The four fundamental fundamental equations of electromagnetism.

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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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109 views

Magnetic field in materials with non-constant magnetic susceptibility

I'm quite lost what $B$ and $H$ is. It seams to me that most of the texts I read do quite poor job in explaining them properly. They are explained only in cases when magnetic susceptibility is ...
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496 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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992 views

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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322 views

Understanding Dynamic light scattering

I'd like to understand the physics of dynamic light scattering experiment. In particular I want to understand the basic relation between relaxation time $\tau_q$ and the diffusion coefficient $D$: ...
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1answer
93 views

How to solve “EM wave equation” for the field of uniformly moving charge?

Is it possible to show that the field of a uniformly moving charge, which is according to Biot-Savart law is given by... $${\bf E}({\bf r},t)=kq\left(\frac{1-v^2/c^2}{(1-v^2 \sin^2 ...
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191 views

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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728 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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122 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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128 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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164 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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208 views

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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130 views

$D$ 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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577 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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483 views

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 ...
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283 views

Electromagnetic inertia due to advanced radiation?

The scalar potential $\phi$ and vector potential $A$ at a distance $r$ from a charge $q$ are given approximately by $$\phi = \frac{q}{r}$$ $$\mathbf{A} = \frac{q\mathbf v}{r}$$ where the constants ...
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272 views

Magnetostatics of Current-Carrying wire

A question has been nagging at me about Faraday's Law as related to a wire with a constant current: If you have a circular loop of wire with some small resistivity, connected to a battery so that it ...
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Why must this boundary condition be met? (Electromagnetic wave at interface between two mediums)

My textbook says that The laws of Electromagnetic Theory (Section 3.1) lead to certain requirements that must be met by the fields, and they are referred to as the boundary conditions. ...
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Do the relations between E/B and D/H contain higher order multipole terms?

Jackson writes in section 1.4 (third edition) that \begin{align*} D_\alpha &= \epsilon_0 E_\alpha + \left(P_\alpha - \sum_\beta \frac{\partial Q'_{\alpha\beta}}{\partial x_\beta} + \ldots \right) ...
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Maxwell's equation in curved spacetime - how come? And experimental evidence?

I'm trying to understand the generalization of Maxwell's equations to curved spacetime. In FLAT (Minkowski) SPACETIME: If we define the "four-potential" as $$\ ...
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Is Gauss' law valid for time-dependent electric fields?

The Maxwell's equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ is derived from the Gauss law in electrostatics (which is in turn derived from Coulomb's ...
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Where does the $\partial \vec{E}/\partial t$ term from Maxwell's equation go in Ampere's Law?

One of Maxwell's Equations (ME) is: $$\nabla\times\vec B = \mu_0\vec J+\epsilon_0\mu_0 \frac{\partial \vec E}{\partial t}.$$ While Ampere's Law (AL) is: $$\nabla\times\vec B = \mu_0\vec J.$$ ...
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Special Relativity: Transforming Maxwell's equations

I'm working through Einstein's original 1905 paper*, and I'm having trouble with the section on the transformation of Maxwell's equations from rest to moving frame. The paper proceeds as follows: ...
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94 views

Why is $\mu_0$ missing in EM formulas in Peskin and Schroeder?

In this post, $\hbar=c=1$ units are used throughout. It is well known that the action of classical electromagnetism is given by $$\mathcal S_{\text{Maxwell}} = \int ...
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Why ONLY Maxwell's equations are the basic equations of electromagnetism?

In electromagnetism we say that all the electromagnetic interactions are governed by the 4 golden rules of Maxwell. But I want to know: is this(to assume that there is no requirement of any other ...
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204 views

Question about units of mass, $M = (L^{3})(T^{-2})$?

In section 5 of the "Preliminary: On the measurement of quantities" chapter (page 3) in "A treatise on electricity and magnetism" Maxwell uses, total length, $s=mt^{2}/{2r^{2}}$to show that ...
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Does $E$ cause $B$ or does $B$ cause $E$ in Maxwell's equations?

From the Maxwell's equations we get $$\frac{\partial E}{\partial x} = -\frac{\partial B}{\partial t}$$ and $$\frac{\partial B}{\partial x} = -\mu_0\epsilon_0\frac{\partial E}{\partial t}$$ ...
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652 views

Magnetic B Field of Point Charge Not at Constant Velocity

I'm working on an N-body simulator for charged particles. I know that moving charged particles generate a magnetic field, and another moving charged particle could be effected by this magnetic field. ...
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3answers
94 views

Meaning of the Vector Wave Equation

So I thought I would try my luck here on physics stack exchange about an intuitive meaning of the Vector Wave Equation. I know there are a lot of resources out there that explain this equation, but ...
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367 views

Why is the displacement current term needed in the Maxwell's equations?

Why did Maxwell believe that a displacement current term needed to be added to Ampere's circuital law? I have found loads of answers online about the plates acting as capacitors but i don't ...
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Why does $E=\nabla\phi$ follow from $\nabla\times E=0$?

I understand that using one of Maxwell's equations, $$\vec{\nabla} \times \vec{E}(\vec{x})=0,$$ it can be said that $$\vec{E}(\vec{x})=-\vec \nabla \phi(\vec{x}).$$ However, I can't find or ...
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Solution of simple problems using only Maxwell equations in differential form

Solve simple electrostatic or magnetostatic problems using only Maxwell equations. For example: In every book there is an excercise to find a magnetic field outside a thin wire of radius $a$ with ...
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2k views

How to use Ampere's Law for a semi-infinite wire with current?

Suppose that there is a semi-infinite wire which extends to infinity only in one direction. There are no other circuit elements at the other end(finite end) of the wire and the current does not loop. ...
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203 views

A James Clerk Maxwell Disproof

One of my favorite physicists to learn about was James Clerk Maxwell, for the fact that he unified the study of E&M in physics and he would often disprove theories that did not work as a ...
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Curl of an electromagnetic wave

I can't understand the concept of the curl of an electromagnetic wave. $$ \nabla \times E = -\frac{\partial \textbf{B}}{\partial t} $$ All of the examples I find show a current through a conductor, ...
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1answer
922 views

Retrieving Maxwell's equations from the minimum action principle

I'm currently working at the start of Alexei Tsvelik's book Quantum Field Theory in Condensed Matter Physics. I'm kinda stumped on a few essential steps. Starting with the action: $$S = \int dt \int ...
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494 views

The truest/most general Maxwell's equations in isotropic, linear, inhomogeneous media with sources

Sources use $\mu H=B$ and $\epsilon E= D$, assuming homogeneous media. Obviously if $\mu$ is space varying, $\nabla . (\mu H)$ need not be equal to $\nabla . B$ What is the most general form for ...
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173 views

Where do Maxwell's equations come from?

I recently started learning the basic forms (integrals) of the Maxwell's equations, and everything that is related to electromagnetism seems to be derived from these fundamental equations. Now my ...
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355 views

parity invariance of Einstein, Maxwell and Dirac Lagrangians

How can we show that Einstein, Maxwell and Dirac Lagrangians are parity invariant?
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888 views

Lorentz Invariance of Maxwell Equations

I am curious to see a simple demonstration of how special relativity leads to Lorentz Invariance of the Maxwell Equations. Differential form will suffice.
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902 views

How is this classical “paradox” resolved in electromagnetism?

A magnet and a coil move relative to each other. In the frame of reference of the magnet, there is a magnetic field and consequently a force acting on the charges in the coil according to the Lorentz ...
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1answer
69 views

What causes electromagnetic waves to propagate in free space?

In free space, $\rho=0$ and $J=0$, so there are no electromagnetic sources/sinks. Maxwell's equations thus reduce to: $\nabla\cdot E = 0$ $\nabla\cdot B = 0$ $\nabla\times E = -\frac{\partial ...
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1answer
116 views

Why only gauge transformations in electromagnetism?

first of all, I need to say that I'm a mathematician, so this question may sound a little stupid. Keeping this is mind, please, try to use coordinate-free notations. Along this question, I will use ...
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2answers
224 views

Boundary conditions for Maxwell's equations at the interface between two media

Consider the following simple Maxwell's equations: $$ \nabla\cdot\mathrm{D}=\rho $$ $$ \nabla\times\mathrm{E}+i\omega\mathrm{B}=0 $$ $$ \nabla\cdot\mathrm{B}=0 $$ $$ ...
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170 views

Can someone reconcile the Boltzmann transport equation with the Maxwell equations for photons/light?

Having taking courses in both physics and nuclear engineering, I've noticed that the two fields tend to describe photons/light in two different settings. In nuclear engineering, the radiative ...
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614 views

Electromagnetism duality theorem

Concerning Electromagnetism, textbooks often refer to the Duality Theorem. Sometimes it is presented like this: «Consider the Maxwell's Equations (with phasors) and a known field $\mathbf{E}_1$, ...
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1answer
210 views

How can electrons move along the conductive wire? ( seems to be a paradox )

Tangential components of the electric field across an interface between two media, with no impressed magnetic current densities along the boundary of the interface, are continuous. So: $ n \times (E_2 ...
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1answer
492 views

Uncertainty-principle and the Maxwell formalism of electromagnetic waves

An electromagnetic wave (like a propagating photon) is known to carry it's electric and magnetic field-vectors perpendicular and each depending on the differential change of the other thus "creating" ...
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1answer
522 views

Electrodynamics and the Lagrangian density

Could anyone tell me what equations can I obtain from the Lagrangian density $${\cal L}(\phi,\,\,\phi_{,i},\,\,A_i, \dot A_i,\,\,A_{i,j})~=~\frac{1}{2}|\dot A+\nabla\phi|^2-\frac{1}{2}|\nabla \times ...