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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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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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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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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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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$\mathcal{\underline{J}}(\underline{r},t)=\rho(\underline{r},t) \underline{v}(\underline{r},t)$ 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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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261 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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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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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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172 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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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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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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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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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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$* 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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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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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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Pulsar distance estimation

This is quite an interesting problem in astrophysics so I thought it would be a good idea to ask here so we can archive the solution for future reference. Consider a pulsar that emits pulses of ...
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Electromagnetic wave in a prism

Imagine an electromagnetic plane wave entering perpendicular to one of the faces of a prism with the form of a triangle rectangle, which is made of a certain material of refraction index $n$. The wave ...
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Magnetic field $\vec{A}$ as momentum potential

I was reviewing some topics on electromagnetic field theory and I came across the following interesting assertion: the electromagnetic moment $P_{EM}$, which is defined in vacuum as: $$P_{EM}=\frac{1}...
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Green's function in a region between a conductor sphere and two charged spheres inside, with point charges inside of each

Please, help me. I have to find the Green's function in the following region, but I don't have any idea how to find it: I have a conducting spherical shell of radius a; in the center there are 2 ...
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How is Poisson's Equation solved numerically?

This question is of pure interest. I would like to know, how a mixed boundary value problem like the following can be solved numerically: Lets say I have two conducting plates (not necessarily ...
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Hamilton equations of motion for matter fields coupled to general relativity in ADM formalism

Do you know what are the Hamiltonian formalism analogs of the Klein-Gordon equation and/or the Maxwell equations in general relativity? Showing how these equations of motion for matter in the ...
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Relativistic Resistors

I would like to simulate what happens if you move electric circuits at relativistic speeds. At first, I would like to check the resistor. If I move a wire in the simplest case with speed $v$ along ...
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Can inhomogeneity in the medium accelerate particles

Suppose I have a charge which is moving in through a medium with constant velocity. Now, what will happen to the charge as it encounters an inhomogeneity in density? whether it will accelerate or ...
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Given an electromagnetic field in a frame of reference, find all other frames of reference where the electric and magnetic field are parallel

This is actually an exercise in Landau-Lifshitz's book. Their solution goes as follows. After we have found a frame of reference where $\mathbf E$ and $\mathbf B$ are parallel (let's call the common ...
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Calculating Radiation Pressure from plane waves on Boundary Surface

Suppose we have an incident Electromagnetic plane wave $E_I = E_{0I} e^{i(k_1 z - ωt)} \hat{x}$ and $B_I = \frac1{v_1} E_{0I}e^{i(k_1 z - ωt)} \hat{y}$ heading towards a surface $z=0$ between two ...
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Conservation law charge in plane-wave

When considering a charged particle in a plane-wave field, it is possible to show that the 2 following quantities are conserved $\boldsymbol{p}_{\perp} - e\boldsymbol{A}_{\perp}$ and $p_z - \gamma$ ...
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Motion of a particle near a charged plane

Consider a positive charge density in the $x-y$ plane, its electric field is $\vec{E}=\frac{\sigma}{2\epsilon_0}\hat{z}$. At moment $t=0$ a particle with positive charge $q$ begins to move with ...
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Magnetic permeability dispersion

Why is it that in Books they cover only the properties of the dispersion of the dielectric function but not The one of the magnetic permeability? I mean the function μ(ω)... It is like the dispersion ...
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Solution of wave equation not obeying maxwell equation

I was reading ch. 9 of classical electrodynamics of dr. griffith's. there he wrote that if a electric/magnetic field satisfy maxwell's equation then they must solve the wave equation which is $$ \frac{...