What is the magnitude of the force on a charged particle due to electromagnetic radiation?

Suppose there is an electromagnetic wave moving forward in the $\mathbf{\hat{k}}$ direction. Its electric/magnetic field components are given by: $$\mathbf{E} = E_0 \sin(kz - \omega t) ...
4
votes
4answers
1k views

Why are the classical electron radius, the Bohr radius and the Compton wavelength of an electron related to each other?

Using the definition of the fine-structure constant $\alpha = \frac{4 \pi \epsilon_0 \hbar c}{e^2}$ and the Compton wavelength of an electron $\lambda_c = \frac{h}{m_e c}$ the classical electron ...
4
votes
1answer
420 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 ...
4
votes
2answers
182 views

Applicability of the concept of voltage in electrodynamic circuits

In electrostatics, we have $$\nabla \times \vec{E} = 0$$. Hence, we can define a scalar potential $V$, where $$\vec{E} = -\nabla V$$. We know from Faraday's law that $$\nabla \times \vec{E} = ...
4
votes
2answers
78 views

Stored energy and momentum in a magnetic field?

How is it possible for a magnetic field to store energy and momentum? And can deliver it to another object(charge/dipole) or field? I can't depict it. I know it occurs but how? For example, the ...
4
votes
1answer
261 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
1answer
3k 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
106 views

Why are agglomerated gold nanoparticles black?

I put a drop of aqueous red colloidal gold on a glass. After the drop dried I saw that remaining nanoparticles were black instead of red. Why black? Does it mean that plasmon resonance is so strong ...
4
votes
2answers
1k views

Deriving Heaviside-Feynman formula for the electric field of an arbitrarily moving charge from Lienard-Wiechert potential

I've been trying to derive this (which Feynman warns takes a lot of work) for a couple of days now, without success. My current best derivation which however doesn't give the right answer is: First, ...
4
votes
2answers
196 views

In Jackson's expression for the electrostatic Green function, why is the Laplacian taken with respect to the primed coordinates?

Jackson writes, The function $1/|\mathbf{x} - \mathbf{x}'|$ is only one of a class of functions depending on the variables $\mathbf{x}$ and $\mathbf{x}'$, and called Green functions, which satisfy ...
4
votes
1answer
322 views

Did the Goudsmit-Uhlenbeck analysis of spin consider relativity?

It's frequently mentioned in introductory quantum mechanics texts that Goudsmit and Uhlenbeck conjectured that the magnetic moment of an electron was due to angular momentum arising from the electron ...
4
votes
1answer
387 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 ...
4
votes
1answer
270 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 ...
4
votes
1answer
254 views

Soft Bremsstrahlung: why $\hat{k}\cdot\mathbf{v}= \mathbf{v}'\cdot\mathbf{v}$?

On page 181 in Peskin & Schroeder they say that we consider the integral (intensity) $$\tag{1}\mathcal{I}(\mathbf{v},\mathbf{v}') = ...
4
votes
1answer
147 views

Motion in a Paul trap: $2n^{\text{th}}$ harmonic with larger amplitude than $n$th harmonic

Using a Paul trap, we captured the motion of a light charged particle (based on a rotating potential applied by AC current). Our rotational frequency was 50 Hz, and so when we used the FFT on the ...
4
votes
1answer
237 views

Orthogonality between $\vec{E}$ and $\vec{H}$ waves with space-dependent amplitudes

I am able to prove in a few lines that the electrodynamic field vectors $\vec{E}$, $\vec{H}$ and $\vec{S}$ are all orthogonal to each other considering that $\vec{E}$ and $\vec{H}$ are coherent plane ...
4
votes
1answer
125 views

What is the intensity of this light?

I am struggling with a derivation that calculates the cross sections for Mie scattering and since the incident light is considered to be a x-polarized plane wave I thought that we would have $$I_i = ...
4
votes
1answer
42 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
24 views

Characterisation of passivity

I'm a mathematician trying to work on some problems involving metamaterials. I have some trouble to understand the notion of passive media. Informally, this means that (without sources), a medium ...
4
votes
0answers
127 views

Why is there no induced current in this loop? [closed]

This problem comes from Barron's SAT Subject Test Physics book. A loop of wire and a bar magnet are moving relative to one another. Which motion in the diagrams shown below will NOT induce a ...
4
votes
2answers
212 views

Instantaneous Coulomb interaction in QED

It seems I am stuck with a (at a first sight) trivial problem. It's from the "Quarks and Leptons" (Halzen, Martin) book page $141$, where one considers the following integral: $$\tag{1} T_{fi} = ...
4
votes
0answers
112 views

Accelerated electromagnetic system leads to divergent calculation?

Consider the above system comprising a pair of oppositely charged parallel plates, connected by a rigid rod of length $r$, constrained to move in the x-direction. The forces on the plates from the ...
4
votes
2answers
244 views

What is the area in Faraday's law if we have only a piece of metal moving in a magnetic field?

If a piece of metal of length $l$ is moving with a speed $v$ in a region where there is a uniform magnetic field $B$ perpendicular to it, there will be a potential difference across its terminals ...
4
votes
14answers
2k views

Metallic and glass sphere of same size released at a height

This question was in my exam today : A metallic and glass sphere of same size were dropped at same height. Which sphere would hit the ground first and why? I have thought about several things and ...
3
votes
5answers
561 views

Euclidean geometry in non-inertial frame

Refer, "The classical theory of Fields" by Landau lifshitz (Chap 3). Consider a disk of radius R, then circumference is $2 \pi R$. Now, make this disk rotate at velocity of the order of c(speed of ...
3
votes
2answers
229 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?
3
votes
3answers
558 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
votes
1answer
979 views

Width of a photon. And its length

Everyone is always talking about photon's wavelength. But what about its dimensions? What is length and width of it? And does it even have a point to think about such things? Or those dimensions are ...
3
votes
2answers
248 views

Illegal gauge condition in electrodynamics

Just a quick sanity check here: I'm preparing a tutorial for a class on classical electrodynamics and I wanted to show an example of a gauge condition which leads to a contradiction, so I simply ...
3
votes
2answers
172 views

Relating Poyntings theorem to Lenz and Faraday's law?

In system's similar to a motor, where the armature begins to accelerate simultaneously there is induced $-\epsilon$ to reduce the applied current(hence the applied power $P(t)$ is also reduced), or ...
3
votes
1answer
194 views

Method of image charge for cylindrical conductor

I am simply puzzled that only for spherical and planar conducting surfaces the method of images is applied. Is it (really) impossible to find image charge or charge distribution which can simulate the ...
3
votes
6answers
3k 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 ...
3
votes
1answer
107 views

Tensor notation

I'm trying to understand the Maxwell Stress tensor notation. I'm given that each element in the tensor is given by ...
3
votes
1answer
310 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 ...
3
votes
1answer
1k views

Meaning of terms and interpretation in the electric multipole expansion

In section 3.4.1 of Griffiths' Introduction to Electrodynamics, he discusses electric multipole expansion. He derives the formula or the electric potential of a dipole, which I follow, but right ...
3
votes
2answers
117 views

Does light interact with electric fields?

We know that light is an electromagnetic wave and it does interact with charges. It contains magnetic field and electric field oscillating perpendicularly but when we apply an electric or magnetic ...
3
votes
3answers
2k views

How do the electric or magnetic fields contain momentum?

I have recently come to know that the electric and magnetic field contain both linear and angular momenta, which are known functions of the electric and magnetic fields at any given point in space and ...
3
votes
2answers
102 views

Are all fluorophores dipoles?

Lately I'm reading about surface enhanced fluorescence. In many articles I can see that fluorophores are called "dipoles". Is it because that they can be modelled by a vibrating electric dipole? Or ...
3
votes
1answer
712 views

Lorentz force equation from relativistic Lagrangian

The relativistic Lagrangian is given by $$L = - m_0 c^2 \sqrt{1 - \frac{u^2}{c^2}} + \frac{q}{c} (\vec u \cdot \vec A) - q \Phi $$ I need to derive, $\displaystyle \frac{d\vec p}{dt} = q \left( \vec E ...
3
votes
1answer
56 views

Problem - Demonstration of electromagnetic energy conservation

I want to solve the following problem from my Classical Electrodynamics' book: Consider a pontual mass body, $m$, with charge $q$, which moves with an uniform velocity $v$ in a region where an ...