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Questions tagged [maxwell-equations]

A set of four equations that define electrodynamics. They comprise the Gauss laws for the electric and magnetic fields, the Faraday law, and the Ampère law. Together, these equations uniquely determine the electric and magnetic fields of a physical system. Do not use this tag for the thermodynamical equations known as Maxwell's relations.

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Demystifying the connection between magnetic and electric fields

Part (1): In the classical theory of electromagnesitm, as given by Maxwell, we know that by just looking at the four famous equations: An electric field has a source: there are charged particles (...
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Why all theories are Lorentz invariant?

Ok, in studying of Maxwell equations we have violation of Galilean relativity. This implies necessity of other transformations which make Maxwell equations covariant (invariant in form) under this ...
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Is Gauss' law valid for time-dependent electric fields?

The Maxwell's equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ is derived from the Gauss law in electrostatics (which is in turn derived from Coulomb's ...
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Why are the $\mathbf E$ and $\mathbf B$ fields of an electromagnetic wave mutually perpendicular?

Why are the wave number $\mathbf k$ and the electric and magnetic fields $\mathbf E$ and $\mathbf B$ are perpendicular to each other? I know it but I haven't thought about it deeply. How can I prove ...
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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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The necessity of the B field

It is fairly easy using basic special relativity to arrive at the conclusion that the magnetic force effect on nearby charges of wires carrying currents on nearby charges is only due to the length ...
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Comparison of covariant form of Maxwell equations with Einstein's GR

We know, the the vector form of Maxwell equations \begin{align} \vec\nabla\cdot\vec{E} &= 4\pi\rho \label{Diff I}\\ \vec\nabla\times\vec{B} &= \dfrac{4\pi}{c} \vec{j}+\dfrac{1}{c}\dfrac{\...
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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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Maxwell's equation in free space from wave equations of electric and magnetic field

How to go from the wave equations of electric and magnetic field and $$ \boldsymbol{\nabla}\cdot \mathbf E = 0 \quad \text{ and } \quad \ 0 = \boldsymbol{\nabla}\cdot\mathbf B, $$ to the remaining ...
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Confusion on Maxwells equations and Gauge Transformations

I know a little bit about electrodynamics but I don't understand the validity of Gauge Transformations. In particular I am confused on how the theory can be consistent among different gauges, in ...
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What does the non-zero divergence of $\textbf{H}$-field say about magnetic monopoles?

It is always true that $\boldsymbol{\nabla}\cdot \textbf{B}=0$ (implying that there are no magnetic monopoles). However, $\boldsymbol{\nabla}\cdot \textbf{H}\neq 0$ when $\boldsymbol{\nabla}\cdot \...
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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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Derivative of the electromagnetic tensor invariant $F_{\mu\nu}F^{\mu\nu}$

The electromagnetic field tensor is $F_{\mu\nu}=\partial_\mu A_\nu - \partial_\nu A_\mu$. I am trying to calculate the quantity $$ \frac{\partial(F_{\alpha\beta}F^{\alpha\beta})}{\partial(\partial_{\...
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Maxwell's equations from continuum limit

In appendix A.6 of Schroeder's Thermal Physics, he mentions (in regards to classical fields): The usual approach is to first pretend that the continuous object is really a bunch of point particles ...
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Frames of reference of Maxwell's Equations

The Maxwell's Equations are one of the most famous sets of equations physics have ever known. But just as different sets of equations are applicable to different frames of reference, where are Maxwell'...
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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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Interpreting the inhomogeneous wave equations for $\vec{E}$ and $\vec{B}$

Starting from Maxwell's equations, \begin{align} \nabla \cdot \vec{E} & = \frac{\rho}{\epsilon_0} & \nabla \cdot \vec{B} & = 0 \\ \nabla \times \vec{E} & = - \frac{\partial \vec{B}}{\...
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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 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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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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Electric Field in a uniform time-varying Magnetic field

Suppose a homogenous Magnetic Field $\vec{B}$ in vacuum that varies with time, but always points in the z-direction. This induces a curl in the Electric Field $\vec{\nabla} \times \vec{E} = -\frac{\...
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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. ...
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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 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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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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A question on the unification of electricity and magnetism

As far as I understand it, Maxwell's equations unify the theories of electricity and magnetism, however, I don't see how they show that the electric field, $\mathbf{E}$ and the magnetic field, $\...
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Current geometry and Ampere's law

Under the right circumstances, Ampere's law $\oint \vec H\cdot d\vec \ell=I_{encl}$ can be used to deduce the field $\vec H$ at a point from the current enclosed by the circuit which produces $\vec H$....
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Do divergence and curl of Lorentz force have some physical meaning?

Time ago I started thinking about this: if we take the well known Lorentz Force expression, namely $$\mathbf{F} = q\left(\mathbf{E} + \mathbf{v}\times\mathbf{B}\right)$$ and we operate $\nabla\cdot \...
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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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Justification of Physical Laws [closed]

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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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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Write electromagnetic field tensor in terms of four-vector potential

How can we know that the electromagnetic tensor $F_{\mu\nu}$ can be written in terms of a four-vector potential $A_{\mu}$ as $F_{\mu \nu} = \partial_{\mu} A_{\nu} - \partial_{\nu} A_{\mu}$? In 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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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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Is the speed of light dictated by Vacuum Permittivity, Vice Versa or Neither?

Instinct, and my limited knowledge of Maxwell's Equations and the Wave Equation tell me that the first statement is true. By my interpretation, the relationship between the frequencies and ...
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Significance of the Dual Electromagnetic Tensor $\tilde{\mathbf{F}}$/its derivation

In the context of Maxwell's equations, I was wondering whether there was any physical significance to the dual EM Field Tensor and/or its various derivations. It has components: $$\tilde{\textbf{F}} = ...
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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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Is there any particular reason why Faraday's and Ampère's laws are valid?

I know that the Maxwell equations are usually the explanation for all electromagnetic phenomena, but I would like to know why those are valid, if there is any reason for them.
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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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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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Stumped on understanding a Feynman lecture about force from wire on magnet

I must (sheepishly) admit that I'm stumped on a beginning page of The Feynman Lectures Volume 2. I have included a picture from the page. [Let me know if I'm breaking copyright, or if I can include ...
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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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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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How do you find the magnetic field corresponding to an electric field?

If we are given the electric field $\vec E$ how can I find the corresponding magnetic field? I think I can use Maxwell's equations? In particular, $\nabla\times \vec E= -{\partial \vec B\over \partial ...
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Why does gradually increasing refractive index coating reduce reflection?

Why does gradually increasing refractive index coating reduce reflection? EDIT: As @Michael Seifert nicely describes in his answer, reflection only occurs if there is an abrupt change in refractive ...
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Why is divergence and curl related to dot and cross product?

I've been reading Griffith's intro to electrodynamics and I've been a bit confused on his explanation of divergence and curl. I don't understand how divergence is the dot product of a gradient acting ...
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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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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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Is light transverse electromagnetic (TEM) or transverse magnetic (TM) wave?

My apologies if this is a duplicate. I have been trying to understand the differences between Maxwell's solutions. So far I gathered that TEM requires free current and at least 2 conductors ...