The four fundamental fundamental equations of electromagnetism.

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How can the Huygens-Fresnel principle be derived from the Maxwell equations?

The Huygens-Fresnel principle states that every point to which a luminous disturbance reaches becomes a source of a spherical wave. I have been trying to understand this considering a infinite screen ...
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176 views

Why do magnetic field lines describe a force?

My professor stated the four Maxwell equations, as well as the "Lorentz force" equation $$ \mathbf{F} = q\left(\mathbf{E}+\frac{1}{c}\mathbf{v} \wedge\mathbf{B}\right) \tag{1} $$ He said that this ...
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Is my simulation result for unpolarized light correct?

This is a follow-up of this question. After that, I picked up some knowledge of FDTD (an algorithm for solving Maxwell's equations) and simulated following scene: Pic 1 As the picture shows, a ...
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916 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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Metric of following spacetime and refractive index

Let's have metrics $$ ds^{2} = f(\mathbf r)dt^{2} - h(\mathbf r )\delta_{ij}dx^{i}dx^{j}. $$ Hot to show that motion of light in spacetime with this metrics is equal to motion in continuous media with ...
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Why is glass much more transparent than water?

There is a related question (Why glass is transparent?) but I am coming at it only from Maxwell's equations. One can determine the skin depth $δ$ for poor conductors like (pure) water and glass using ...
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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 ...
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Physical meaning of Maxwell's equations and origin of EM waves

Is it possible to describe the physical meaning of Maxwell's equations and show how they lead to electromagnetic wave, with little involvement of mathematics ?
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Do Maxwell's equations independently impose constraints on the speed of light?

My question is about the relations and equations that makes us to impose constraints on the velocity at which electromagnetic waves propagate. Do Maxwell's equations independently impose constraints ...
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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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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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How to interpret the continuity conditions in the PDEs (for example, Maxwell equations) originated in physics?

I am currently working on PDEs in physics, mostly Maxwell equations. I am a mathematics graduate student, and this question has been haunting me for years. In PDE theory, or more specifically the ...
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Does existence of magnetic monopole break covariant form of Maxwell’s equations for potentials?

Absence of magnetic charges is reflected in one of Maxwell's fundamental equations: $$\operatorname{div} \vec B = 0 \text{ (1).}$$ This equation allows us to introducte concept of vector potential: ...
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Maxwell's equations invariant under all linear transformations?

Maxwell's equations in tensor notation read: \begin{align} \partial_\mu F^{\mu\nu} &= J^\nu \\ \partial_{[\lambda}F_{\mu\nu]} &= 0 \end{align} Consider doing a general coordinate ...
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Exactly how is the constant measured velocity of light deduced from Maxwell's equation?

For electromagnetic radiation the velocity of propagation is $c = 1/\sqrt{\mu_0 \epsilon_0}$. Since both $\mu_0$ and $\epsilon_0$ do not vary in any inertial frame, then $c$ must be constant in any ...
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649 views

What is the experimental evidence that light is an electromagnetic wave?

Do we have any experimental evidence to confirm that light is an electromagnetic wave? Or is it confirmed simply by Maxwell's equations showing a similarity in speed?
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509 views

When studying electrodynamics do we assume Maxwell's Equations or derive them?

This question is because something made me confused. I always thought that the idea behind electrodynamics was to postulate some things, like Coulomb's law in electrostatics and so on, and then ...
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630 views

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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Twistor Function for Coulomb Field

In an article by Penrose in Hughston and Ward "Advances in Twistor Theory", it is claimed that the twistor function $$ f(Z^\alpha) = \log{\frac{Z^1Z^2 - Z^0Z^3}{Z^2Z^3}}$$ produces an anti-self-dual ...
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Faraday's Law and Galilean Invariance

In Jackson's text he says that Faraday law is actually: $$ \oint_{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} = -k\iint_{\Sigma} \frac{\partial \mathbf B}{\partial t} \cdot ...
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63 views

Would Michelson-Morkey experiment measure wind in non-vacuum?

If we derive the speed of light from the Maxwell equations we will find it's a function of the permittivity and permeability of the medium. Now let's play with the thought that we are living in a ...
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What was the improvement that Maxwell did to the electromagnetic field equations and why?

What was the improvement that Maxwell did to the electromagnetic field equations and why? I understand that he combined the main equations so that you could get a wave equation for the vectors of ...
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Galilean invariance of a subset of Maxwell equations

I read in Feynman's proof of Maxwell equations the statement that the subset of Maxwell equations comming from the Bianchi identity: $$ \nabla \cdot {\bf B} = 0, \quad \nabla \times {\bf E} + ...
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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 ...
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How can one meaningfully say that one field generates the other in an EM-wave?

This is a follow up question to: Do the electric and magnetic components of an electromagnetic wave really generate each other? Clearly there are nuances of how one states the "mutual induction" ...
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Why do these calculations of EM fields for a magnet and wire loop seem inconsistent?

Suppose you have a conducting circular wire loop and a magnet moving towards each other. They move along the $z$ direction with nonrelativistic constant speed $v$. Let the $B$ field of the magnet in ...
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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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Did Maxwell invent the math to describe the ideas of electromagnetism?

Did he invent surface and line integrals, or did they already exist when he formulated his equations. If they did, already exist, how did they come about in pure math?
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Neither Biot-savart nor Ampere Law can solve this problem?

I'm confused about the use of the Ampere's Law and the Biot-Savart Law due the inconvenience of each law. I want to calculate the magnetic field due to current carrying a circular loop over itself, ...
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Why is the magnetic field of a spherically symmetric current zero?

We now ask about the magnetic field produced by the currents in this situation. Suppose we draw some loop $\Gamma$ on a sphere of radius $r,$ as shown in Fig. 18–1. There is some current through ...
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What empirical evidence is there for displacement current?

I wonder what more or less direct measurements of the displacement current exist. I know that the existence of em waves demonstrates its existence, though somewhat indirectly. I also know that there ...
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872 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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About the uniqueness of the displacement current

In the Maxwell-Ampère equation, i.e.: \begin{equation} \nabla\times\vec{B} = \mu_0 \vec{J} + \mu_0\epsilon_0 \frac{\partial \vec{E}}{\partial t} \end{equation} the $\vec{J}_d$ term: $$ \vec{J}_d := ...
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Maxwell equations invariant under Lorentz transformation but not Galilean transformations

Why Maxwell equations are not invariant under Galilean transformations, but invariant under Lorentz transformations? What is the deep physical meaning behind it?
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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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What electric field vector should I use for modeling unpolarized light?

Regardless of computational cost, light is a kind of electromagnetic wave, so it can be simulated with Maxwell's equations. If we want to simulate light with Maxwell's equations, we need to express ...
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Derivatives of delta function and equation of continuity for a single charge…

For a single charge $e$ with position vector $\textbf R$, the charge density $\rho$ and and current density $\textbf{j}$ are fiven by: \begin{equation} \rho(\textbf{r},t)= ...
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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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Do Maxwell equeations change somehow after Higg's boson finding?

When I was in some physics -lesson, probably something to do with Quantum Physics -- the teacher said that certain Maxwell equations would change if the Higg's boson is found. It is also possible that ...
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“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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Maxwell's equations of Electromagnetism in 2+1 spacetime dimensions

What would be different in the theory of electromagnetism if instead of considering the equations of Maxwell in 3+1 spacetime dimensions, one would consider 2+1 spacetime dimensions?
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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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How is Biot-Savart law verification of Maxwell's 4th equation for steady current?

Please provide some theoretical procedure which equates Biot-Savart law with the Maxwell's 4th equation for steady current, which is Ampere's law $$\quad \nabla\times{\bf B} = \mu_0{\bf J}.$$
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Why does a function $\psi(v)$ appear when a Lorentz transformation is applied on Maxwell's equations?

In his 1905 paper, Einstein applies Lorentz transformation on Maxwell's equations, and relates the electric force $(X,Y,Z)$ and magnetic force $(L,M,N)$ in an inertial frame $K$ with spectime ...
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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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280 views

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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400 views

Plane wave complex notation

As far as I know, the function: $$ \vec{E}(\vec{r},t)=\vec{E_0}\cdot e^{i(\vec{k}\cdot \vec{r}-\omega t)} \hspace{2cm}(1) $$ is a mathematical solution of the wave equation: $$ \nabla^2 ...
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What is the physical significance of the Dipole Transformation of Maxwell's Equations?

The Question Given Maxwell's equations of the form \begin{align} \bar{\nabla}\times \bar{B} = \dfrac{4\pi}{c} \bar{J} + \partial_0 \bar{E} \\ \bar{\nabla}\times \bar{E} = -\partial_0 \bar{B} \\ ...
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Electromagnetic black hole?

So I was thinking about something for the past while Consider a large spherical foam-ball with homogeneous density. Where a foam ball is defined as an object that can absorb matter with 0 friction ...
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639 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. ...