The four fundamental fundamental equations of electromagnetism.

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Confusion in reaction force of Ampere's Force Law [on hold]

I am reading Maxwell's "A Treatise on Electricity and Magnetism" and I have some confusion in the following pages: The element ds is resolved into its components $\alpha$ and $\beta$;and the ...
3
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0answers
43 views

Lagrangian of classical electromagnetism without $A_{\mu}$ field [duplicate]

Is there a Lagrangian reproducing Maxwell's equations without the use of the scalar and vector potential? Obviously $\mathcal{L} = -\frac14F_{\mu \nu}F^{\mu \nu}$ doesn't work since in terms of $E$ ...
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1answer
32 views

How can a sinusoid be a steady current? [duplicate]

As far as I understand it, a steady/stationary/constant current is defined to have $dJ/dt=0$ (i.e., no explicit time dependence). So I would say that sinusoids cannot produce steady currents, yet ...
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1answer
41 views

Intuition differential ampere's law

Ampere's differential law states that - $$\nabla \times {\bf B} = \frac{4 \pi \, {\bf J}}{c}$$ I know to derive amperes integral form from special relativity, and to use stokes theorem in order to ...
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57 views

Conformal invariance of Maxwell equation in presence of external current

It is known that pure electrodynamics in curved space-time is invariant under Weyl transformations $$ \tag{1} g_{\mu\nu} \to \Omega(x)g_{\mu\nu}, \quad F_{\mu \nu} \to \Omega^{-1}(x)F_{\mu\nu}. $$ ...
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1answer
47 views

About the closed line integral of electric field intensity

In electrostatics, we know that the closed line integral of electric field is zero : \begin{equation} \oint\limits_{C} \mathbf{E}\left(\mathbf{x}\right) \boldsymbol{\cdot} \mathrm{d}\mathbf{x}=\;\;...
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0answers
26 views

wave equation in dielectric medium [closed]

Maxwell's equations: $$\nabla \cdot \mathbf{E} = \frac {\rho} {\epsilon}$$ $$\nabla \times \mathbf{E} = - \frac {\partial \mathbf{B}} {\partial t}$$ $$\nabla\cdot \mathbf{B} = 0$$ $$\nabla \times \...
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2answers
40 views

How do charges accumulate even though current flows through a capacitor?

I don't understand why do charge accumulate on each plate of capacitor.I learned about displacement current which flows through the gap of the capacitor and this makes the circuit continuous.But why ...
2
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2answers
61 views

DC current in a wire

I'm sure that this question was addressed here before, but I failed to find any other instances, so with your permission I ask the question myself. I'm experiencing a very disturbing glitch, there is ...
0
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1answer
99 views

Does Maxwells equations imply $R=const*\rho$?

Suppose we have a resistor in a strange shape, filled with a medium of resistivity $\rho$, assuming only maxwells equations apply, is it true that R is proportional to rho, even for very low ...
3
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2answers
34 views

Why does current follow a conductor above a ground plane

Suppose there is a conductor above a ground plane. Current flows from a source through the conductor to a load on the other side. Depending on the frequency of the current the return path through the ...
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44 views

Defining electromagnetic stress tensor for non-linear media

In textbooks, the electromagnetic stress tensor (in vacuum also called Maxwell stress tensor) is usually derived for linear media, implying that $$ \vec D = \epsilon_0 \epsilon_r \vec E$$ My question ...
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33 views

Maxwells equations at a point

Why is it that whenever a problem is posed for maxwells equations -say the electric field at some area- that it is only requested for a fixed/given point? It would seem like you would want the field ...
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0answers
41 views

Deriving an equation in Maxwell's “a treatise on electricity and magnetism” [duplicate]

I am reading Maxwell's "a treatise on electricity and magnetism" and I need a derivation of formula 16 $\left(M=\iint\dfrac{\cos\varepsilon}{r}\mathrm ds~\mathrm ds'\right)$ (in the page below) using ...
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1answer
40 views

Rewriting Maxwell's equation in tensor form [closed]

Suppose $F_{ij}=\epsilon_{ijk}B_k $, how to prove the following: $\partial_iB_i=0$ becomes $\partial_iF_{jk}+\partial_jF_{ki}+\partial_kF_{ij}=0$ $B_iB_i$ becomes $F_{ij}F_{ij}/2$ I can see that ...
6
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1answer
370 views

Confusion in Maxwell's derivation of Ampere's Force Law - Part II [closed]

I am reading Maxwell's "a treatise on electricity and magnetism, Volume 2, page 156" about "Ampere's Force Law". I have some confusion in the following pages: My question is of two parts: 1. ...
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0answers
24 views

What is the physical meaning of a magnetic conduction current?

In electrodynamics, it is possible to have an electric conduction current, whereby $J=\sigma_e E$, with $J$ being the current, $\sigma_e$ the electrical conductivity and $E$ the electric field (this ...
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2answers
568 views

Why do we use gauges in Maxwell equation?

While solving the Maxwell's equation we often use the Lorenz or Coulomb gauge, but why is that? Are the equations unsolvable if the gauge is not fixed? Or is it just for the simplicity?
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3answers
926 views

What are the differences between the differential and integral forms of (e.g. Maxwell's) equations?

I would like to understand what has to be differential and integral form of the same function, for example the famous equations of James Clerk Maxwell: How to know where to apply each way? Excuse ...
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1answer
60 views

Tensor notation of Maxwell's equations

Tensor notation of Maxwell's equation read So when we explicitly try to find the Maxwell's equation from the above tensor equation we only get gauss law and curl of B. The div.B=0 and curl of E are ...
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1answer
44 views

Interpreting $\hat{e}_z$ in Maxwell's equations

I'm trying to interpret a form of Maxwell's equations, but I can't seem to figure out where the term $\hat{e}_z$ comes from in the following equation: $ \frac{\partial{\vec{E}_t}}{\partial{z}}+i\frac{\...
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32 views

Propagation Of Wave in Rectangular Waveguide

From what I understand, electric and magnetic fields are perpendicular to one another and the direction of wave propagation.The text book states that the direction of wave propagation in the ...
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1answer
124 views

Is it true that $\frac{d}{dt}\int_S \mathbf{B} \cdot d \mathbf{a}$ goes to zero if the amperian loop delimiting $S$ contracts indefinitely?

I suppose to have an ordinary magnetic field: in the answer I'm not interested to involve Dirac delta: the integral goes to zero. I want to focus on another point: an infinitesimal physical quantity ...
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15 views

Derivation of Poynting theorem in matter

In most textbooks I have read they derive the Poynting theorem using the Maxwell's Equation in vacuum and the fact that the force density $f=\pmb{E} \cdot \pmb{J}$. Then they just generalize it ...
3
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1answer
96 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 \theta/c^2)^{3/2}}\...
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3answers
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How is the curl of the electric field possible?

Taking the curl of the electric field must be possible, because Faraday's law involves it: $$\nabla \times \mathbf{E} = - \partial \mathbf{B} / \partial t$$ But I've just looked on Wikipedia, where it ...
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14 views

Why does a 2-sided propagating EM wave become 1-sided if B is made proportional to E?

If you simulate the propagation of an electromagnetic wave in 1D free space (no charges or currents) with initial conditions of $E\neq0$ and $B=0$, and you look at a movie of $E$ vs time, then after ...
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31 views

Problem with understanding boundary conditions in electromagnetism

In some books on electrodynamics they stress that electric current won't radiate if it is placed on a perfect electrical conductor (PEC), citing image theory: exactly opposite current will appear and ...
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3answers
177 views

Maxwell's equations - underdetermined - uniqueness

Maxwell's equations can be seen as two dynamical equations (the two curl equations), and two constraint equations (the two divergence equations). So we have 6 unknowns ($E_x,E_y,E_z,B_x,B_y,B_z$). ...
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1answer
75 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 B}...
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1answer
55 views

Derivatives involving four vectors [closed]

The Schrödinger lagrangian for complex fields is $$L=\frac{1}{2m}(D_i \psi)^* Di \psi - \frac{i}{2} \left[\psi ^* D_0 \psi - (D_o \psi)^* \right] - \frac{1}{4}F^{\mu \nu}F_{\mu \nu}$$ Where $D_\...
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48 views

How do the mode expansion of the $A_\mu$ field satisfy Maxwell's equations?

I want to show that the mode expansion $$A^\mu(x)=\int\frac{d^3\vec{p}}{(2\pi)^32E_\vec{p}}\sum_r\left[\epsilon^\mu_r(\vec{p})a_r(\vec{p})e^{-ip\cdot{x}}+\epsilon^{\mu*}_r(\vec{p})a^\dagger_r(\vec{p})...
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21 views

Which formulas would tell me the gradient of an electromagnetic field at an arbitrary distance from a pole? [duplicate]

I'm a newbie to physics and was wondering where I can read about electromagnetic gradients. From what I understand (and my intuition) electromagnetic fields create force gradients around its poles. ...
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1answer
57 views

Questions about Biot-Savart law and Ampere's law

A textbook I'm studying with described finding vector magnetic potential $\vec{\text{A}}$ from Biot-Savart law as below. $\vec{\text{H}_2}=\int_{\text{vol}}\frac{\vec{\text{J}_1}\times\hat{\text{a}...
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19 views

wave propagation modelling

what is the best modelling technique for modelling mm-wave propagation in electromagnetic environment. Right now,am working on how to use use Transmission-line matrix (TLM) and ray-tracing techniques
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1answer
68 views

In a waveguide, where does the energy in attenuated waves go?

In an electromagnetic waveguide, there is generally a "cutoff frequency." Electromagnetic waves with a frequency that is lower than this cutoff frequency will not propagate at all -- i.e., they will ...
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2answers
83 views

Maxwell's equations from differential forms

I found the following in some lecture notes I took some time ago: $$ \mathbf{E}=-\text{grad}\Phi-\partial_t\mathbf{A}\\ \mathbf{B}=\mathrm{rot}\mathbf{A} $$ These are the electromagnetic fields ...
4
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2answers
147 views

Missing Hypothesis in Electromagnetism Texts

In the Feynman Lectures, Chapter 21, I find the statement We have solved Maxwell's equations. Given the currents and charges in any circumstance, we can find the potentials directly from these ...
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1answer
50 views

Is Gauss law still true in dielectric material?

In vacuum we have $$\nabla \cdot \mathbf{E} = \frac {\rho}{\varepsilon_0}.$$ Can we still use this formula when there's dielectric material in space? Where $\rho$ is total charge density.
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1answer
27 views

Does the magnetic flux spin in the same direction when the electric field is growing and collapsing?

I have three concentric iron pipes, stacked inside each other. It looks like a bulls-eye when viewed from above. To the innermost and outermost pipes I have connected a battery through a switch. ...
2
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3answers
98 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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2answers
51 views

Derivation of Displacement current term in Ampere's Law

I have a quick question: In deriving the displacement current term for Ampere's Law, my book has the line: $$\Phi_E= \int_S \mathbb{E} \cdot \hat{n} da= \int_S \frac{\sigma}{\epsilon_0} da = \frac{Q}...
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47 views

Does Gauss flux theorem hold in relativity?

Does the Gauss flux theorem, stated in the classical electrostatics as $\iint{\vec{E}}\cdot{\vec{dS}}=q/\epsilon_0,$ hold in the case of relative motions. For instance if we observe a charged body ...
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Relating noise spectral densities of magnetic flux and voltage

My problem is as follows. I generate a voltage $V$. This voltage is applied to a resistor R, producing a current $I$. This current is then passed through a superconducting coil, producing a magnetic ...
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63 views

Maxwell's equations

In Jaynes' Probability Theory, he states: There are many more analogies. In physics we are accustomed to finding that any advance in knowledge leads to consequences of great practical value, but ...
2
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1answer
58 views

Homogenuous Maxwell Equations in the Language of Differential Forms

I understand that if I define electric field to be $E=E_i dx^i$, magnetic field to be $B=B_1 dx^2 \wedge dx^3 + B_2 dx^3 \wedge dx^1 + B_3 dx^1 \wedge dx^2 $, and field strength to be $F= dx^0 \wedge ...
2
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1answer
117 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
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Non-standard representation of the free electromagnetic plane wave

The usual representation of a free electromagnetic wave in vacuum looks like this: The blue parts are the local electric field, while the green parts are the local magnetic field. The circularly ...
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133 views

Reflection at a conducting surface. Why the presence of surface current would require infinite electric field at the boundary?

While I was reading about electromagnetic waves in conductor, precisely about Reflection at a conducting surface on Introduction to electrodynamics by David J. Griffiths I came across some difficulty ...
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Is there any property of a neutrino that prevents it from being considered the missing monopole that will make Maxwell's equations symetric

The zero in Gauss's magnetic law, is it an approximation? Could it be in reality be a really tiny number like the magnetic field strength of a neutrino? Neutrinos are members of the Lepton family ...