The four fundamental fundamental equations of electromagnetism.

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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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54 views

When can I use Helmholtz equation for electraomagnetic wave

The complete Maxwell wave equation for electromagnetic field using the double curl operator "∇×∇×". Only when the transverse condition is hold, this operator can equal to the Laplace operator and form ...
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26 views

Purpose of magnetic charge and current density

I am aware that introducing a magnetic charge density and a magnetic current density makes Maxwell's equations much more symmetric. But in what situations/problems is this beneficial? Could someone ...
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46 views

Deriving Maxwell's equation from the Lagrangian of an electromagnetic field with a charge density $\rho$

I want to derive Maxwell's equation from the Lagrangian of an electromagnetic field with a charge density of $\rho$ The Lagrangian is given by $$L={1\over2}(\epsilon_0E^2-{1\over\mu}B^2)-\rho\phi+\...
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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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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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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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1answer
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How to draw + and - and $\nabla \times E$ on a circular wire?

Faraday's Law: $$\vec{\nabla}\times\vec{E}=-\frac{\partial\vec{B}}{\partial t}$$ Circulation of electric field: For time-varying magnetic field and a closed wire, How can we add + and - pole ...
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216 views

Why should gluons move at a speed determined by $\mu_0$ and $\varepsilon_0$?

I understand that the speed of light can be derived from Maxwell's equations, giving $c=\frac{1}{\sqrt{\mu_0\varepsilon_0}}$ I furthermore understand how the principle of invariance of laws w.r.t. ...
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1answer
65 views

What are some experiments verifying Maxwell's 4th equation?

Please give me the link to some paper, website or book that you know about which discusses in detail some experiments which quantitatively verify Maxwell's 4th equation, which is $$\quad \nabla\times{...
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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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82 views

Magnetic monopole using differential forms

I'm trying to understand the different variations of the Maxwell's equations using differential forms. The Maxwell's equations are $$dF=0\\ *d*F=J$$ where $F$ is the electromagnetic tensor ($F=dA$) ...
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1answer
82 views

Maxwell equation correct statements [closed]

Do these four statements correctly define the 4 Maxwell's equations or do I need to add or change something in it ? 1)Gauss's law: The net electric flux passing through any closed surface is $\large \...
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Can a Set of “Maxwell's Equations” for Newtonian Gravitation be Derived from Newton's Force + Special Relativity?

When I learned about electromagnetism in my first year of undergraduate school, Maxwell's equations were derived roughly in the following way (see also here or in [1]): Gauss's law for a static ...
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1answer
112 views

Proof that Maxwell equations are Lorentz invariant

In Peskin and Schroeder page 37, it is written that Using vector and tensor fields, we can write a variety of Lorentz-invariant equations. Criteria for Lorentz invariance: In general, any equation ...
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1answer
33 views

magnetic force from v=0 and dB changing

magnetic force is defined as: $ \mathbf{F}=q \mathbf{v} \times \mathbf{B}$ so if v=0 there is no force. However Faraday's law states that if $d\mathbf{B}\neq0 $ then we have an induced emf even ...
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31 views

derivation of the electic displacement D

I've been revising Maxwell equations recently and tried to prove that the electric displacement $ \mathrm{\nabla \cdot D = 0}$ in the electrostatic approximation ($\mathrm{E = - \nabla} f$). My steps ...
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1answer
92 views

Maxwell's Equation

I was reading a book and I found the following equation. I'm not good at physics and I couldn't understand where does it come from, can anyone explain me why is it valid? $$ \mathbf E = -\nabla\phi - \...
3
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1answer
226 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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1answer
108 views

Maxwell equations in 2+1 D

I have a problem with the Maxwell equations in (2+1) dimensions using differential form. Following J. Baez "Gauge Fields, Knots and Gravity" page 93 (or any other book), the equations are \begin{...
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1answer
58 views

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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RF cavity Field Maps using Poisson Superfish

This may be a slightly obscure question but I'm trying to use Poisson Superfish to generate field maps for single cell of an ILC SRF Cavity. There are examples in the documentation for radio ...
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1answer
178 views

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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1answer
36 views

What are some of the empirical proofs of electromagnetic polarization? [closed]

I am aware of how polarization follows from Maxwell's equations, and how it is possible in transverse waves in general. I also know that Huygens, in his great Treatise on Light, first discovered and ...
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1answer
49 views

Demonstration for the existence of longitudinal electrostatic oscillations

How could I demonstrate that in a linear, homogeneous and isotropic medium without losses but electrically charged, Maxwell's equation admit as solutions longitudinal electromagnetic waves, beyond ...
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1answer
57 views

Determining the phase delay between H and E fields

I want to determine the phase delay between H and E fields in a medium with losses and not electrically charged. In this medium we also have $\sigma_c\approx \varepsilon \omega$. The enunciation of ...
0
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1answer
132 views

how do photons move with respect to EM (I'd like to picture wave magnitudes frame by frame) [duplicate]

(I'm aware treating photon as particle and talking about its position is not exactly, conceptually right but I think it makes sense, at least in the point of view of a beginner. Please just assume ...
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3answers
177 views

How to propagate $E_x (x,t) = \exp(-t^2/\tau^2-i\omega_0 t) \exp(-x^2/w_0^2)$ in finite difference time domain (FDTD) analysis

Finite difference time domain (FDTD) allows to solve differential equations for time evolution. For example, we can analyze ultra-short pulses in free space by solving the Maxwell's equations. The ...
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62 views

Distribution of current, charge and EM radiation from a centrally AC fed ball-shaped antenna

As far as I can understand, it is generally accepted that every classical electromagnetic phenomena can be explained by five equations: Maxwell's four equations and the Lorentz force law. However you ...
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26 views

Effective Medium

Please consider the following problem : A plane wave of wavenumber k is incident on an infinite slab which is inhomogeneous in the z direction. Also assume harmonic time dependence and that the ...
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1answer
66 views

How far will a 1Hz EM Wave propagate if it's source oscillator is running for exactly one second? [closed]

If you have an Oscillator set on 1Hz and you let it run for exactly one second connected to an Antenna , how far will the generated EM Wave travel ?
6
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1answer
254 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 previously ...
7
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1answer
559 views

Do photons decay as they travel in free space

From maxwell's equations, it occurred to me that photons are stable. Decrease in electric field creates magnetic field and vice versa and somehow there is a harmony that allows photon to exist as long ...
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4answers
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How wrong are the classical Maxwell's equations (as compared to QED)?

Now, I don't really mean to say that Maxwell's equations are wrong. I know Maxwell's equations are very accurate when it comes to predicting physical phenomena, but going through high school and now ...
7
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1answer
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How can KVL & KCL be derived from Maxwell equations?

How can KVL (Kirchhoff's Voltage Law) & KCL (Kirchhoff's Current law) be derived from Maxwell equations in lumped circuits? (Lumped network: if $d$ is the largest dimension of the network and $\...
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2answers
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Does displacement current exist after the capacitor gets fully charged?

The displacement current is due to changing electric field. Since, after the capacitor gets fully charged there is no changing electric field there is no displacement current.(capacitor connected to a ...
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3answers
2k views

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
45 views

In magnetostatics, is there any relation between flux and current?

I have noted while trying to find analogy between electrostatics and magnetostatics, for the equation, flux = charge/epsilon, is there any corresponding equation in magnetostatics, relating magnetic ...
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21 views

In electrostatics, what is the actual relation between flux density and flux

I know, in magnetostatics, unit of flux in webers. And unit of flux density B is webs per metre square. its clear. Now in electrostatics, unit of flux is volts metre. And unit of flux density D is ...
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231 views

Does Biot-Savart law apply in changing electric field or it needs a modification just like Ampere's law, to become as true as Maxwell's 4th equation?

Does Biot-Savart law apply in changing electric field or it needs a modification just like Ampere's law, to become as true as Maxwell's 4th equation? In the update to Ampere's circuital law, the ...
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78 views

Would a super conductive insulation completely prevent the propagation of a magnetic field from a wire where it is wrapped around?

I have limited understanding about super conductors and see them as expelling magnetic fields purely due to eddy currents produced without resistance opposite the magnetic field. I have read that ...
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2answers
817 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 ...
4
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1answer
63 views

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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6answers
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What was Feynman's “much better way of presenting the electrodynamics” — which did **not** appear in the Feynman lectures?

Does anyone know what Feynman was referring to in this interview which appears at the beginning of The Feynman Tips on Physics? Note that he is referring to something that did not appear in the ...
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What unit system puts a bunch of powers of ten in Maxwell's equations?

In what unit system can we get the Maxwell equation in the following form (section 1.2 from Lewin's book Advanced Theory of Waveguide) $$\nabla\times \vec E = -10^8\mu \frac{\partial \vec H} {\...
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2answers
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Is it possible to generalize the Maxwell equations to higher dimensions?

The usual Maxwell equations are for 3 spatial dimensions, right? Is it possible to generalize them to 2 spatial dimensions or 4 spatial dimensions?
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Maxwell in multiple dimensions: What happens to curl?

I read this answer a while ago, and while thinking about $\nabla$, I realized something. Since the cross product can be written as a determinant, in higher dimensions we require extra vector inputs. ...
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1answer
194 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 $...