The four fundamental fundamental equations of electromagnetism.

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Why magnetic monopole found in spin ice don't modify the Maxwell's Equations?

Magnetic monopole predicted by Dirac nearly a century ago was found in spin ice as quasi-particle(2). My question is Why magnetic monopole found in spin ice don't modify the Maxwell's Equations? (I ...
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How to interpret the continuity conditions in the PDEs (for example, Maxwell equations) originated in physics?

I am currently working on PDEs in physics, mostly Maxwell equations. I am a mathematics graduate student, and this question has been haunting me for years. In PDE theory, or more specifically the ...
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Does existence of magnetic monopole break covariant form of Maxwell’s equations for potentials?

Absence of magnetic charges is reflected in one of Maxwell's fundamental equations: $$\operatorname{div} \vec B = 0 \text{ (1).}$$ This equation allows us to introducte concept of vector potential: ...
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438 views

Maxwell's equations invariant under all linear transformations?

Maxwell's equations in tensor notation read: \begin{align} \partial_\mu F^{\mu\nu} &= J^\nu \\ \partial_{[\lambda}F_{\mu\nu]} &= 0 \end{align} Consider doing a general coordinate ...
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Exactly how is the constant measured velocity of light deduced from Maxwell's equation?

For electromagnetic radiation the velocity of propagation is $c = 1/\sqrt{\mu_0 \epsilon_0}$. Since both $\mu_0$ and $\epsilon_0$ do not vary in any inertial frame, then $c$ must be constant in any ...
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What is the experimental evidence that light is an electromagnetic wave?

Do we have any experimental evidence to confirm that light is an electromagnetic wave? Or is it confirmed simply by Maxwell's equations showing a similarity in speed?
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When studying electrodynamics do we assume Maxwell's Equations or derive them?

This question is because something made me confused. I always thought that the idea behind electrodynamics was to postulate some things, like Coulomb's law in electrostatics and so on, and then ...
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Twistor Function for Coulomb Field

In an article by Penrose in Hughston and Ward "Advances in Twistor Theory", it is claimed that the twistor function $$ f(Z^\alpha) = \log{\frac{Z^1Z^2 - Z^0Z^3}{Z^2Z^3}}$$ produces an anti-self-dual ...
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Faraday's Law and Galilean Invariance

In Jackson's text he says that Faraday law is actually: $$ \oint_{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} = -k\iint_{\Sigma} \frac{\partial \mathbf B}{\partial t} \cdot ...
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Would Michelson-Morkey experiment measure wind in non-vacuum?

If we derive the speed of light from the Maxwell equations we will find it's a function of the permittivity and permeability of the medium. Now let's play with the thought that we are living in a ...
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What was the improvement that Maxwell did to the electromagnetic field equations and why?

What was the improvement that Maxwell did to the electromagnetic field equations and why? I understand that he combined the main equations so that you could get a wave equation for the vectors of ...
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Galilean invariance of a subset of Maxwell equations

I read in Feynman's proof of Maxwell equations the statement that the subset of Maxwell equations comming from the Bianchi identity: $$ \nabla \cdot {\bf B} = 0, \quad \nabla \times {\bf E} + ...
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How can one meaningfully say that one field generates the other in an EM-wave?

This is a follow up question to: Do the electric and magnetic components of an electromagnetic wave really generate each other? Clearly there are nuances of how one states the "mutual induction" ...
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Why do these calculations of EM fields for a magnet and wire loop seem inconsistent?

Suppose you have a conducting circular wire loop and a magnet moving towards each other. They move along the $z$ direction with nonrelativistic constant speed $v$. Let the $B$ field of the magnet in ...
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950 views

Integral vs differential forms of Maxwell's equations

As stated in this post, the integral and differential Maxwell equations should be identical. However, in a text I was reading it states that The integral forms of Maxwell’s equations describe the ...
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203 views

Did Maxwell invent the math to describe the ideas of electromagnetism?

Did he invent surface and line integrals, or did they already exist when he formulated his equations. If they did, already exist, how did they come about in pure math?
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Why do magnetic field lines describe a force?

My professor stated the four Maxwell equations, as well as the "Lorentz force" equation $$ \mathbf{F} = q\left(\mathbf{E}+\frac{1}{c}\mathbf{v} \wedge\mathbf{B}\right) \tag{1} $$ He said that this ...
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What empirical evidence is there for displacement current?

I wonder what more or less direct measurements of the displacement current exist. I know that the existence of em waves demonstrates its existence, though somewhat indirectly. I also know that there ...
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666 views

How are the Lorentz force, Maxwell's third law and Faraday's law of induction clasically related?

Faraday's law of induction can be used in any situation where the magnetic flux is changing through a closed conducting loop. While giving the correct answer, it seems to me that for the following ...
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Maxwell Equations don't give unique Electric Field?

Consider the class of electric fields given by $$\mathbf{E}=\begin{cases} \ln (Cr)\hat{z} & 0\leq r < R\\ 0 & r> R \end{cases}$$ where $C$ is a constant and $r$ is the polar-distance ...
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About the uniqueness of the displacement current

In the Maxwell-Ampère equation, i.e.: \begin{equation} \nabla\times\vec{B} = \mu_0 \vec{J} + \mu_0\epsilon_0 \frac{\partial \vec{E}}{\partial t} \end{equation} the $\vec{J}_d$ term: $$ \vec{J}_d := ...
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Physical meaning of Maxwell's equations and origin of EM waves

Is it possible to describe the physical meaning of Maxwell's equations and show how they lead to electromagnetic wave, with little involvement of mathematics ?
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Maxwell equations invariant under Lorentz transformation but not Galilean transformations

Why Maxwell equations are not invariant under Galilean transformations, but invariant under Lorentz transformations? What is the deep physical meaning behind it?
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Problem with Maxwell's theory

What exactly is the problem with classical Maxwell theory and the blowing up of energy at $r=0$? Does it have any other problems on the classical level?
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What electric field vector should I use for modeling unpolarized light?

Regardless of computational cost, light is a kind of electromagnetic wave, so it can be simulated with Maxwell's equations. If we want to simulate light with Maxwell's equations, we need to express ...
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Derivatives of delta function and equation of continuity for a single charge…

For a single charge $e$ with position vector $\textbf R$, the charge density $\rho$ and and current density $\textbf{j}$ are fiven by: \begin{equation} \rho(\textbf{r},t)= ...
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Derivation of the speed of light using the integral forms of Maxwell's Equations

Having just finished physics 2, I've been (slightly) exposed to showing that light is a wave with speed $1/\sqrt{\mu _0 \epsilon _0 }$ using the differential forms of Maxwell's equations, though this ...
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158 views

Do Maxwell equeations change somehow after Higg's boson finding?

When I was in some physics -lesson, probably something to do with Quantum Physics -- the teacher said that certain Maxwell equations would change if the Higg's boson is found. It is also possible that ...
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“And God said…and there was light.” What does these equations mean? [duplicate]

Today while I was on the Internet I came across an interesting picture, that caught my eye. It's : I don't have to explain why this picture seems interesting to someone who knows the meaning and ...
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841 views

Maxwell's equations of Electromagnetism in 2+1 spacetime dimensions

What would be different in the theory of electromagnetism if instead of considering the equations of Maxwell in 3+1 spacetime dimensions, one would consider 2+1 spacetime dimensions?
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221 views

Why does a function $\psi(v)$ appear when a Lorentz transformation is applied on Maxwell's equations?

In his 1905 paper, Einstein applies Lorentz transformation on Maxwell's equations, and relates the electric force $(X,Y,Z)$ and magnetic force $(L,M,N)$ in an inertial frame $K$ with spectime ...
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Do the fields exist without electric charges? [closed]

I read in an old book on electrodynamics by Pauli that theoretically there does not exist any need of charges to be there. Fields can even exist without the charges but still independent fields ...
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Classical Viewpoint on Electromagnetism

Note: This question may be difficult or impossible to answer within the rules of these forums due to its philosophical nature. I will delete the question if I am violating the rules. Onto the ...
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372 views

Plane wave complex notation

As far as I know, the function: $$ \vec{E}(\vec{r},t)=\vec{E_0}\cdot e^{i(\vec{k}\cdot \vec{r}-\omega t)} \hspace{2cm}(1) $$ is a mathematical solution of the wave equation: $$ \nabla^2 ...
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What is the physical significance of the Dipole Transformation of Maxwell's Equations?

The Question Given Maxwell's equations of the form \begin{align} \bar{\nabla}\times \bar{B} = \dfrac{4\pi}{c} \bar{J} + \partial_0 \bar{E} \\ \bar{\nabla}\times \bar{E} = -\partial_0 \bar{B} \\ ...
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511 views

Electromagnetic black hole?

So I was thinking about something for the past while Consider a large spherical foam-ball with homogeneous density. Where a foam ball is defined as an object that can absorb matter with 0 friction ...
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473 views

How would you define electrostatics and magnetostatics starting from Maxwell's equations?

I'm reading Griffith's text, and he starts by defining Electrostatics as requiring the source charges don't move. I've seen a few slightly different definitions of electrostatics and magnetostatics. ...
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453 views

Information content of the electrostatic Maxwell equations vs Coulomb's Law vs Poisson's Equation

In electrostatics, we have Maxwell's equations: $\nabla \cdot E = \rho$ $\nabla \times E = 0$ These four equations (the second line standing for three equations) can also be written in terms of the ...
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How do you find the magnetic field corresponding to an electric field?

If we are given the electric field $\vec E$ how can I find the corresponding magnetic field? I think I can use Maxwell's equations? In particular, $\nabla\times \vec E= -{\partial \vec B\over \partial ...
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Divergence of non conservative electric field

I'm looking for the proof that the 1st Maxwell equation is valid also on non conservative electric field. When we are talking about a electrostatic field, the equation is ok. We can apply the Gauss ...
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Maxwell's equations in integral form using differential geometry

So I've been trying to convert from Maxwell's equations in terms of differential forms to the integral versions of Maxwell's equations that we know from vector calculus. We have, in vector calculus ...
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333 views

Why do high voltage transmission line workers need a Faraday cage suit?

In this video the high voltage transmission line workers are wearing a Faraday cage suit. Why is this needed? Without the Faraday cage, the resistance of the human would be very high compared to the ...
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113 views

What does it physically mean to take the curl of the curl of a field (wave equation derivation)?

What does it physically mean to take the curl of the curl of a field in the derivation of the electromagnetic wave equation from Maxwell's equations, as presented here, on Wikipedia? Why was it a ...
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121 views

How did special relativity change physicists views on the two prominent inverse square laws (ie Newton grav and Coulomb's law)?

On page 107 in Hartle's Gravity -- An introduction to Einstein's General Relativity, he says the following With the success of special relativity it became apparent that the Newtonian theory of ...
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155 views

How can Maxwell theory be viewed in terms of two-layer structure?

I'm trying to learn more about Maxwell equations and stumbled upon an essay by professor Freeman J. Dyson from Princeton. He explained Maxwell theory in a very interesting way. The modem view of ...
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156 views

When to use which representation for an electric field

In class we covered three types of possibilities to evaluate the electric field for static problems. Unfortunately, most physics textbooks cover these ways without addressing the question of ...
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Assumptions when calculating $\vec{B}$ using Ampère's (circuital) law

When considering the same setup as in this question, i.e. a straight, infinitely long wire carrying the current $I$, Ampère's circuital law $$\oint_C \vec{B} \cdot \mathrm{d}\vec{r} = \mu_0 ...
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$D$ and $H$ in macroscopic Maxwell's equation: auxiliary or constitutive?

I'm not a physicist. I want to understand the macroscopic Maxwell's equations. But after reading Wikipedia and other Googled stuffs, I got very confused. In particular, $D$ and $H$ have two different ...
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538 views

Understanding the Ampere's Law

We want to study the magnetic field at point $P$. So, from the figure we take that: $\oint_{L_1} B\cdot dl=\mu_0 I_1$ $\oint_{L_2} B\cdot dl=\mu_0 I_2$ $\oint_{L_3} B\cdot dl=\mu_0 I_2$ The ...
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Why is there no (time derivative of charge density) in the $B$ field in Jefimenko's equations?

I was going through Griffiths chapter on potentials and fields just to brush up on a few old things. He gets to Jefimenko's equations by this general path: Maxwell's equations Introduce scalar and ...