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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64 views

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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24 views

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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38 views

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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712 views

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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27 views

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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272 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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82 views

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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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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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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58 views

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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1answer
73 views

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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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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47 views

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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26 views

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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22 views

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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28 views

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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34 views

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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37 views

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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1answer
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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2answers
77 views

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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3answers
778 views

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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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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49 views

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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1answer
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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1answer
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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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1answer
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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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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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68 views

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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37 views

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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144 views

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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49 views

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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60 views

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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1answer
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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} - ...
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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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1answer
49 views

How are plane waves, $p$-forms, and Maxwell's equations related? [closed]

I am very new to the concepts of $p$-forms and trying to get a better grasp of physicist use them to state Maxwell's equations. Wikipedia has a picture of a plane wave ...
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1answer
110 views

Is this even possible to understand this proof? [closed]

Can someone explain what kind of sorcellery is this proof about Maxwell's equations: http://proofs.wiki/Maxwell%27s_equations_predict_that_the_speed_of_light_is_constant. Is this a joke?
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Validity of Maxwell's equations with no aether or relativity?

In From Paradox to Reality: Our Basic Concepts of the Physical World by Fritz Rohrlich page 55 it states that [...] just doing away with the ether would not have resolved all problems. The ...
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1answer
197 views

“And God said…and there was light.” What does these equations mean? [duplicate]

Today while I was on the Internet I came across an interesting picture, that caught my eye. It's : I don't have to explain why this picture seems interesting to someone who knows the meaning and ...
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1answer
47 views

For AC current is it better to have a solid or a strandled wire?

For alternating current in wires there are two effects that make energy losses (increase effective resistance): Skin effect which comes since alternating current produces alternating magnetic field ...
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2answers
199 views

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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1answer
65 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 ...
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3answers
207 views

Derivation of the speed of light using the integral forms of Maxwell's Equations

Having just finished physics 2, I've been (slightly) exposed to showing that light is a wave with speed $1/\sqrt{\mu _0 \epsilon _0 }$ using the differential forms of Maxwell's equations, though this ...
3
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2answers
133 views

Do the fields exist without electric charges? [closed]

I read in an old book on electrodynamics by Pauli that theoretically there does not exist any need of charges to be there. Fields can even exist without the charges but still independent fields ...
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2answers
111 views

Deriving Maxwell's Equations from Electromagnetic Tensor

Given $ F_{\mu\nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu} $ It is obvious that the diagonals are zero, as $ F_{ii} =\partial_{i}A_{i} - \partial_{i}A_{i} = 0 $ And, ...
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Given $\tilde {E}$, which formula should I use to find $\tilde {H}$

Given $\tilde {E}$, there exist two formulas in my book (Cheng) to compute $\tilde {H}$: Maxwell's formula: $\nabla \times \tilde {E} = -j\omega\mu \tilde {H}$ Plane wave formula: $\tilde {H} = ...
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329 views

Does light change phase on refraction?

I have seen a lot about when light undergoes a phase change when it is reflected. But does it undergo a phase change when refracted and if so why and if not why not?
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Combination of Maxwell equations and other form of Maxwell equations

In reference to this paper on arXiv, page three, we have the following: We know that the Bianchi Identites are $\partial_{[\alpha F_\beta\gamma]} = 0$ and are equivalent to $$\nabla \cdot B =0 $$ ...
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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?