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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Classical electrodynamics as an $\mathrm{U}(1)$ gauge theory

Preface: I haven't studied QED or any other QFT formally, only by occasionally flipping through books, and having a working knowledge of the mathematics of gauge theories (principal bundles, etc.). ...
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211 views

Trouble with Classical Derivation of Cherenkov Radiation Mechanism — Magnetic Field Intensity

I've been going through a translation of Frank and Tamm's original theory on Cherenkov radiation published by Jelley in 1958, and the bottom line is that I'm stuck on one of the intuitive leaps that ...
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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 ...
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117 views

Is there a theorem about “Electromagnetic Miracles”?

I listened to a lecture several years ago in which the speaker claimed that there is a theorem that shows that violation of charge conservation under classical electrodynamics is impossible in the ...
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127 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 ...
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1answer
391 views

Divergent self-energy of point charges in Classical Electrodynamics

Assuming the electron to be a classical point particle, if one calculates the self-energy one finds $$U=-\frac{e^2}{8\pi\epsilon_0r}$$ which diverges as $r\rightarrow 0$. Therefore, the measured mass ...
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58 views

Why can infinite planes be approximated as Gaussian surfaces?

A little background: I'm an undergraduate studying Electrodynamics, currently in Chapter 8 of Griffiths. A question I came across (8.4 part a for those curious) asks for a calculation of the force ...
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80 views

$\mathcal{\underline{J}}(\underline{r},t)=\rho(\underline{r},t) \underline{v}(\underline{r},t)$ from Maxwell equations

In classical EM theory one can use the following equations as independent: $$\nabla \times \mathcal{\underline{E}}(\underline{r},t)=-\frac{\partial \mathcal{\underline{B}}(\underline{r},t)}{\partial ...
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96 views

Perturbative Techniques In Finding Electric Field of Symmetric Distributions

Lets say we have a uniform sphere of charges at the origin (at retarded time = 0) with some velocity and we are interested in the field at a point along the x-axis (normal to the surface of the sphere)...
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106 views

Number of Independent postulates in Electrodynamics

We know that there are two ways to get charge conservation in electrodynamics by using the following action: $$S[A]~=~\int\! d^4x {\cal L},$$ $$ {\cal L} ~=~{\cal L}_{\rm Maxwell} + {\cal L}_{\rm ...
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2answers
169 views

How does a charge distribution evolve with time? (in classical electrodynamics)

It is often stated that, in classical electrodynamics, the electric and magnetic fields determine uni vocally the dynamics of a charge distribution distribution (how it evolves in time). I can more or ...
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247 views

Free charge movement in an electric field - including bremsstrahlung

Let us imagine a free, negatively charged object that is in rest and placed in an elecric field of a point positive charge. The positive charge has a huge mass and cannot move, so we consider only the ...
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47 views

Questions about the energy density and momentum density in linear media

Precisely which energies are accounted for in the energy density of a linear medium given by $$u = \frac{1}{2}\left(\epsilon E^2 + \frac{1}{\mu}B^2\right)?$$ For example, is there a kinetic energy ...
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157 views

Maxwell stress tensor for electromagnetic wave

Sorry if this is a naive question but I've been struggling in trying to proof this for a week. Consider an electromagnetic wave with wave vector $\vec{k}=k\hat{n}$, the Maxwell stress tensor can be ...
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1answer
84 views

Retarded time in Larmor's formula

Let $q$ be the charge of a particle whose motion is $\mathbf y(t)$; let $\boldsymbol \beta = \dot {\mathbf {y}}/c $. Let also $\mathbf x$ be a point in space, and $r=|\mathbf x|$, $\mathbf n = \mathbf ...
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Electrodynamics,Laplace equation

Well the classical image charge problem in electrodynamics,clearly shows a slick way of dealing with some symmetric cases.But that seems somewhat a way of doing back calculations.So could anyone link ...
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49 views

Convergence to electrostatic equilibrium in a conductor

I am interested in proving mathematically that a conductor always converges to equilibrium in the surface. We model it as follows: We have an ohmic conductor, which means that it is a $3$-manifold $M ...
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27 views

How to calculate the electrical conductivity of an insulating dielectric?

So I am told that the dispersion relation for an EM wave in a conducting medium is: $$k^2 = \mu_0 \epsilon \omega^2 + i\omega \mu_0 \sigma_n$$ where $k$ is the wavevector, $\omega$ is the angular ...
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81 views

Interaction of charges and EM wave striking the surface of a conductor

Microscopically, what exactly happens between the charges on the surface of a conductor and the $E$ and $H$ components of the obliquely incident EM wave (in a classic viewpoint of field theory)? We ...
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2answers
654 views

Why does Griffiths's book say that there can be no surface current since this would require an infinite electric field for an incident wave?

In sec. 9.4.2 Griffiths shows the well known boundary conditions for E and B fields, one of them is this: $$\frac{1}{\mu_{1}}\textbf{B}_{1}^{\parallel}-\frac{1}{\mu_{2}}\textbf{B}_{2}^{\parallel}=\...
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53 views

Charge density relaxation, where does the charge go?

I have read that the charge distribution in conducting medium will redistribute to the boundary and cancel out the electric field inside the medium. According to my understanding, This occurs because ...
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133 views

A question about gauge transformations in classical electrodynamics and gauge transformations

Consider the free Maxwell's equations without being coupled to matter fields, for simplicity. The equations are invariant under $$A_\mu(x)\to A_\mu(x)+\partial_\mu\chi(x)\tag{1}$$ where $\chi(x)$ is ...
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372 views

Why does an EMF develop diametrically in the rotating disk in a magnetic field?

please use the image as a reference i understood that there will be an emf generated here, since the lorentz force will act on the electrons causing them to move towards the center of the disk.. as ...
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Relevance of Gauge Transformations in Physical Interpretations of a System

In the simple example of a stationary electric field (and some other quantum mechanical examples) it is shown in the papers https://arxiv.org/pdf/physics/0506203.pdf https://arxiv.org/pdf/1302.1212....
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1answer
71 views

How to prove this matrix differential for Born-Infeld theory?

Consider the Born-Infeld Lagrangian, page 30 of Born-Infeld Action and Its Applications by Cong Wang. $L_{BI} = \sqrt{\det (1+ F)}$ where $F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$. I ...
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111 views

What are the pragmatic solutions to point charge self-force/self-energy in relativistic simulations?

(I'm considering classical relativistic mechanics and classical electrodynamics throughout this post.) Usually, you calculate the motion of charges due to an external electromagnetic field, or you ...
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71 views

does an accelerated charge would be slower relative to an neutral particle due to radiating and lose energy ? both in free fall

this part from this article https://en.wikipedia.org/wiki/Paradox_of_a_charge_in_a_gravitational_field "Putting together these two basic facts of general relativity and electrodynamics, we seem to ...
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270 views

Deriving the classical electromagnetic point charge Lagrangian from the Abelian Yang-Mills Lagrangian density

Can I derive the point charge Lagrangian $$ L = -\frac{mc^2}{\gamma} - \frac{1}{c} J_{\mu} A'^{\mu}\tag{1} $$ from the Abelian Yang-Mills Lagrangian $$L = \int d^3x [ - \frac{1}{16 \pi} F_{\mu ...
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87 views

Ampere's law, do I include the electric field causing the current?

Let's say I have a long, straight wire with a time varying current, $I$ through it. Now if I take a circular Amperian path around this loop wire (and concentric with it) there is both a current $I$ ...
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272 views

Motion of a charged particle in a “solid” charged sphere (accounting for radiation)

Consider a particle (point charge) with charge $q$ and mass $m$ that crosses into a uniformly charged sphere (with charge $Q$ and radius $R$). The trajectory of the particle is a diameter of the ...
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55 views

Are there limits to human/devices perception?

As far as i know, measurement devices present measurements based on something that affects the device's particles, for instance, forces, heat, tension, voltage... My question is, given that every ...
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Induced emf in a circular conducting wheel

Consider a conducting wheel with $N \in \mathbb{N}$ spokes which is completely in a homogenous magnetic field $\vec{B}$ perpendicular to the wheel plane.        &...
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115 views

Polarizable molecule in E-field

If we have a linear molecule with a dipole moment $\mu$ in a static electric field $E$, the potential is given by $V = - \langle \mu,E \rangle$. What is the appropriate equation for the potential if ...
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174 views

Vector potential and gauge in electromagnetism

In a paper by Zimmerman [JOURNAL OF APPLIED PHYSICS 114, 044907 (2013)], it is stated that the Lorenz gauge in electromagnetism is the only gauge with real physical meaning. How do I reconcile this ...
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49 views

Where does 1/Gamma characteristic angle come from in EM Radiation?

Very curious as to where this angle comes from? It describes the peak of radiation for almost all radiation regimes, but I am having a difficult time seeing where it comes from. Also, the physical ...
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137 views

Mie Scattering for spheres with constant dipole moment

I was wondering whether there exists a theory that describes Mie Scattering for spheres that have a constant dipole moment. Since there are theories that describe Mie scattering in the case of a ...
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617 views

Boundary Condition for Perfect Conductor in Uniform Magnetic Field

When I was studying the perfect conductor scattering (Section 10.1) in Jackson's book, I was confused by the calculation for magnetic dipole induced by the incident wave. He simply said like "set the $...
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64 views

When can a center of mechanical momentum frame be found for an electromagnetic system?

In classical mechanics, a center of mechanical momentum frame can always be found for a system of particles interacting with one another locally. For an electromagnetic system where the charges ...
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23 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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149 views

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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28 views

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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22 views

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
133 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 ...
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1answer
48 views

How to calculate induced emf of moving rod?

I have the following exercise: A copper rod with length L is moving on two frictionless conducting rails, in a distance a from an very long straight conductor. The rods resistance: R. Ignore any self ...
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36 views

$* d * $ operator — Digest the (differential/geometry) meaning

I like to digest better: the $* d * $ operator in Maxwell differential form equation the $* D * $ operator in Yang-Mills differential form equation We already knew that in Maxwell differential ...
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1answer
48 views

Repulsive force from charge accumulation in a capacitor plate?

During a charged state of a capacitor (Regardless of the type of capacitor), Simple parallel plate: .png Parallel plate with dielectric material in the gap: ]3 Supercapacitor: How is the ...
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Effects generated from a supercapacitor placed in a time varying external magnetic field?

The diagram above, showcases the simple outlook of a supercapacitor's interior and combining it with a full circuit loop. If an exterior magnetic field is introduced in all the operating states of a ...
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2answers
91 views

The Electromagetic Tensor and Minkowski Metric Sign Convention

I am trying to figure out how to switch between Minkowski metric tensor sign conventions of (+, -, -, -) to (-, +, +, +) for the electromagnetic tensor $F^{\alpha \beta}$. For the convention of (+, -,...
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29 views

Space translation of coordinates, classical field theory

Consider the Lagrangian density $L = -\frac{1}{4}F_{\mu\nu}F^{\mu \nu}$ with $F_{\mu \nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu} $. After deriving the Euler-Lagrange equations for this ...
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1answer
62 views

Divergence of current density and electric field within a wire

In the following exercise: I concern myself with the validity of my interpretations of (b). Here I am more confident slightly. The divergence of the current density is merely $- d \rho / dt$, so as ...