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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Lagrangian of Charged Particle Evaluated On-Shell

I am trying to calculate the Lagrangian of a charged particle in background gauge field evaluaed on-shell. Let $A^{\mu}(x)$ be a gauge field. The action of a charged particle in this background gauge ...
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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 field from displacement currents in a capacitor, and an applied exterior magnetic field

If an exterior magnetic field ($B$) is applied to oppose or support the magnetic field produced by the displacement currents ($B_D$), what would happen to the electric field within the gap? And the ...
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Moving a conductor with the presence of both E & B fields?

If a conductor is charged from an exterior electric field, moved in a magnetic field perpendicular to the E-Field, the velocity's direction is also perpendicular to both the B-field and E-field. How ...
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Magnetic field induced from the conductive capacitor plates?

If a capacitor is being charged or in the process of discharge, there is current flowing in/out of the conductive plate, besides the magnetic field produced by the displacement currents($B_{dc}$) in ...
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Why do thermal hotspots in a metallic nanoparticle do not match it's optical hotspots?

I am a little bit confused here. When a metallic nanoparticle is impinged with light at its resonance, the electric field is greatly enhanced at the surface along the polarisation of the wave(suppose ...
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Why is beam forming more energy efficient than a straight up omnidirectional signal?

Someone tried to explain the process of beam forming to me, and how beam forming is far more efficient than an omnidirectional signal of similar amplitude. This seemed obvious at the time: the power ...
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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 ...
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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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Is the dynamics of a classical (non quantum) electron in general relativity an open research question?

In a study of classical electrodynamics the dynamics of an electron appears to be an open question - on which a lot of interesting work has been completed, for example Hendrick Lorentz and Paul Drude, ...
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Apparent paradox in electrodynamics problem

A few days ago I saw on Veritasium a video about electrodynamics and relativity Veritasium video and it got me thinking a bit about the nature of light. Between minutes 1:10 and 2:40 Derek from ...
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Lorentz force, force on conductors

We generally say that Lorentz force acts on the charge particles. but when we keep a current carrying conductor in a wire, we say the wire experience a force. now how we explain it?
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Accelerated electret

An electret is something that holds an electric charge. Typically it is a piece of plastic with charges stuck inside that can't get out. Suppose you stuck an electret with a large negative charge ...
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General proof of independence of TM and TE modes in a waveguide

In electromagnetic field analysis for a typical waveguide that has a uniform cross section along its axial direction (say $z$), we often describe the E and H fields conveniently in terms of their ...
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A doubt in Yang-Mills procedure

My question is this: I saw the next relation in a Yang Mills theory paper: $$L_{i}P^{\mu \nu}_{i}=P^{\mu \nu}$$ With $L_{i}$ a generator of su(2) and for any $P^{\mu \nu}_{i}$. But I can't ...
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Dipole Receive Antenna: Derivation of circuit representation

Many textbooks cover generation of electromagnetic radiation via transmit antenna and then invoke a reciprocity theorem for the antenna acting as a receiver. I'm wondering, can you derive the ...
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Determining charge distribution from electric field (Griffiths 4th)

I am trying to teach myself Electrodynamics by following Griffiths' book. This is probably what's considered a "homework question", but as I don't have an instructor to ask for help, I'm hoping ...
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motion of a conductor in a varying magnetic field, is motional emf still valid?

If a conductor moves within a uniform constant magnetic field, the magnetic force would separate the charges leading to an induced emf. And if the conductor was stationary, and the magnetic field were ...
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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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Problem verifying Gauss's law

I am trying to verify Gauss's law, differential form, SI units, non-special relativity regime, ignoring time retardation, by performing the differentiation on the left-side of the equations to see if ...
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Conflicting definitions of Current Density J?

I am reading up on dipole/multipole radiation in Zangwill's Modern Electrodynamics (2013) and I am getting super confused about the units and convention of current density. On Page 735, equation 20....
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Example 4.2 of Griffiths introduction to electrodynamics

So i was doing the chapter electric fields in matter and in example 4.2 ,the author asks to find electric field due to uniformly polarized sphere of radius R. So i think there is no free charge hence ...
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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{...
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Linear, surface and volume currents

How can I find all the linear, surface and volume currents if I have given the magnetic field $\vec B(r,\theta , \phi )$ $=$ $\frac {aB_0}{r\sin \theta}\vec e_{\phi}$ for $a \gt 0$, otherwise $\vec B(...
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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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Electrostatic force between half cylinder and dielectric plate

The problem is as follows: A half cylinder of radius $R$ and length $L>>R$ is formed by cutting a cylindrical pipe made of an insulating material along a plane containing its axis. The ...
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Discontinuity of the magnetic field $\vec B(r,\theta , \phi )$ $=$ $\frac {aB_0}{r\sin \theta}\vec e_{\phi}$

I got the magnetic field given as following: $\vec B(r,\theta , \phi )$ $=$ $\frac {aB_0}{r\sin \theta}\vec e_{\phi}$ $\;$ for $\;$ $\theta \gt [0,\pi /4]$ $\;$ and $\;$ $\vec B(r,\theta , \phi )$ ...
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Negative Joule heating?

In general Joule-heating a.k.a. Ohmic heating due to an electromagnetic field interacting with a conducting medium leads to dissipation of energy, which is converted into mechanical energy (or is it ...
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175 views

Parity transformation property of $\epsilon^{\mu\nu\sigma\rho}$ and $F_{\mu\nu}$ (and $G_{\mu\nu}^a$)

The Lorentz invariant term $\epsilon^{\mu\nu\sigma\rho}F_{\mu\nu}F_{\sigma\rho}$ is not parity invariant. To show this one needs to find the parity transformation property of $F_{\mu\nu}=\partial_\mu ...
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470 views

Magnetic field inside a rotating, accelerating cylindrical shell of charge

The problem: A cylindrical thin shell of electric charge has length $l$ and radius $a$, where $l \gg a$. The surface charge density on the shell is $\sigma$. The shell rotates about its axis with ...
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Plane wave approximation

Consider a proton in harmonic motion along vertical direction. http://physics.weber.edu/schroeder/mrr/MRRtalk.html Near a point source, direction of electric field is along the curve. https://en....
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Electric Force in Vacuum

Lets say we have a point charge $A$ in a vacuum, and a similarly charged point $B$ some distance away which detects the field, and feels a force of attraction or repulsion. There are electric field ...
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Why does a magnetic field “curl” around a current carrying element? [duplicate]

From all the texts I've read, it's always stated that the magnetic field would either curl or warp around the the current flowing within a conductive element, yet, I never was clarified as to why that ...
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Relationship between electronic current and electron momentum?

I remembered when reading Laughlin's famous argument for quantum Hall, it implied the actual current should be proportional to the electron's mechanical momentum ($p-eA/c$) instead of $p$ itself. Why ...
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Why should a conductor loop moving towards a magnet have an induced current?

If we place a bar magnet along the x axis, the magnetic field near its poles would be parallel to the x axis. Now, let's bring a circular loop near the the magnet, moving the loop along the x axis. ...
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Gauge invariant scalar which is not Lorentz-invariant

I'm looking for examples of the following descriptions: A gauge invariant scalar which is not Lorentz-invariant A Lorentz covariant scalar For 1. I was thinking about the scalar potential A (for the ...
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Problem in understanding Differential form of Gauss's Law

I am well aware of the integral form of Gauss's Law and the mathematical deduction through which it is reduced to the differential form. But I think I have a flaw in my understanding of divergence. ...
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boundary condition of perpendicular component of electric field of a thin sheet

This question is in reference to Introduction to Electrodynamics by David Griffith By Gauss's law: $\oint_{S} \vec{E}.d\vec{a}=\frac{Q_{enclosed}}{\epsilon_{0} }$ where $Q_{enclosed}$ is the ...
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Motion of a charge in magnetic field

Let us assume, we have a charge (let's say an electron) at rest in a uniform magnetic field (assume magnetic field is along z-direction). Suddenly magnetic field is switched off in a very short span (...
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Simple pendulum with magnetic bob through a circular loop

I'm developing a project for my electromagnetism course and the idea is to make a simple pendulum that has a magnetic bob, and the bob passes through a circular loop induced with some current. i.e. a ...
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Is a purely classical description of lasers possible?

Laser action is usually described in terms of photons and stimulated emission. In 1972, Borenstein and Lamb published a paper* claiming that lasers can be described classically on the basis of ...
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How many degrees of freedom does an electromagnetic field have? How to correctly count them?

How many independent degrees of freedom does a most general classical electromagnetic field have in presence of sources? What is the correct way to count them? In terms of the components of the ...
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Is the description of the gravitational field as a vector field and a tensor field compatible?

By electric or magnetic fields we mean the vector fields $\vec{E}(\vec{r},t)$ and $\vec{B}(\vec{r},t)$ respectively. But a gravitational field in Newtonian theory is a vector field that $\vec{g}(\vec{...
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Nature of Current in AC Circuit under the presence of Capacitors

In AC circuits under the presence of a capacitor and an AC power source the current leads by a phasor factor of $π/2$ with respect to the potential difference across the capacitor at any point of time ...
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Why divergence of Electric field is defined differenly as $\nabla \cdot \mathbf {E} ={\frac {4\pi \rho}{\varepsilon}}$ in f dependence of $\sigma$?

The derivation of Frequency dependence of conductivity in "Classical Electrodynamics - Greiner" uses following definition for Divergence of Eletric Field. $$\nabla \cdot \mathbf {E} ={\frac {4\pi \...
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Application of the principle of causality to classical electrodynamics

I am reading Griffiths' Introduction to Electrodynamics in which he shows that the retarded and advanced potentials, e.g. the retarded scalar potential $$ V(\mathbf{r},t) = \frac{1}{4\pi\epsilon_0} \...
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“Redefinition” of momentum in Schwinger's Classical Electrodynamics

I'm asking this question because I'm currently engaged in self-study of the book "Classical Electrodynamics" by J. Schwinger, et al. In particular I'm reading chapter 4, section 1, on the force on an ...
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In Maxwell equations, why time derivatives only appear together with Curl?

In the four maxwell's equations, the time dependence only appear in curl of $E$ and $B$ but not divergence. My question was that: Why time dependence only appear in curl? what's the implication? (I ...
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Motional Electric Field

When a conductor moves through an electric field, charge carriers inside it experience the Lorentz force, which takes the form $\mathbf{F} = q \mathbf{v} \times \mathbf{B}$. As the positive and ...