The four fundamental fundamental equations of electromagnetism.

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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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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 ...
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39 views

Can we prove that EM waves are transverse from Gauss's law of magnetism? [duplicate]

Can we use $ \mathbf B \cdot d\mathbf s=0$ to prove transverse nature of EM waves?
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4answers
105 views

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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Am I too young? [closed]

I am only 14 years old but I dream of being a physicist what we learn in school seems very simple for me I am a freshmen and I learn Igsce syllabus and I don't seem to find it hard at all , but i am ...
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2answers
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Problem related to application of Maxwell's equation for point charge moving uniformly

Maxwell's 4th equation which describes magnetic field, has two terms: $$ \oint \mathbf{B}\cdot d\mathbf{l}=\mu I+\mu \varepsilon \frac{\mathrm{d}\Phi}{\mathrm{d}t}$$ Now, I wanted to derive the ...
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1answer
90 views

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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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
63 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 ...
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1answer
150 views

How is Biot-Savart law verification of Maxwell's 4th equation for steady current?

Please provide some theoretical procedure which equates Biot-Savart law with the Maxwell's 4th equation for steady current, which is Ampere's law $$\quad \nabla\times{\bf B} = \mu_0{\bf J}.$$
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75 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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150 views

How did Maxwell conclude that light is an electromagnetic wave? [closed]

I was looking at the answers for "Why is light called an 'electromagnetic wave' if it's neither electric nor magnetic?", especially the answer by NikolajK that references a Wikipedia article and the ...
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1answer
79 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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0answers
96 views

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
98 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
30 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
89 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 - ...
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1answer
104 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 ...
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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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19 views

How Maxwell's equations are derived from fundamental equations for electrostatic and magnetostatic models [duplicate]

How Maxwell's equations are derived from fundamental equations for electrostatic and magnetostatic models.
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38 views

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
100 views

Motion of Thompson's jumping ring

Thompson's jumping ring experiment is set up as follows: There is a force acting on the ring $F(x)$ where $x$ is the vertical displacement. The force is due to the $90^\circ$ out of phase flux ...
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1answer
35 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
172 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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47 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
53 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 ...
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1answer
131 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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0answers
61 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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25 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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3answers
174 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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1answer
59 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 ?
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1answer
553 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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1answer
224 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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2answers
213 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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1answer
42 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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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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2answers
189 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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76 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 ...
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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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?
3
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1answer
186 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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4answers
486 views

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 ...
4
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1answer
169 views

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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3answers
131 views

In terms of the Ampere-Maxwell law, why is $\vec {E}=0$ in a wire of a capacitor circuit?

I'm currently studying from "Introduction to Electromagnetics" by D.J. Griffiths. In the book the significance of the displacement current term is explained by looking a non-steady capacitor circuit ...
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28 views

Single slit diffraction treated as a differential equation

I want to find the values of electromagnetic fields that result from single slit diffraction. This should be possible by solving maxwell's equations for appropriate boundary conditions. But I'm not ...
2
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1answer
459 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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37 views

Two equal charges accelerating parallel to each other

Let's say constant acceleration for simplicity. Ignore possible logistic concerns, such as what is accelerating them or how they stay in path. Lets just assume they are in a conduit made of a solid ...
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0answers
39 views

Pefectly electrically conducting Neumann boundary conditions

I have a rather subtle question regarding necessary boundary conditions. To solve Maxwell's source-free equations as an initial boundary value problem in a volume $\Omega$ bounded by a perfectly ...