The four fundamental fundamental equations of electromagnetism.

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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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0answers
70 views

One more time about the connection of Weyl tensor and gravitational waves

There is differential identity with Weyl tensor and energy-momentum tensor: $$ D^{\lambda}C_{\lambda \alpha \sigma \beta} = 4 \pi G \left(D_{\sigma}T_{\alpha \beta} - D_{\beta}T_{\alpha \sigma} + ...
5
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2answers
289 views

Exterior (covariant) derivatives and electromagnetism

I'm porting Maxwell's equations to curved spacetime and am having trouble reconciling the tensor and forms treatments. I think the problem boils down to a misunderstanding on my part concerning the ...
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2answers
588 views

Neither Biot-savart nor Ampere Law can solve this problem?

I'm confused about the use of the Ampere's Law and the Biot-Savart Law due the inconvenience of each law. I want to calculate the magnetic field due to current carrying a circular loop over itself, ...
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3k views

Maxwell's Equations using Differential Forms

Maxwell's Equations written with usual vector calculus are $$\nabla \cdot E=\rho/\epsilon_0 \qquad \nabla \cdot B=0$$ $$\nabla\times E=-\dfrac{\partial B}{\partial t} \qquad\nabla\times ...
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3answers
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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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1answer
106 views

Metric of following spacetime and refractive index

Let's have metrics $$ ds^{2} = f(\mathbf r)dt^{2} - h(\mathbf r )\delta_{ij}dx^{i}dx^{j}. $$ Hot to show that motion of light in spacetime with this metrics is equal to motion in continuous media with ...
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3answers
338 views

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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2answers
1k views

What constitutes displacement current? [duplicate]

In the chapter electromagnetic waves I was introduced with the concept of displacement current inside a capacitor. Since the region inside the capacitor is a dielectric there is no charge carriers in ...
0
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1answer
193 views

Surely force on shell can't be balanced by field momentum?

Imagine a particle with charge $q$ at rest at the origin. It is surrounded by a concentric spherical insulating shell, also at rest, with charge $Q$ and radius $R$. At time $t=0$ I apply a constant ...
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1answer
238 views

Maxwell's equations as the particular case of massive vector field equation

There was a discussion (please look to the comments on my answer) about getting Maxwell's equations for free spin-1 field by using massive spin-1 representation's equations. I'll start from the ...
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1answer
690 views

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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368 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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1answer
185 views

Reaction-at-a-distance: Do charged plates immediately repel each other?

Imagine that we have a pair of parallel plates, $A$ and $B$, separated by some distance as in Fig. $1$ above. At time $t_1$ we simultaneously charge both the plates. This could be done by ...
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4answers
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Do Maxwell's equations independently impose constraints on the speed of light?

My question is about the relations and equations that makes us to impose constraints on the velocity at which electromagnetic waves propagate. Do Maxwell's equations independently impose constraints ...
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2answers
390 views

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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1answer
293 views

Gauss's / Divergence theorem in Classical electrodynamics for the Electric field [duplicate]

Can somebody explain the proof of Gauss's theorem / divergence theorem taking the vector as electric field $$\iiint(\nabla\cdot\vec E)\mbox{ d} V=\iint \vec E \cdot\hat{n} \mbox{ d} ...
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1answer
582 views

Are Lorentz force and maxwell's equations independent? [duplicate]

The Lorentz force and Maxwell's Equations gives answers to many physics problems, and the answers given by both methods are consistent. For example, consider the problem of a conducting rod of ...
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74 views

Maximise magnetic force at one point while minimizing at another

Is it possible to have a magnet that attracts one object strongly, but not another object behind that first object? Given an (electro-) magnet M above two thin parallel steel sheets P1 and P2 in the ...
3
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1answer
333 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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1answer
359 views

Solution Maxwell's equations cylinder

I face some trouble solving Maxwell's equations inside a cylinder with perfect conductor boundaries (in 3D) ? We work with cylindrical coordinates $(r, \phi, z)$ and we make the assumption that fields ...
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174 views

Solving the source free Maxwell equations for plane waves

I've been trying to solve the maxwell equations: $$\nabla\cdot\vec{D}=0,\quad \nabla\cdot\vec{B}=0$$ $$\nabla\times\vec{E}=-\frac{\partial \vec{B}}{\partial t},\quad \nabla\times\vec{H}=\frac{\partial ...
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Lorentz and Galilean transformation

I read about Lorentz and Galilean transformation in a book of modern physics some days back, but couldn't clearly understand the difference between the two? Also it was stated there that maxwell's ...
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2answers
135 views

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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890 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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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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1answer
137 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
95 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
343 views

An Electromagnetic Paradox?

The above diagram represents an isolated system with two masses $M$, at position $X$, and $m$, at position $x$, connected together by an extended spring. Each mass is connected by rigid rods to ...
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1answer
444 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
99 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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577 views

Is there any relation between weak and strong fields, similar to electric and magnetic fields?

Is it possible to unify the strong, weak, electric and magnetic field just by Maxwellian type equations? (Maxwell by adding a small change - unified electric and magnetic field, then Einstein's ...
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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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4answers
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What could magnetic monopoles do that electrically charged particles can't?

I understand the significance to physics, but what can a magnetic monopole be used for assuming we could free them from spin ice and put them to work? What would be a magnetic version of electricity? ...
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1answer
329 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
453 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
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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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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
148 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
627 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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1answer
367 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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3answers
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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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2answers
141 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 ...
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1answer
146 views

Show that the plane of incidence is perpendicular to the surface of reflection

Is it possible to derive from the boundary conditions of the Maxwell equations for E and H, that the plane of incidence for an EM wave is perpendicular to the reflection surface? How? If not, what ...
3
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1answer
203 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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2answers
231 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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781 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 $q$ $$ ...
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1answer
381 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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1answer
480 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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863 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: ...