Questions tagged [classical-electrodynamics]

Classical electrodynamics is the discipline that studies electromagnetic phenomena – such as electric and magnetic fields, radiation, and the dynamics of charged bodies – in classical terms.

Filter by
Sorted by
Tagged with
0
votes
1answer
38 views

Electromagnetic waves, displacement currents and capacitors

This is a question from HC Verma’s concepts of Physics Vol 2: Electromagnetic Waves. It’s a question which is a continuation of the previous question, therefore I’ve combined both of them. Q. A ...
2
votes
0answers
47 views

Is there a near zone inverse Doppler shift?

Engheta et al. found such an effect in free space in 1980, published as On the Near-Zone Inverse Doppler Effect August 1980 IEEE Transactions on Antennas and Propagation 28(4) Yehuda Ben-...
-1
votes
2answers
45 views

Does action at distance in electromagnetism violate energy conservation?

Consider two charges A and B separated at distance D. charge B is attached on spring and can move towards and away from charge A. Now charge A is brought closer to charge B and then it is taken back ...
3
votes
1answer
114 views

Can we talk about velocity field and acceleration field in 1D?

It's well know that a charged particle radiate when it is accelerated. We can rely on two different formulas. The first one it's from Jefimenkos : $$\mathbf{E}(\mathbf{r}, t) = \frac{1}{4 \pi \...
5
votes
2answers
270 views

Faraday's law. And Faraday's law of induction

Can anyone properly tell me the difference between the two, and which one historically came first. A majority of sources directly connect "emf" to flux but the 'flux rule' isn't absolute. It isn't ...
0
votes
1answer
61 views

What's wrong with the theory of an electromagnet? [on hold]

Let's imagine we have a uniform magnetic field pointing directly upwards, filling the whole space, so $\mathbf B(\mathbf r)=B\mathbf k, B>0$ for all points in $\mathbb R^3$. This can be seen as a ...
0
votes
0answers
40 views

How exactly is electric field produced and propagated? [closed]

i wanted to know how does electric field exists in space, and how does a charge create it or how is force/energy transmitted to test charge through the source charge, does the charge produce some kind ...
1
vote
1answer
17 views

Are Fresnel Equations with Complex Indices and Angles always valid?

This question-answer pair came after i was asked the following question and realized i had to do some research of my own to answer it fully, and to be sure that the answer is „yes“, in the sense ...
0
votes
0answers
39 views

Conformal Invariance of Maxwell's Equations

I am currently doing some conformal field theory (in four dimensions) and want to show the invariance of Maxwell's equations under conformal transformations, in particular \begin{align} \partial_\...
0
votes
1answer
31 views

Magnetic Field in Perfect Electric Conductor

I know that one of Maxwell's equations states that the curl of the electric field is proportional to the time derivative of the magnetic field. We know that the electric field in a perfect electric ...
0
votes
1answer
29 views

Nature of electromagnetic absorption by quantum and classical systems

Forgive me for lack of formality and possibly incorrect understanding, but hopefully someone can both help to explain the intuition and also add mathematical formalism. In classical electrodynamics, ...
0
votes
0answers
16 views

How does the Beer-Lambert law arise from a collection of dipoles?

The Beer-Lambert law says that one solution to the macroscopic Maxwell’s equations is one which demonstrates an exponential decay of light intensity in the direction of incidence. Consider a ...
1
vote
1answer
36 views

Velocity-dependent potentials and the dissipation function

From this previous question Charge, velocity-dependent potentials and Lagrangian where the citation is shown at the page 22, §1.5 of the book Classical Mechanics of Goldstein, we read that "an ...
1
vote
1answer
51 views

Formulation for the fluence from energy-density

I'm struggling to find a mathematical expression for the total fluence of a traveling electromagnetic wave (through vacuum). Though its not really a physics problem rather than a problem with basic ...
0
votes
0answers
21 views

Electric dipole in a larger dipole field

I have a problem describing a smaller dipole moving in a field from a larger 'static' eletric dipole. I've derived the potential energy $V = \frac{pp'}{4\pi\epsilon_0 r^3}[3\cos\theta\cos\theta' + \...
0
votes
2answers
109 views

Solution to Maxwell-Lorentz equations

I am trying, without success, to find an example (preferably simple) of solution for the Maxwell-Lorentz equations, i.e., the coupled system of Maxwell equations + dynamics of a charged particle given ...
0
votes
1answer
57 views

$1/4$ coefficient in QED Lagrangian [duplicate]

What is the reason 1/4 coefficient in the tensor multiplication of the electromagnetic field strength? $$\mathscr{L} = -\, \frac{1}{4} \, F_{\mu \nu} \, F^{\mu \nu}. \tag{1}$$
0
votes
1answer
3k views

Confusion in the derivation of the potential of a magnetic shell

I am reading an old book on electromagnetism (THE MATHEMATICAL THEORY OF ELECTRICITY AND MAGNETISM) and I have some confusion in the following pages: First let me clarify what a "magnetic shell" is: ...
0
votes
1answer
38 views

In classical electrodynamics, what are the equations of motion for a pair of point charges?

I know the equations for a (point) charge in a background electromagnetic field, and for the electromagnetic field due to a fixed current. What are the general equations, for the evolution of an ...
0
votes
1answer
35 views

What happens to the charge density under parity?

A question came to me when I tried to think about the parity prperties of the Maxwell's equations. The charge density $\rho(\vec{r})$ actually stands for a scalar quantity $\rho(x,y,z)$. Since the ...
0
votes
0answers
26 views

Expanding the Green's function in spherical harmonics

Hello and thanks for reading. I'm currently working through electrodynamics from Purcell supplemented by Jackson and online notes. I've read up the basic cases demonstrating the method of image ...
0
votes
1answer
24 views

Can the electromagnetic field be defined for the Compton effect?

As far as I know, the Compton Effect can only be explained by using Quantum Electrodynamics, given an incoming electromagnetic wave there is a probability that a photon with different wavelength than ...
2
votes
2answers
887 views

Electric potential vs induced emf

Suppose we have a changing magnetic field in the $z$ direction and a conductive ring of radius r inside the magnetic field lying in the $xy$ plane. Then we have an induced emf: $$ ε= -{{dΦ} \over {dt} ...
-1
votes
1answer
231 views

The use of Helmholtz decomposition

Examining the article on Wikipedia Helmholtz decomposition, compatible with the explanations of the book Introduction to Electrodynamics $4^{\mathrm{th}}$ edition David J. Griffiths §1.6 the theory of ...
0
votes
1answer
46 views

Does the electric field of a charged particle really contribute to its mass? [duplicate]

An electron at rest creates a static distribution of an electric field around it. Wherever the particle moves, it carries or drags the field with itself. Does this electric field contribute to the ...
0
votes
2answers
479 views

Multipole expansion of the electromagnetic field

In Jackson's Classical Electrodynamics, section 9.7, he develops the multipole expansion of the electromagnetic fields in terms of the vector spherical harmonics and the spherical Bessel and Hankel ...
0
votes
0answers
33 views

Faraday disk - Electric fields

I was thinking about an experiment when you let a homogenous metallic disc spin in a homogeneous magnetic field, that is parallel with the axis of the disk. If you connect the center of the disk to ...
5
votes
1answer
541 views

Maxwell Stress Tensor at material boundaries

I am trying to grasp the meaning of the Maxwell Stress tensor $T_i^j$ at material boundaries. Concretely, I am trying to calculate the force between two waveguides. The results are given in an article ...
0
votes
0answers
22 views

How much energy, momentum, and/or angular momentum are lost to radiation in Rutherford scattering?

Inspired by this question: Consider two charged particles, of masses $m_1$ & $m_2$ and charges $q_1$ and $q_2$. They approach each other from a great distance, interact via their electromagnetic ...
0
votes
0answers
17 views

RF Transmission Loss

I am aware that an ideal 3rd order circuit with R=0 will oscillate forever, but even this this is not true. Power is dissipated through the em waves. How does one calculate the losses due to these ...
1
vote
2answers
89 views

Derivation: (lossless case) Plane waves have no electric field component in the direction of propagation

Set up Assume that a wave is propagating in the $\hat{z}$ direction with the $E$-field polarized along the $\hat{x}$ direction. In the lossless case, $$0 = \nabla \cdot E = \frac{\partial E_x}{\...
0
votes
1answer
23 views

Relation Between Current and velocity of electrons

In a conductor, all the electrons are few to move to conduction bands. If we say that magnitude Current is increased (I= dq/dt) can we infer that the velocity with which the electrons flow also ...
0
votes
1answer
32 views

Does a uniformly moving charge induce electric quadrupole moment densities in surrounding space?

The electric field of a uniformly moving charge is cylindrically symmetric around an axis parallel to its velocity vector. It varies inversely to the square of the distance. The electric field of a ...
-2
votes
2answers
86 views

What is “power per unit frequency” in black body radiation? [duplicate]

What is the meaning of power radiated by a black body per unit frequency? If you have a black body with a frequency filter around it set to 530nm and you calculate the energy radiated in 1 second you ...
1
vote
2answers
166 views

Can a charge moving in an open trajectory qualify as current?

It is sometimes said that a point charge is equivalent to an electric current. If it were a steady current, I should be able to find it from Ampere’s law or Biot-Savart’s law. Even if the current is ...
4
votes
3answers
1k views

Why is divergence and curl related to dot and cross product?

I've been reading Griffith's intro to electrodynamics and I've been a bit confused on his explanation of divergence and curl. I don't understand how divergence is the dot product of a gradient acting ...
0
votes
1answer
142 views

Why does electric field undergo a discontinuity when we cross $any$ surface charge $σ$?

According to Griffith's book on electrodynamics, electric field always undergoes a discontinuity when crossing a surface charge $σ$. I do understand that in certain cases like the surface of a ...
0
votes
2answers
122 views

Semi-classical derivation of maximal magnetic field in the Universe

I'm looking for all (or most) theoretical semi-classical derivations of the maximal magnetic field intensity that there may be in the Universe. As an example, this paper evaluate a maximal field of ...
2
votes
2answers
55 views

Deriving Current density of a Moving Point Charge Using the Continuity-Equation

Problem: We know, a point charge at position $\mathbf{r}_q$ has the charge density $$\rho_q(\mathbf{r})=q\delta(\mathbf{r}-\mathbf{r}_q) \tag{2}$$ if it moves with the velocity $\mathbf{v}$, we get ...
0
votes
2answers
41 views

Evaluating an Integral with a Cross Product

Problem: A infinite thin spherical shell with radius $r_0$, centered around the origin, is homogeneously charged with surface-charge-density $\sigma$ and rotates with the constant angular verlocity $\...
0
votes
3answers
41 views

'Electrostatic field of a circuit' What does it mean?

I've recently gotten into electrodynamics, I've studied electrostatics & magnetostatics, so far I know these facts: Electrostatic fields are produced by static charge configurations Magnetic ...
9
votes
3answers
3k 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, ...
1
vote
0answers
26 views

Difference between monopole moment and charge or mass itself?

I'm trying to understand the difference between monopole moment and charge or mass itself. What I found is related to magnetic monopole that is irrelevant. I want to know in multiple expansion of ...
0
votes
0answers
21 views

Classical Electromagnetic scattering

What are the best resources (books/lectures/articles) to learn Classical Electromagnetic Scattering (forward and inverse modelling)? I am an Electrical Engineer so I would prefer some resource which ...
0
votes
2answers
207 views

Torque on a disk with charge

Imagine you have a disk with some number of charged metallic spheres spaced equally around a disk at some distance from the center of the disk and those spheres are mechanically attached to the disk. ...
0
votes
2answers
210 views

Continuity equation involving vectors

A time dependent point charge $q\left ( t \right )$ at the origin $\rho\left ( \vec{r},t \right )=q\left ( t \right )\delta ^{3}\left ( \vec{r} \right ) $, is fed by a current $$\vec{J}\left ( \vec{r},...
1
vote
1answer
134 views

What is the frequency distribution of the electromagnetic wave emitted by a charge accelerating along a given trajectory?

Charged particles radiate when accelerated.From a few other answers from Physics Stack exchange like What is the frequency of a photon emitted by an accelerated charged particle? and How ...
6
votes
4answers
366 views

How is it possible for the induced emf to take negative values in Faraday's Law of induction?

Faraday's Law of induction states that the work done per unit charge by the (induced) electric force along a loop of wire, or the emf, is minus the rate of change of magnetic flux through the loop/...
0
votes
0answers
207 views

Are the retarded and advanced field solutions to the Lienard-Wiechert potentials identical?

In Dirac's paper Classical theory of radiating electrons, he considers a radiating electron accelerated by an electromagnetic field. He writes the actual field as the sum of the field generated by the ...