The four fundamental fundamental equations of electromagnetism.

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Derivation of Maxwell's equations [on hold]

I derived the equations of Maxwell in a current free medium, last year about this time (I need help editing this). I made use of complex quantities, and Cauchy-Riemann relations. In this derivation ...
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Does a Static E-field Increase the Gauge Invariant Vector Potential Without Bound?

The gauge invariant formulation of Maxwell's Laws (7.13): Indicates that the transverse electric field is the time derivative of the transverse vector potential. This gauge invariant vector ...
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What does it physically mean to take the curl of the curl of a field (wave equation derivation)?

What does it physically mean to take the curl of the curl of a field in the derivation of the electromagnetic wave equation from Maxwell's equations, as presented here, on Wikipedia? Why was it a ...
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How does a synchronous motor know to increase current when the mechanical load is increased?

Consider a very simple singe phase synchronous motor, such as the one shown in figure 1. This motor will not be self starting, but if an AC voltage is applied and the permanent magnet is given an ...
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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 ...
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Aether/Ether in Electrodynamics?

From reading Maxwell's original papers on the formulation on the dynamics of electromagnetism, I saw that Maxwell kept mentioning aether in his paper. I know today in modern physics the Michelson ...
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Is Maxwell's field the wave function of the photon?

In his ArXiv paper What is Quantum Field Theory, and What Did We Think It Is? Weinberg states on page 2: In fact, it was quite soon after the Born–Heisenberg–Jordan paper of 1926 that the idea ...
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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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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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Faraday's law in free space explaining away the constant vector?

Let's say that I have a plane electromagnetic wave travailing in free space, and I know the electric field part to be $\vec E$. If I am using Faraday's law to get the magnetic field part I will get ...
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269 views

Integral vs differential forms of Maxwell's equations

As stated in this post, the integral and differential Maxwell equations should be identical. However, in a text I was reading it states that The integral forms of Maxwell’s equations describe the ...
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Why does the electric field vanish at infinity?

When $r \rightarrow \infty$, $E \rightarrow 0$ for a point charge or set of charges or a finite charge distribution. While this seems obvious, I cannot find a reason why this is true when inspecting ...
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Knotted solutions of Maxwell's equations in flat vacuum - do they really exist?

The paper http://arxiv.org/abs/1502.01382 claims that such solutions exist and that a number of specialists know them since a long time. Is this paper correct? Jackson's text on electrodynamics does ...
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339 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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183 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
335 views

Electric field from current without Maxwell's law of induction

A long, straight wire carries a current that decreases linearly with time. What is the direction of the induced electric field outside the wire? I would interpret this as follows: a current ...
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1answer
20 views

Does displacement current occur in an inductor?

We have learned in school that displacement current comes about due to a change in electric field flux per time in a capacitor (Ampere-Maxwell Law). Does the same displacement current come about in an ...
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622 views

Proof of equality of the integral and differential form of Maxwell's equation

Just curious, can anyone show how the integral and differential form of Maxwell's equation is equivalent? (While it is conceptually obvious, I am thinking rigorous mathematical proof may be useful in ...
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Analytical solution to Maxwell's equations in 3D

I'm working on solving Maxwell's equation numerically and have implemented Yee's algorithm in Matlab. In order to check if the algorithm is implemented succesfully, I need an analytical solution to ...
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132 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 ...
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How are the Lorentz force, Maxwell's third law and Faraday's law of induction clasically related?

Faraday's law of induction can be used in any situation where the magnetic flux is changing through a closed conducting loop. While giving the correct answer, it seems to me that for the following ...
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Would a rotating magnet emit photons?

If a magnet is rotating, around an axis perpendicular to the axis north-south axis of the magnet (which I assume to be cylindrical symmetrical), in space (so no-gravity/freefall or friction), should ...
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192 views

Do the integral forms of Maxwell's Equations have limited applicability because of retardation?

In the usual bookwork treatment, it is easy to show that the differential and integral forms of Maxwell's equations are equivalent using Gauss's and Stokes's theorems. I have always thought that ...
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How did special relativity change physicists views on the two prominent inverse square laws (ie Newton grav and Coulomb's law)?

On page 107 in Hartle's Gravity -- An introduction to Einstein's General Relativity, he says the following With the success of special relativity it became apparent that the Newtonian theory of ...
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Why magnetic monopole found in spin ice don't modify the Maxwell's Equations?

Magnetic monopole predicted by Dirac nearly a century ago was found in spin ice as quasi-particle(2). My question is Why magnetic monopole found in spin ice don't modify the Maxwell's Equations? (I ...
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Interpretation of the displacement current

From Maxwell's equations, why is the displacement current viewed as a source for a magnetic field? If the displacement current were moved to the other side of the equation it would like like a current ...
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Free charge density and current in an ohmic material

I have come across what seems a paradox -or at least an exotic conclusion- regarding current conduction in an ohmic material. It is well known that free charge density can only be zero on an ohmic ...
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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 ...
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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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Problem with Maxwell's theory

What exactly is the problem with classical Maxwell theory and the blowing up of energy at $r=0$? Does it have any other problems on the classical level?
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Anyone know of a flow chart or list of common/useful consequences of Maxwell's equations?

I just recently started to appreciate the Maxwell equations. I had never really take the time to study them but I feel like I'm finally more familiar with them. I've noticed that it seems like a lot ...
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1answer
62 views

How to propagate a planar e/m field in free space using plane waves?

I read this great answer to this question: Numerical software to manipulate a light beam in its plane wave representation? The main thing that I am trying to clear in my head is the following: ...
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Can a charge moving in an open trajectory qualify as current?

It is sometimes said that a point charge is equivalent to an electric current. If it were a steady current, I should be able to find it from Ampere’s law or Biot-Savart’s law. Even if the current is ...
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Why does charge build up at the boundary surface of two media?

On a homework problem, we are asked to to use the first two Maxwell equations, $$\nabla\cdot \mathbf{B} = 0$$ $$\nabla \cdot \mathbf{D} = \rho$$ to show that along the boundary surface of two ...
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Recovering all of Maxwell's equations from the variational principle

Whether you can get the first couple of Maxwell equations from a variational principle? In the second volume of the Landau theoretical physics said that it is impossible.
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Help understanding electromagnetism integral from exercise in MTW? [closed]

I was skimming through Misner, Thorne and Wheeler's book Gravitation looking for exercises to challenge myself with and came across the following exercise on page 178: Verify that the variational ...
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43 views

Can someone reconcile the Boltzmann transport equation with the Maxwell equations for photons/light?

Having taking courses in both physics and nuclear engineering, I've noticed that the two fields tend to describe photons/light in two different settings. In nuclear engineering, the radiative ...
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Field Vectors and satisfying Maxwell's equations

If I have an electric field that its direction is parallel to the direction of the wave propagation, it will not satisfy Gauss's law for vacuum. However we can say it satisfies Gauss's law for ...
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How to experimentally reconstruct Maxwell's equations from scratch

What are the minimal experiments would one need to perform in order to reconstruct Maxwell's equations from scratch, assuming even the concepts of $\vec E$ and $\vec B$ are unknown? While I'm not ...
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Why do different wavelengths travel at different speeds through a medium? [duplicate]

Someone gave an explanation in another question: "Maxwell's equations predict that in a linear medium with permittivity ϵ and permeability μ, the speed of light in the medium will be v=1/ϵμ. When ...
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403 views

why is advanced radiation absent?

the Lienard-Wiechert green functions have future and past null cones of radiation. Maxwell equations allow for a continuous range of mixtures between the retarded and advanced components, but we have ...
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53 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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Why is $\mu_0$ missing in EM formulas in Peskin and Schroeder?

In this post, $\hbar=c=1$ units are used throughout. It is well known that the action of classical electromagnetism is given by $$\mathcal S_{\text{Maxwell}} = \int ...
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How to calculate the magnetic and electric fields in an electrical system with arbitrary geometry? [closed]

What physics and mathematics are involved in calculating the fields around an electrical system of arbitrary geometry? Is it possible to describe a system in 3D, assign physical properties to the ...
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Why did Heaviside eliminate the magnetic potential from Maxwell's Equations?

Maxwell's original equations had magnetic potential, but Heaviside eliminated this variable. What was the reason for Heaviside's removal of the magnetic potential?
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Finding scattering cross section for a sphere

I am trying to determine the scattering cross-section for a sphere ($\sigma_s$). I have filled a scattering matrix $F(\phi,\theta)$ for all $\theta$ from $0$ to $180$ degrees and all $\phi$ from $0$ ...
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Galilean and Lorentz Covariance in Julian Schwinger's book Electrodynamics

In the book Electrodynamics (pp. 8-11) Julian Schwinger "derives" (in this special case) the complete Maxwell equations from the Coulomb potential using only the Galilean transformation $$ ...
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Does the anisotropic Fermat eikonal equation predict the extraordinary ray direction given by Poynting vector?

Does the anisotropic Fermat eikonal equation predict the extraordinary ray direction given by Poynting vector?
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Why is the displacement current term needed in the Maxwell's equations?

Why did Maxwell believe that a displacement current term needed to be added to Ampere's circuital law? I have found loads of answers online about the plates acting as capacitors but i don't ...
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Maxwell's Equations, cast in terms of magnetic vector potential [closed]

Derive $$ \nabla \times \frac{1}{\mu_r} \nabla \times A + \mu_0 \sigma \frac{\partial A}{\partial t} + \mu_0 \frac{\partial}{\partial t} \left( \epsilon_0 \epsilon_r \frac{\partial A}{\partial t} - ...