The four fundamental fundamental equations of electromagnetism.

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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} + ...
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2answers
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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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2answers
622 views

Why is glass much more transparent than water?

There is a related question (Why glass is transparent?) but I am coming at it only from Maxwell's equations. One can determine the skin depth $δ$ for poor conductors like (pure) water and glass using ...
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1answer
131 views

Electric Potential at nano scale

I’ve a got a question; and I am hopeful that you can provide any information or direct me to a better resource. I'm not a physicist; so please correct me if I'm wrong. Scanning Probe Microscopy (SPM) ...
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1answer
87 views

Maxwell equations and Fourier decomposition

I'm currently working on maxwell equations and in order to lower the fields dimension, we perform a Fourier decomposition (according to $\theta$) due to the system symmetry. For any vector field ...
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2answers
600 views

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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1answer
276 views

Maxwell's Equations in curved spacetime

I know that we can write Maxwell's equations in the covariant form, and this covariant form can be considered as a generalization of these equations in curved spacetime if we replace ordinary ...
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0answers
93 views

Can universe be a closed manifold?

I had a question at MSE which gave a rise to another question. Maxwell equations can be written in form $$d\star F = J$$ Then by Stokes theorem we have $$ \int_U J = \int_U d \star F = ...
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4answers
893 views

Are the Maxwell equations a correct description of the wave character of photons?

In basic quantum mechanics courses, one describes the evolution of quantum mechanics chronologically. Interference experiments with particles showed that particles should have a wave character; on the ...
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1answer
169 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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3answers
303 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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2answers
134 views

Is there any correlation between mass-energy equivalence and Maxwell's 4th equation?

I wonder, how came in both equations proportionality constant is exactly $c^2$? $$c^2(\nabla \times B) = \partial E/\partial t$$ where $E$ - electric field $$c^2m = E$$ where $E$ - energy I am ...
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4answers
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Displacement Current - How to think of it?

What is a good way to think of the displacement current? Maxwell imagined it as being movements in the aether, small changed of electric field producing magnetic field. I don't even understand that ...
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1answer
128 views

Maxwell's Equations-Relativity

How did Maxwell develop the magnetic field without relativity? Was it purely experimental? I don't see how else he would have developed any understanding for the magnetic field.
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1answer
374 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 ...
6
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3answers
3k views

Faraday's law - does the induced current's magnetic field affect the change in flux?

I've had this conceptual problem with Faraday's law and inductance for a while now. Take the example of a simple current loop with increasing area in a constant field (as in this answer). So ...
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1answer
253 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" ...
4
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2answers
128 views

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 ...
2
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1answer
388 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 ...
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3answers
723 views

Divergence equations (Maxwell)

Let $\mathbf{E}(r,t),\mathbf{B}(r,t)$ be two vector fields (in $\mathbb{R}^3$), s.t. they satisfy fot $t=0$ the equations: $\nabla \cdot \mathbf{B}(r,0)=0.$ $\nabla \cdot ...
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0answers
138 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 ...
0
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3answers
491 views

Advanced Heaviside-Feynman formula implies electromagnetic inertia?

The Heaviside-Feynman formula (see Feynman Lectures vol I Ch.28, vol II Ch. 21) gives the electric and magnetic fields measured at an observation point $P$ due to an arbitrarily moving charge $q$ $$ ...
3
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2answers
202 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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2answers
444 views

Electron model under Maxwell's theory

I was not able to recall my memories, so: What is the formula that states the frequency of electrons revolving around nucleus is equal to the frequency of light (or photon) emitted (or radiated)? (I ...
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1answer
247 views

Faraday's Law and magnetic monopoles

The magnetic monopoles does not exist which can be shown by $ \int {\vec{B} \cdot d\vec{A}} = 0 $. But in Faraday's Law of electromagnetic induction, we clearly show the EMF induced is the time rate ...
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3answers
814 views

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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1answer
245 views

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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2answers
442 views

A Paradox in Special Relativity

Two inertial frames K and k’ are considered. They are in relative uniform motion along the x-x’ direction with relative speed =v. In the frame K’ we have a cuboidal piece of dielectric [at rest wrt ...
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3answers
843 views

Can light exists in $2+1$ or $1+1$ spacetime dimensions?

Spacetime of special relativity is frequently illustrated with its spatial part reduced to one or two spatial dimension (with light sector or cone, respectively). Taken literally, is it possible for ...
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3answers
5k views

What does this quote about the four dimensional divergence of an antisymmetric tensor mean?

In the beginning, God said that the four dimensional divergence of an antisymmetric second rank tensor equals zero and there was light. Can someone explain what is the meaning of this quote by ...
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2answers
76 views

What's so special about wave solutions of EM?

Maxwell's equations allow for wave solutions via oscillations between electric and magnetic field content. Couldn't we generate electric waves also if that solution didn't exists? Imagine there was ...
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1answer
1k views

Maxwell's Correction to Ampere's Law

I have not yet officially studied Electromagnetism but am trying to teach myself at the moment. I understand Maxwell's equations in the context of Magneto- and Electrostatics: they are equivalent, ...
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1answer
333 views

why is advanced radiation absent?

the Lienard-Wiechert green functions have future and past null cones of radiation. Maxwell equations allow for a continuous range of mixtures between the retarded and advanced components, but we have ...
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1answer
149 views

Determine the flow and amplitude equation for thermal energy (with Del operator)

It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ...
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455 views

Faraday law, third Maxwell's equation in Mathematica

Three question about this equation: $ \displaystyle\nabla\times\mathbf{E}=-\frac{\partial \mathbf{B}}{\partial t} $ 1 If I solve this equation with Mathematica, I find the magnetic field ...
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1answer
86 views

Idea of precursors of the electro-magnetic waves

The idea of the material Maxwell equation is almost clear. But I'm curious about the idea that except for material equation the pure Maxwell equation should work, but in harder sense: more currents ...
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4answers
275 views

The necessity of the B field

It is fairly easy using basic special relativity to arrive at the conclusion that the magnetic force effect on nearby charges of wires carrying currents on nearby charges is only due to the length ...
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2answers
339 views

Invariance of Maxwell's Equations under inverting variables - Reference and use

Some months ago, an ArXiv paper mentioned in passing that Maxwell's Equations were invariant under reciprocating the variables, or at least this results in a dual set of Maxwell Equations. (Actually I ...
3
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1answer
259 views

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 ...
3
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1answer
139 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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637 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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769 views

Positive emf? What does positive emf mean?

Could someone please explain to me why we want to take the "magnitude" of the emf?
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1answer
280 views

Gravimagnetic monopole and General relativity

Review and hystorical background: Gravitomagnetism (GM), refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein ...
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2answers
1k views

Conservation of Energy and the Poynting Theorem

Conservation of energy in an electrical circuit can be expressed by Ampere's law $$\nabla \times \textbf{B} = \mu_o \textbf{J} + \epsilon_o \mu_o \frac {\partial \textbf{E}} {\partial t}$$ when ...
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1answer
377 views

Solution to the Maxwell's equation

Question goes as Show that the solutions to the Maxwell's equations $$ \nabla \times \vec H = \frac 1 c \frac{\partial \vec E}{\partial t}+\frac {4\pi} c \vec J, \hspace{ 2 mm} \nabla \times ...
2
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2answers
247 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 $D$: ...
2
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2answers
199 views

Applying $\nabla\times\mathbf{B} = \mu_0\mathbf{J}$ in the presence of magnetic shielding

2012-06-13 - Revised question in experimental format (This is a thought experiment for which RF experts may have an immediate answer.) I'll assume (I could be wrong) the possibility of creating a ...
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1answer
575 views

How can the Huygens-Fresnel principle be derived from the Maxwell equations?

The Huygens-Fresnel principle states that every point to which a luminous disturbance reaches becomes a source of a spherical wave. I have been trying to understand this considering a infinite screen ...
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2answers
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Why did Feynman's thesis almost work?

A bit of background helps frame this question. The question itself is in the last sentence. For his PhD thesis, Richard Feynman and his thesis adviser John Archibald Wheeler devised an astonishingly ...
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4answers
639 views

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 ...