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Questions tagged [maxwell-equations]

A set of four equations that define electrodynamics. They comprise the Gauss laws for the electric and magnetic fields, the Faraday law, and the Ampère law. Together, these equations uniquely determine the electric and magnetic fields of a physical system. DO NOT USE THIS TAG for the Maxwell-Boltzmann distribution, or the thermodynamical equations known as Maxwell's relations.

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Flux change through a loop

I'm having difficulties understanding this thing. It would be lovable if someone could show me its derivations and prove it: In a conducting loop, there is a relationship between the total displaced ...
AhmedSahraoui's user avatar
4 votes
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Lorentz force error in the present 2024 version of the gravitoelectromagnetism Wikipedia page? [closed]

I noticed that the Gravitoelectromagnetism (GEM) Wikipedia page has been edited recently. The factor of 4 in the GEM Lorentz force equation is now missing. But the GEM field equations are identical to ...
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Maxwell stress tensor on a capacitor late given a dielectric

Given a capacitor with large plates (area $A$) separated by a dielectric with relative permittivity $\varepsilon_r$ and thickness $g$, I believe the Maxwell stress tensor states that the force on each ...
asyndeton256's user avatar
3 votes
2 answers
154 views

The puzzling interaction between an anapole moment and external fields

Consider an electrical current distribution with only an [anapole, or toroidal moment] but no electrical or magnetic multipole moments, like this current on a torus: Its magnetic field is completely ...
Jos Bergervoet's user avatar
18 votes
3 answers
3k views

Is there a second-order non-linear addition to Maxwell's equations?

Maxwell's equations are famously linear and are the classical limit of QED. The thing is QED even without charged particles is pretty non-linear with photon-photon interaction terms. Can these photon-...
Aravind Karthigeyan's user avatar
1 vote
2 answers
84 views

Divergence of Electric Field of Point Charge is always zero [closed]

I might have a bug in my brain, but I just can't figure this out. Please help. According to the first of the Maxwell Equations, we have $$ \nabla\cdot\vec{E}=\frac{\rho}{\epsilon_0}. $$ And we have ...
tobi-v's user avatar
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Deriving the Cable Equation from Maxwell's Equations

My goal is to reach equation 12 on this wikipedia page: Cable Theory. The demonstration is usually done by making an infinitesimal circuit, but I would like to get there via Maxwell's Equations by ...
Ícaro Lorran's user avatar
1 vote
2 answers
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Which magnetic field is the one in the inductance equation?

Any self induction problem that can be solved via $emf=-N\frac{\Delta \phi}{\Delta t}$ should be equivalently solvable via $-L\frac{\Delta i}{\Delta t}$. What if the coil is already existing in a ...
Jack's user avatar
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What step is missing from this transformation of the Clausius-Mossotti relation into the Garnett-Maxwell equation?

When deriving the Maxwell-Garnett equation for composite systems (host material with dielectric particles disposed in it), the steps generally taken are Step 1) Equate the Clausius-Mossotti equation ...
user7077252's user avatar
5 votes
1 answer
301 views

EM 4-potential vs gravity 4-potential?

In classical field theory, the electrostatic and gravitational fields have very similar differential forms: $$\vec \nabla\cdot \vec{E}=\frac{\rho}{\varepsilon_0}$$ $$\vec \nabla\cdot \vec{g}=-4\pi G\...
Lagrangiano's user avatar
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How is the local field in a dielectric material calculated?

I have read in different sources (text, video, amongst others) that the local field in a dielectric material placed within a capacitor can be easily calculated as the sum of 4 electric fields: $E_{...
user7077252's user avatar
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1 answer
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J. J. Thomson's "on momentum in the electric field": can it be true physically?

J. J. Thomson imagined a physical system consisting of one electric field source (charge $q$ or else) and one magnetic field source (magnetic monopole $g$ or maybe magnet or something else), with $q$ ...
Ayhan Yuzubenli's user avatar
1 vote
1 answer
94 views

General Solution to Maxwell's Equations with Duhamel's Principle

In one dimension, it is easy to prove that if two solutions $\{u_1, u_2\}$ are known to $\mathcal{L}u(t) = 0$ where $\mathcal{L} \equiv{a(t)\partial_t^2+b(t)\partial_t+c(t)}$, the general solution to ...
Cody Payne's user avatar
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Why is there attenuation or amplification of the electric field depending on the sign of angle?(Maxwell's equations in free space)

If you solve Maxwell's equations in free space for a complex $\epsilon$ you get this equation: $\triangledown^{2}E = -\mu \left |\epsilon\right |e^{i\phi}\omega^{2}E$. Compared to the equation when $\...
ElectronicsBeginner's user avatar
-2 votes
1 answer
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Generalised wave equation from Maxwell's equations [closed]

I was playing around with Maxwell's equations and I've found a linear combination of the electric and magnetic fields which also satisfies a wave equation, but I don't know the implications of this. I ...
Lagrangiano's user avatar
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2 votes
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How to derive $\partial^{\nu}F^{\mu\alpha} + \partial^{\alpha}F^{\nu\mu} + \partial^{\mu}F^{\alpha\nu}=0$ for the Electromagnetic field tensor? [closed]

The problem says to show that $$\partial_{[\mu}F_{\alpha\nu]}=F^{\mu\alpha, \nu} + F^{\nu\mu,\alpha} + F^{\alpha\nu,\mu}=0$$ stems from Maxwell equations. I haven't been able to find this anywhere on ...
TiredStudent's user avatar
10 votes
1 answer
951 views

Reformulation of Maxwell's equations in the event of finding a magnetic monopole

If we ever obtain empirical confirmation of the existence of magnetic monopoles, how would Maxwell's classical equations be re-written? I'm assuming we'd only need to set the divergence of the ...
Lagrangiano's user avatar
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Expression for intensity in quantum vs. classical electromagnetics

I am wondering how the following expression for intensity in terms of the quantized fields is derived: $$ I = \frac{2\epsilon_0 c}{P} \int_0^P \langle E^-(t) E^+ (t) \rangle dt $$ where $P$ is the ...
photonica's user avatar
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Where comes the Biot-Savart formula from? [duplicate]

I learned about the Biot-Savart Law recently. I understand how to calculate magnet fields with it, but where does this formula $$dB=...$$ come from? My professor just told me we do that in theoretical ...
jurek's user avatar
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22 votes
5 answers
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Does a time varying electric field always generate a Magnetic field?

I have come across this problem from 200 Puzzling physics problems A charged spherical capacitor slowly discharges as a result of the slight conductivity of the dielectric between its concentric ...
Rishikesh's user avatar
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2 answers
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Understanding time reversal symmetry in Classical Physics

By looking at Newton's second law, we can immediately infer said equation is symmetric in time: $$m\frac{d^2\vec{r}}{dt^2}=\vec{F}(\vec{r},t)$$ since we can change $t\to -t$ and everything remains ...
Lagrangiano's user avatar
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4 votes
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Can we impose Coulomb gauge without using temporal gauge in source-free Maxwell electrodynamics?

Coulomb gauge is $$\vec{\nabla} \cdot A=0$$ Now, from expression for electric field in terms of potentials $\vec{E}=-\vec{\nabla} \phi-\frac{\partial \vec{A}}{\partial t}$ and Gauss Law $\vec{\nabla} \...
Nairit Sahoo's user avatar
2 votes
0 answers
64 views

Causality in Maxwell's equations

I have just read Jefimenko's notes on the causality violation it would pose to claim "varying electric fields give place to magnetic fields and viceversa" since both fields take place at the ...
Lagrangiano's user avatar
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What is the induced electric field in a moving conducting material in a magnetic field?

I've been taught that the induced EMF in a conductor is the rate of change of flux in it, but Maxwell's equation $$ \nabla\times\vec{E} = -\dfrac{\partial\vec{B}}{\partial t}, $$ only states so for ...
Duta Kartvelishvili's user avatar
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0 answers
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Why the tensor form of the Maxwell equation without any sources only contain two equations? [duplicate]

This is the Maxwell equation written in the book in vacuum, but when I plug the strong tensor Fσρ into formula to calculate, found that it seems to be missing two equations (the divergence of the ...
Mihari Oyama's user avatar
1 vote
1 answer
101 views

In Maxwell’s Fluid Analogy, is the Magnetic Field the “Wake”?

Does Maxwell's analogy of incompressible fluids extend so far that the magnetic part of a wave created by a moving electric charge is like the "wake" of a moving body through fluids? What is ...
Teragreg's user avatar
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1 answer
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Wrapping a Voltmeter Around a Solenoid

I just read this really interesting paper by Robert H. Romer and it has me curious: what would happen if you wrapped the positive lead of a voltmeter once around a solenoid with a linearly increasing ...
Dominic Stewart-Guido's user avatar
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Solving divergence and curl equations numerically

I've recently come to learn about Jefimenko's general solution for Maxwell's equations as well as the FDTD method in electromagnetic optics, and that has got me thinking whether I myself can solve ...
Lagrangiano's user avatar
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2 votes
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In magnetrons, is it the accelerating electrons or alternating fields within the anode that produce the microwaves?

Doing a report for a school project and want to get to the bottom of the radiation source within a microwave oven: According to Maxwell's equations don't the accelerating electrons (accelerating ...
Hearn's user avatar
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1 answer
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Why are Maxwell's equations true?

Einstein's field equations are true, and have been tested. But the question why they are true has been attempted to be answered by string theory, etc. Maxwell's equations are also true, but does ...
DanielFBest's user avatar
1 vote
0 answers
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Faraday Cage with respect to Maxwell's Equations

I could really use your help in understanding how a Faraday cage and Maxwell's Equations come together. From my understanding: For the electrostatic case, the Faraday cage cancels out an incoming ...
Vibrations's user avatar
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1 answer
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Mathematical definition of ray

I have just begun studying geometrical optics, and there is something mysterious about it. What I want to know is how to derive the definition of ray from Maxwell's equation. In vacuum, ...
Normalbut_Genuine's user avatar
3 votes
2 answers
134 views

Why is $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$?

I'm sorry if this is a duplicate but I didn't find my answer. I'm currently studying maxwell's equations and I know that by comparing the wave equation for either the magnetic or the electric field \...
Axodarap's user avatar
0 votes
3 answers
230 views

Derivation of Maxwell's equations using Lagrangian formalism [duplicate]

Some time ago, I read in Landau's Theoretical Physics Course you could derive Maxwell's equations using the Lagrangian formalism, and I find this to be exciting. Unfortunately, I don't have access to ...
Lagrangiano's user avatar
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1 vote
2 answers
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How do I show that the Electric field can be written as a composition of an irrotational and a solinoidal one?

I know that Helmholtz tells us that any vector field can be expressed as a superposition af an irrotational part and a solinoidal part. So for the electric field we get $$ \begin{equation} \vec{E} = ...
Jocobes's user avatar
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Electromagnetic Diffusion Equation

I am looking at a derivation for the electromagtic diffusion equation. It starts with Maxwells equations for the magneto-quasi-static case ($\frac{\partial \vec{D}}{\partial t} = 0$). $$ \begin{align} ...
Axodarap's user avatar
6 votes
6 answers
2k views

Derivation of Coulomb's law from Maxwell's equations

I'm trying to find sufficient additional conditions to derive Coulomb equation for the electric field generated by a steady point charge in free space from Maxwell equations in said conditions. I know ...
Lorenzo Vanni's user avatar
2 votes
2 answers
111 views

Why does $\oint_C \vec{E}\cdot d\vec{\ell}=0$ imply $\nabla\times \vec{E}=\vec{0}$?

In electromagnetism, the circulation of the $\vec{E}$ field is zero, \begin{equation} \oint_C \vec{E}\cdot d\vec{\ell}=0. \end{equation} With Stokes law, this implies that \begin{equation} \int_S \...
adriaanJ's user avatar
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1 answer
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Do the solutions to Maxwell's equations form a group?

How many solutions are there for Maxwell's equations? (Or rather, is there a finite number of them?) Regardless of how many solutions to these equations exist, could we claim they form a group? If so,...
Lagrangiano's user avatar
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2 answers
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Possibility of complex EM waves

I'm currently studying Quantum Mechanics, and I have just been presented Schrödinger's (time dependent) equation. Of course, the first solution to said equation I've been taught is that of a (complex) ...
Lagrangiano's user avatar
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What is meant by a source-free conductor?

I have recently worked with a source-free conducting slab filled with free space and with an electric field inside, and I have determined the corresponding magnetic field from MW's eq's. Next, I ...
Rasmus Andersen's user avatar
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1 answer
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Solving Maxwell Equations when a charge is put inside a generic conductor

A net point-charge density $\rho_0$ is impressed without speed (no impressed current density) at position r0 at time $t_0$. Relaxation analysis tells us the charge density will decrease exponentially ...
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What is $\lambda$ in Maxwell's EM diffusion equation?

I am reading an old paper from the 1970s regarding a line current EM induction. In the paper they say that (under certain assumptions), Maxwell's equations can be simplified to a diffusion equation of ...
Darcy's user avatar
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1 answer
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Understanding sources (charge and current densities) in Jefimenko Equations

Let's consider the two Jefimenko Equations: $$E(r,t) = \frac{1}{4πϵ_0}∭_V[\frac{e_{r-r'}}{|r-r'|^2} ρ(r',t_r' )+ \frac{1}{c} \frac{e_{r-r'}}{|r-r'|} \frac{∂ρ(r',t_r')}{∂t} - \frac{1}{c^2} \frac{1}{|...
Kinka-Byo's user avatar
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1 answer
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Proof of speed of light from Maxwell's equations in integral form

Is it possible to prove that $$\displaystyle c = \frac 1 {\sqrt{\epsilon_0 \mu_0}}$$ using Maxwell's equation in integral form? Recently, I saw this kind of proof by Professor Walter Lewin in one of ...
Vinay5101's user avatar
1 vote
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Problem in calculation of spherically symmetric Laplacian in electrodynamics

I have come across the following operation in two electrodynamics textbooks, which I find problematic: When evaluating an integral over a Laplacian in a spherically symmetric function, the radial term ...
Jonathan Huang's user avatar
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0 answers
54 views

Where does the $\eta^{\mu\nu}$ come from? (Maxwell Lagrangian, QFT) [duplicate]

From the Lagrangian in Maxwell theory $$L = -\frac{1}{2}(\partial_{\mu} A_{\nu})(\partial^{\mu} A^{\nu}) + \frac{1}{2}(\partial_{\mu}A^{\mu})^2 - A_{\mu}J^{\mu}$$ I have to calculate $\frac{\partial L}...
Heidegger's user avatar
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4 votes
1 answer
192 views

Field equations for Maxwell and Einstein tensors in a weak field limit

I am following this paper here (arXiv here). What I want to do is derive equations ($2.7$) and ($2.8$) given in section $2$. While the authors include the higher order Euler Lagrangian terms in their ...
ShKol's user avatar
  • 322
0 votes
3 answers
131 views

Divergence of $H$ Maxwell equation

In the below screenshot from this paper (link below), why is the 2nd Maxwell equation ($\nabla \cdot H = 0$) not automatically satisfied when the 4th Maxwell equation is satisfied? I don't understand ...
photonica's user avatar
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2 votes
0 answers
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Hawking radiation from photons?

I am reading a lot of papers that derive the Hawking temperature solving either the Klein Gordon equation for scalar fields or the Dirac equation for spin $\tfrac12$ particles via tunnelling ...
Nicola Muttoni's user avatar

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