The four fundamental fundamental equations of electromagnetism.

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365 views

Justification of Physical Laws [on hold]

I'm a maths student, and I've studied quite a lot of mathematical physics. All my courses have a similar style - we state the laws of the system, and then deduce the physical consequences as theorems. ...
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3answers
169 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 ...
3
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0answers
48 views

Number of Independent postulates in Electrodynamics

We know that there are two ways to get charge conservation in electrodynamics by using the following action: $$S[A]~=~\int\! d^4x {\cal L},$$ $$ {\cal L} ~=~{\cal L}_{\rm Maxwell} + {\cal L}_{\rm ...
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4answers
263 views

Maxwell Equations don't give unique Electric Field?

Consider the class of electric fields given by $$\mathbf{E}=\begin{cases} \ln (Cr)\hat{z} & 0\leq r < R\\ 0 & r> R \end{cases}$$ where $C$ is a constant and $r$ is the polar-distance ...
0
votes
1answer
310 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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2answers
35 views

Trouble understanding Electric flux and gauss law

Well, i know that the electric flux is the number of field lines passing a certain area, but (1)what does that mean? I can't the concept itself. I know it have many applications, gauss law one of them,...
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1answer
164 views

Spherical magnet inside a solenoid

When passing a bar magnet through a long solenoid why is it that the induced emf when the magnet is in the middle of the solenoid is zero? And if a spherical magnet is put inside the solenoid, will ...
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4answers
3k 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 ...
3
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1answer
25 views

Transmission line model proof?

Why 2 distributed lines is represented with series inductor and resistor along with parallel capacitor and resistor? What is the motivation for that? In circuit theory I Knew the assumptions to ...
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1answer
131 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 ...
3
votes
2answers
670 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 ...
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1answer
158 views

How can electric field representation be obtained from Enge representation using Maxwell's equations?

Suppose we have a long electric capacitor. Let $L$ be its length ($z$ coordinate), $W$ its width ($y$ coordinate), and $D$ its full height (full aperture; $x$ coordinate). Let $L\gg W\gg D$. The ...
2
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1answer
116 views

Maxwell's equations in covariant form

Maxwell's equations of electrodynamics in vector calculus form are \begin{align} \nabla \times \mathbf{B} - \partial_t \mathbf{E} & = \mathbf{J} \\ \nabla \cdot \mathbf{E} & = \rho \\ \nabla ...
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2answers
38 views

Colors of the Earth from space, an “average” of particular emitters?

When we're say about 100 km above Earth's ground and look down to it and see the Amazonian region as green, is this green color a sort of "average" of greens from trees from that forest or is the "...
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2answers
151 views
6
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1answer
433 views

Biot-Savart law from Ampère's with multivariate calculus

Let us assume the validity of Ampère's circuital law $$\oint_{\gamma}\mathbf{B}\cdot d\mathbf{x}=\mu_0 I_{\text{linked}}$$where $\mathbf{B}$ is the magnetic field, $\gamma$ a closed path linking the ...
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0answers
66 views

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

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
44 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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4answers
835 views

Least-action classical electrodynamics without potentials

Is it possible to formulate classical electrodynamics (in the sense of deriving Maxwell's equations) from a least-action principle, without the use of potentials? That is, is there a lagrangian which ...
0
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1answer
37 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 ...
0
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1answer
45 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 ...
0
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1answer
435 views

What are the boundary conditions for EM waves normally incident on the interface between two dielectric media?

An EM wave, amplitude $E_0$, frequency $\omega_0$, is incident upon a material with relative permittivity (dielectric function) $$\varepsilon \left( z \right) = \left\{ \begin{gathered}{\varepsilon ...
-1
votes
1answer
56 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}=\;\;...
3
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2answers
40 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 ...
2
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2answers
46 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
64 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
100 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 ...
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0answers
45 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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0answers
42 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 ...
6
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1answer
378 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. ...
1
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1answer
41 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 ...
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4answers
701 views

How would you define electrostatics and magnetostatics starting from Maxwell's equations?

I'm reading Griffith's text, and he starts by defining Electrostatics as requiring the source charges don't move. I've seen a few slightly different definitions of electrostatics and magnetostatics. ...
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0answers
36 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 ...
8
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2answers
573 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?
5
votes
3answers
940 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 ...
1
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1answer
68 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 ...
5
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1answer
948 views

Maxwell equations and symmetry

Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry? I believe the homogeneous Maxwell equations obey parity and time ...
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1answer
45 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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0answers
33 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 ...
3
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2answers
205 views

How can Maxwell theory be viewed in terms of two-layer structure?

I'm trying to learn more about Maxwell equations and stumbled upon an essay by professor Freeman J. Dyson from Princeton. He explained Maxwell theory in a very interesting way. The modem view of ...
17
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3answers
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Deriving the speed of the propagation of a change in the Electromagnetic Field from Maxwell's Equations

I've been told that, from Maxwell's equations, one can find that the propagation of change in the Electromagnetic Field travels at a speed $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (the values of which can ...
3
votes
1answer
98 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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0answers
16 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 ...
6
votes
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 ...
0
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3answers
702 views

How to derive the expression for the electric field in terms of the potential?

How can I derive that $$\vec{E}=-\vec{\nabla}\phi-\frac{\partial \vec{A}}{\partial t}$$ where $\phi$ is the scalar potential and $\vec{A}$ the vector potential?
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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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0answers
32 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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1answer
45 views

Relation between displacement current, dielectric and time varying Electric field

I know that displacement current is produced in dielectric material due to dipole moment. I also know that displacement current is produced by time varying electric field (according to maxwell ...
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3answers
180 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 ($E_x,E_y,E_z,B_x,B_y,B_z$). ...
45
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7answers
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Do Maxwell's Equations overdetermine the electric and magnetic fields?

Maxwell's equations specify two vector and two scalar (differential) equations. That implies 8 components in the equations. But between vector fields $\vec{E}=(E_x,E_y,E_z)$ and $\vec{B}=(B_x,B_y,B_z)$...