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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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Do Maxwell's Equations overdetermine the electric and magnetic fields?

Maxwell's equations specify two vector and two scalar (differential) equations. That implies 8 components in the equations. But between vector fields $\vec{E}=(E_x,E_y,E_z)$ and $\vec{B}=(B_x,B_y,B_z)$...
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1answer
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How does this “simple” electric train work?

In this YouTube video, a dry cell battery, a wound copper wire and a few magnets (see image below) are being used to create what can be described as "train". It looks fascinating but how does this ...
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4answers
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What is momentum really?

Wikipedia defines momentum as in classical mechanics: In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object. However, an ...
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5answers
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What is the answer to Feynman's Disc Paradox?

[This question is Certified Higgs Free!] Richard Feynman in Lectures on Physics Vol. II Sec. 17-4, "A paradox," describes a problem in electromagnetic induction that did not originate with him, but ...
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Does a magnetic field do work on an intrinsic magnetic dipole?

When you release a magnetic dipole in a nonuniform magnetic field, it will accelerate. I understand that for current loops (and other such macroscopic objects) the magnetic moment comes from moving ...
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Recommended books for advanced undergraduate electrodynamics

What books are recommended for an advanced undergraduate course in electrodynamics?
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1answer
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Boundary conditions / uniqueness of the propagators / Green's functions

My question(s) concern the interpretation and uniqueness of the propagators / Green's functions for both classical and quantum fields. It is well known that the Green's function for the Laplace ...
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4answers
2k views

The problem of self-force on point charges

Allow me to preface this by stating that I am a high school student interested in physics and self-studying using a variety of resources, both on- and off-line, primarily GSU's HyperPhysics website, ...
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2answers
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Theoretical penetration limit for evanescent waves

Consider a problem in classical electrodynamics, when a monochromatic beam experiences total internal refraction when traveling from a medium with $n>1$ to a medium with refractive index $1$ - see ...
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Why is dipole the simplest source in electrodynamics?

I see this sort of statement in many materials, for example this: The smallest radiating unit is a dipole, an electromagnetic point source. and this: The simplest infinitesimal radiating ...
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4answers
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Can two electrons get ever so close as to touch each other?

My friend and I were studying for our EM test when we started to think about what happens to the electric field near an infinite line of charge. $$E = \frac{\lambda}{2\pi\rho\epsilon_{0}}$$ As you ...
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5answers
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Does GR provide a maximum electric field limit?

Does GR provide a limit to the maximum electric field? I've gotten conflicting information regarding this, and am quite confused. I will try to quote exactly when possible so as not to confuse ...
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5answers
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How many photons are needed to make a light wave?

What is the smallest number of photons needed to make a "light wave"? In other words, how many (coherent?) photons start to exhibit classical behavior? For example, how many photons are needed to get ...
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Is classical electromagnetism a dead research field?

Is classical electromagnetism a dead research field? Are there any phenomena within classical electromagnetism that we have no explanation for?
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4answers
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Can we measure an electromagnetic field?

As far as I can check, the Aharonov-Bohm effect is not -- contrary to what is claimed in the historical paper -- a demonstration that the vector potential $A$ has an intrinsic existence in quantum ...
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2answers
642 views

Coulomb gauge fixing and “normalizability”

The Setup Let Greek indices be summed over $0,1,\dots, d$ and Latin indices over $1,2,\dots, d$. Consider a vector potential $A_\mu$ on $\mathbb R^{d,1}$ defined to gauge transform as $$ A_\mu\to ...
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2answers
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Trouble understanding the Bohr model of the atom

In this article it says: The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits") at a certain discrete set of distances from the nucleus. ...
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2answers
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An example which contradict to Newton's 3rd law?

Let a,b be two charged particles. $$\vec{r}_a(0)=\vec{0}$$ $$\vec{r}_b(0)=r\hat{j}$$ $$\vec{v}_a(t)=v_a \hat{i}$$ $$\vec{v}_b(t)=v_b\hat{j}$$ In which both $v_a$ and $v_b$ $<<c$. Then $$\...
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4answers
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Is the electromagnetic mass real?

In his Lectures on Physics vol II Ch.28-2 Feynman calculates the field momentum of a moving charged sphere with charge $q$, radius $a$ and velocity $\mathbf{v}$. He finds that the total momentum in ...
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1answer
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Physical Interpretation of EM Field Lagrangian

Using differential forms and their picture interpretations, I wonder if it's possible to give a nice geometric & physical motivation for the form of the Electromagnetic Lagrangian density? The ...
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3answers
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Maxwells Equation from Electromagnetic Lagrangian

In Heaviside-Lorentz units the Maxwell's equations are: $$\nabla \cdot \vec{E} = \rho $$ $$ \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} = \vec{J}$$ $$ \nabla \times \vec{E} + \frac{\...
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How did Maxwell's theory of electrodynamics contradict the Galilean principle of relativity? (Pre-special relativity)

The Galilean principle of relativity: The laws of classical mechanics apply in all inertial reference systems OR No experiment carried out in an inertial frame of reference can determine the ...
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2answers
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If you run an electric current through a wire loop, do the accelerated charges radiate?

Does an accelerated charge always radiate? For example the current electrons in an electric circuit when moving through a turn they are accelerated, do they radiate because of that acceleration? If ...
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2answers
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What is the mechanism by which magnetic fields do work?

I've seen some conflicted answers to this question in texts and on the web, in the case of a dipole, for example. Do magnetic fields do work directly, or is it their induced electric fields that do ...
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4answers
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How does the emf “know” what the magnetic flux is?

I came across an example in my book where it has the changing flux from a solenoid passing through a larger ring at the end. Here's a picture: How does the large loop (or radius $r_1$) even “know” ...
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2answers
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Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics

How do I definitively show that there are only two propagating degrees of freedom in the Lorenz Gauge $\partial_\mu A^\mu=0$ in classical electrodynamics. I need an clear argument that involves the ...
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3answers
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Maxwell's Stress Tensor

What really is the Maxwell Stress Tensor? I understand that it's derived from $$\mathbf {F} = \int _V ( \mathbf E + \mathbf v \times \mathbf B )\rho \ d \tau$$ Griffiths describes this as "total EM ...
11
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6answers
591 views

Charged particle as observed from an inertial and a non-inertial frame of reference

A charged particle fixed to a frame $S^\prime$ is accelerating w.r.t an inertial frame $S$. For an observer A in the $S$ frame, the charged particle is accelerating (being attached to frame $S^\prime$)...
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3answers
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Is it true that any system of accelerating charges will radiate?

I was recently told by a physics teacher that "any system of charges in which at least some of the charges are executing some sort of accelerated motion, will radiate and lose energy". This refers to ...
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2answers
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What are the dimensions, width and length, of a photon?

Everyone is always talking about photon's wavelength. But what about its dimensions? What is length and width of it? And does it even have a point to think about such things? Or those dimensions are ...
11
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2answers
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Is there a Hamiltonian for the (classical) electromagnetic field? If so, how can it be derived from the Lagrangian?

The classical Lagrangian for the electromagnetic field is $$\mathcal{L} = -\frac{1}{4\mu_0} F^{\mu \nu} F_{\mu \nu} - J^\mu A_\mu.$$ Is there also a Hamiltonian? If so, how to derive it? I know how ...
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1answer
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Noether's first theorem and classical proof of electric charge conservation

How to prove conservation of electric charge using Noether's first theorem according to classical (non-quantum) mechanics? I know the proof based on using Klein–Gordon field, but that derivation use ...
11
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1answer
303 views

If the classical Maxwell theory describes E&M fairly, how well-done is the classical Yang-Mills theory for chromodynamics?

If the classical Maxwell theory describes electrodynamics (electromagnetism E&M) fairly well, how suitable would the classical Yang-Mills theory (say SU(3) color) describe the chromodynamics, and ...
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1answer
935 views

Explanation for speed of an electrical impulse

Our calculus book, Stewart, has a problem where they claim that for a metal cable (inner radius $r$) encased in insulation (outer radius $R$), the speed of an electrical impulse is given by $$v = - ...
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4answers
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Does light actually travel through glass?

I am currently reading about the interactions between light and matter, but I keep coming across conflicting explanations. My initial understanding (using classical electrodynamics) was that light (...
10
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4answers
929 views

Why is classical electromagnetism linear? [duplicate]

When I ask this, I mean it as in when a test charge $q$ is placed in a region that contains two fixed charges $q_1$ and $q_2$, the force acting on it is the vector sum of the forces it would ...
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2answers
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Pseudoscalar action in classical field theory

I was reading Landau and Lifschitz's "Classical Field Theory" and came across a comment that the action for electromagnetism must be a scalar, not a pseudoscalar (footnote in section 27). So I was ...
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1answer
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Recovering all of Maxwell's equations from the variational principle

Whether you can get the first couple of Maxwell equations from a variational principle? In the second volume of the Landau theoretical physics said that it is impossible.
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3answers
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Symmetry in electricity and magnetism due to magnetic monopoles

I was wondering about the differences between electricity and magnetism in the context of Maxwell's equations. When I thought over it, I came to the conclusion that the only difference between the two ...
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3answers
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Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation?

In Physical Review Letters, there was a paper recently published: Masud Mansuripur, Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation, Phys. ...
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1answer
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Semiclassical QED and long-range interaction

I'm interested in the (very) low energy limit of quantum electrodynamics. I've seen that taking this limit does not yield Maxwell equations, but a quantum corrected non-linear version of them. If ...
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2answers
547 views

Electrostatics/ magnetostatics: why is $\int_\text{all space} d\vec r \; \nabla \cdot(\vec A \times \vec B)$ equal to 0?

I'm reading electrodynamics notes and come across that $$\int_\text{all space} \mathrm{d}\vec r \; \nabla \cdot \left(\vec A \times \vec B \right)~=~0$$ in case of magnetostatics and$$ \int_\text{...
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2answers
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Why are EM waves transverse?

I was reading Griffiths' Introduction to Electrodynamics, specifically the section on plane waves. I can see that if we want a transverse wave traveling in the $z$ direction that we are only going to ...
9
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4answers
556 views

Will accelerated observer see radiation from the charge that is at rest in observers's frame?

So I had a huge debate about this with my friends. Imagine that you are in a non-inertial frame of reference. For simplicity, assume that frame is accelerated along x-axis. You have held a charge in ...
9
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1answer
682 views

The spin-orbit interaction for a classical magnetic dipole moving in an electric field

Spin-orbit coupling is one component of the fine structure of atoms, which is explicitly concerned with the interaction of the electrons' spin with their orbital angular momentum. It can be explicitly ...
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0answers
683 views

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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6answers
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Is electromagnetic vector field a sum of E and B?

I have a hard time to fully understand (classical) electromagnetic field theory with respect to Helmholtz's decomposition. Let me start from Helmholtz's theorem: Any vector field of class $C^{\...
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3answers
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How do the electric or magnetic fields contain momentum?

I have recently come to know that the electric and magnetic field contain both linear and angular momenta, which are known functions of the electric and magnetic fields at any given point in space and ...
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3answers
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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, ...
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4answers
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Why does electric field intensity $E$ can be uniquely determined by its divergence and curl? [duplicate]

My question is, the number of following equations $$\nabla\cdot E=\frac{\rho}{\varepsilon}$$ $$\nabla\times E=-\frac{\partial B}{\partial t}$$ is 4 while the number of unknown variables $E=(E_1,E_2,...