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.

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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 ...
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16 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 ...
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How exactly is electric field produced and propagated? [on hold]

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 ...
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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 ...
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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 \...
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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_\...
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1answer
30 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 ...
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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 ...
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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, ...
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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 ...
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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' + \...
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$1/4$ coefficient in QED Lagrangian [duplicate]

What is the reason 1/4 coefficient in the tensor multiplication of the electromagnetic field strength? $$\mathscr{L} = -\, \frac{1}{4} \, F_{\mu \nu} \, F^{\mu \nu}. \tag{1}$$
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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}{\...
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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 $\...
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'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 ...
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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 ...
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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 ...
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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 ...
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4answers
365 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/...
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How does alternating current provide energy? [duplicate]

In my head, direct current makes complete sense; the electrons carry energy around the circuit to something being powered losing its potential and then return to the battery or whatnot to have their ...
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Effect of a current carrying wire on a point charge

Given a point charge $q$ near a wire carrying current as shown, what would be the effect of the magnetic field produced by the wire on this point charge $q$? I think the sign on $q$ is important so ...
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228 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 ...
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Difficulty to understand a chain of equalities

If we start with a functional or integral action \begin{equation} \mathscr{F}(\boldsymbol{\mathcal{A}})=\iiiint_{D} L\Biggl(x_\nu, \mathcal{A}_\mu, \frac{\partial \mathcal{A}_\mu}{\partial x_\nu}\...
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Motion of a charged particle in a constant and uniform magnetic field

Assuming the following relationship has been demonstrated $$r=\frac{m u_{0}\sin \theta_0}{qB\sqrt{1-\left(\dfrac{u_{0}^2}{c^2}\right)}}=\frac{p_0\sin \theta_0}{qB}$$ where $p_0=mu_0/\sqrt{1-\beta^2}$...
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Electromagnetic field with Dyadic Green's function in Non-homogeneous media

I post a question about how to derive integral forms of electromagnetic fields with Green's function in non-homogeneous, isotropic media. The source paper is following; Poon, A. S., O'Driscoll, S., ...
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1answer
72 views

How Is Induction Energy Transferred From a Toroidal Solenoid To An External Conductor During Linear Current Change?

It is widely understood that $\nabla \times \vec A =\vec B = 0$ outside a toroidal solenoid with constant current, $I=k$ ($I = \vec J$ in the below illustration). It is not so widely understood that ...
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35 views

Magnetic compression of plasma?

What is the mechanism for plasma compression in the video below? I provide a still from the video and a link to the actual video on YouTube. https://www.youtube.com/watch?v=gsjWGz3YE5o BTW, is ...
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Charging mist particles

I've used an aquarium mist maker to make mist of water and the mist comes out through a pipe (PVC) of ~ 4cm diameter and ~ 12cm length, I want to charge those mist particles using induction technique. ...
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Drift of a Positron's Position Between two Plates

I am writing code for a 1D case where a positron with charge $e$ and mass $m$ is placed between a charged plate, and a grounded plate in the positive $x$ direction, a distance $d$ away . Let the ...
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93 views

What are change of frame and change of coordinates?

What's the difference between a change of frame and a change of coordinates? I feel like both are transformations on the coordinates but change of frame changes also the vectors.
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How can the first Maxwell equation be valid in non-static cases?

I am thinking in the framework of Classical Gravity, where the speed of the interaction is infinite. Now it is also known that there is a correspondence between Classical gravity and electrostatics, ...
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1answer
33 views

Particle deflection in a magnetic dipole field

Consider a small magnetic dipole of magnetic moment $\vec{\boldsymbol{\mu}} = (\mu_x, \; \mu_y, \; \mu_z)$ sitting at the origin. The magnetic field all around is \begin{equation}\tag{1} \mathbf{B} = ...
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3answers
78 views

How to describe the unit vector for a complex wave vector?

In optics, we often come across complex wave vectors that describe absorption, dispersion, etc. given as: $\textbf{k} = \textbf{k}_{real} + i\textbf{k}_{imag}$ The electric field in phasor notation ...
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Negative real part AC conductivity

I am reading this paper, where the authors are calculating the frequency dependence of the chiral magnetic effect, i.e., ${\bf J} = \sigma^{\text{CME}}(\omega) {\bf B}$. The authors find, see for ...
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1answer
56 views

Lorentz Force Equation

We know that from relativistic Lagrangian for a charged particle is $$L = - m_0 c^2 \sqrt{1 - \frac{u^2}{c^2}} + \frac{q}{c} (\vec u \cdot \vec A) - q \Phi$$ leads to the Lorentz force equation, but ...
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27 views

Force on Dielectric on pulling it out from capacitor

This is the text from Griffiths Electrodynamics for calculating force on dielectric on pulling it out from capacitor when the capacitor is connected to Battery so that voltage of capacitor is fixed: ...