The four fundamental fundamental equations of electromagnetism.

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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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36 views

How to use quantized version of Maxwell equation in photonic entanglement experiment? [on hold]

Can you use maple to demonstrate the quantization of maxwell equation? how to use quantized version of maxwell equation in photonic entanglement experiment? is it used for controlling the magnetic ...
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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
71 views

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 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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63 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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28 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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82 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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36 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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43 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
67 views

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
43 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
98 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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880 views

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
118 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
44 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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1answer
91 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
61 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
144 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 ...
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2answers
117 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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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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1answer
26 views

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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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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58 views

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?
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67 views

Why is $B=\frac{1}{\omega} k\times E$?

Why can we derrive from $B=\frac{k}{\omega}|E|$ the formula $B=\frac{1}{\omega} k\times E$ ? Obviously, because they are perpendicular, but why is it mathematically legitimate?
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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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77 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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4answers
53 views

How seriously should I take the notion of “magnetic current density”

Increasingly I've noticed that people are using a curious quantity $\vec M$ to denote something called magnetic current density in the formulation of the maxwell's equations where instead of $\nabla ...
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Importance of the $\exp (i \bar{k} \cdot \bar{r})$ part of the plane wave equation

I am having trouble grasping how the equation $\bar{E} \left( \bar{r}, t \right) = \bar{E}_{0} \exp \left[ i \left( \bar{k} \cdot \bar{r} - \omega t \right) \right]$ fully describes a plane wave. ...
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70 views

Can Gauss' and Ampere's Laws be written in terms of the divergence of an energy four-vector?

In the first 20 minutes of this video, Susskind derives the continuity equation for charge conservation: $$\dot{\rho}+\nabla\cdot\vec{J}=0$$ (Where $\vec{J}=\frac{\partial\dot{q}^m}{\partial A^m} ...
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Why aren't Faraday's law of induction and Maxwell-Ampere's law (without sources) symmetric?

I was wondering why Faraday's law of induction and Maxwell-Ampere's law (without sources) are not totally symmetric in the sense that Maxwell-Ampere's law has a $\epsilon_0 \mu_0$ term on the right ...
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54 views

Stopping current and Maxwell equation compliance

Preamble: Mathematically, the divergence of an eddy field is zero, thus for the magnetic field $$\nabla\cdot\nabla\times\boldsymbol B = \boldsymbol 0$$ and from the $\nabla\times\boldsymbol B$ Maxwell ...
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How to solve the following set of equations (magnetohydrodynamics with anomaly term)?

Let's have system of equations: $$ \tag 1 [\nabla \times \mathbf E^{(1)}(\mathbf r , t) ] = -\frac{\partial \mathbf B^{(1)}(\mathbf r , t)}{\partial t} , $$ $$ \tag 2 [\nabla \times \mathbf ...
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58 views

Deriving electric field

Can anyone explain where the following expression for the electric field vector comes from? $$ \mathbf E(\mathbf r,t) = -\nabla \phi(\mathbf r,t) - \frac{\partial}{\partial t}\mathbf A(\mathbf r,t) ...
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27 views

Is electricity constant in standard ECG device? [closed]

I am reading the book Bioelectromagnetism by Malmivuo et al. I am thinking if you need to use Maxwell equations in electromagnetism of ECG device. I am not sure if you need to change the current ...
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218 views

Confusion between magnetic field and magnetic flux

I've been learning about electromagnetism and Maxwell's equations (in integral form), and I'm slightly confused. The Ampere-Maxwell law (as I know it): $$ ...
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2answers
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Where does the $\partial \vec{E}/\partial t$ term from Maxwell's equation go in Ampere's Law?

One of Maxwell's Equations (ME) is: $$\nabla\times\vec B = \mu_0\vec J+\epsilon_0\mu_0 \frac{\partial \vec E}{\partial t}.$$ While Ampere's Law (AL) is: $$\nabla\times\vec B = \mu_0\vec J.$$ ...
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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 ...
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Deriving Ampère's Circuital Law from Ampère's Force Law?

Ampère's force $d^2\vec{F_{21}}$ of current element $i_2d\vec{\ell_2}$ on $i_1d\vec{\ell_1}$ is$$d^2\vec{F_{21}}=-\frac{\mu_0}{4\pi}i_1i_2\frac{\hat{r}}{r^2}\left[2(d\vec{\ell_1}\cdot ...
2
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1answer
190 views

A James Clerk Maxwell Disproof

One of my favorite physicists to learn about was James Clerk Maxwell, for the fact that he unified the study of E&M in physics and he would often disprove theories that did not work as a ...
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71 views

Is it necessary for EM fields to be dependent & co-exist in static conditions?

I was having a discussion today with one my colleagues in the lab about the independence and co-existence of EM fields.$$$$ My argument: In time-varying fields: EM fields are necessary dependent, ...
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Finding the magnetic vector potential by calculus of variations

Given the functional $$F[A]=\int_{\mathbb{R}^3}\{\frac{1}{2\mu(x)}|\nabla\times\vec{A}|^2-\vec{J}\cdot\vec{A}\}d^3x$$ with $\vec{A}$ is a candidate vector potential for the field ...
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885 views

What is the meaning of this “let there be light” joke?

A middle school teacher across the restaurant is wearing this shirt, and I certainly don't get it.
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How do you go from quantum electrodynamics to Maxwell's equations?

I've read and heard that quantum electrodynamics is more fundamental than maxwells equations. How do you go from quantum electrodynamics to Maxwell's equations?
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56 views

Can someone show me how Green's function would apply for this simple case?

I'm reading up on some stuff on basic electrostatic here: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/laplace.html Can someone use Green's function to show me the form of $V$? Update: I ...
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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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1answer
46 views

Uniformly charged sphere's electric field

I am facing this topic for the umpteenth time in my college career and, of course, every teacher has explained it in a different way. In this course, to find the expression of the electric field of a ...