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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How to prove that both $\mu_0$ and $\epsilon_0$ don't depend on any frame of references? [duplicate]

Based on my previous question here, lets us step back a little bit. The speed of light $c=1/\sqrt{\mu_0\epsilon_0}$ is assumed as a value that does not depend on the observer because it is just a ...
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Maxwell's equation in curved spacetime - how come? And experimental evidence?

I'm trying to understand the generalization of Maxwell's equations to curved spacetime. In FLAT (Minkowski) SPACETIME: If we define the "four-potential" as $$\ (\mathcal{A}^{0},\mathcal{A}^{1},\...
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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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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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What happens if you try to apply Maxwell's Equations to this quantum mechanical system?

In another post, we discussed the oscillating charge in a hydrogen atom and the weight of opinion seemed to be that there is indeed an oscillating charge when you consider the superposition of the 1s ...
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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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Is Gauss law still true in dielectric material?

In vacuum we have $$\nabla \cdot \mathbf{E} = \frac {\rho}{\varepsilon_0}.$$ Can we still use this formula when there's dielectric material in space? Where $\rho$ is total charge density.
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Ampère's law from Biot-Savart law for linear currents with multivariate calculus

My book, W.E. Gettys's Physics, starts from the Biot-Savart law $d\mathbf{B}=\frac{\mu_0}{4\pi}\frac{Id\boldsymbol{\ell}\times\hat{\mathbf{r}}}{r^2}$, i.e.$$\mathbf{B}(\mathbf{x})=\frac{\mu_0}{4\pi}\...
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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 problems ...
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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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Exterior (covariant) derivatives and electromagnetism

I'm porting Maxwell's equations to curved spacetime and am having trouble reconciling the tensor and forms treatments. I think the problem boils down to a misunderstanding on my part concerning the ...
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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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Is my argument deducing from Maxwells equations the exclusion of faster than light travel flawed?

When Maxwell's equations are solved, one of the solutions is electromagnetic waves that should move at a certain speed ($c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$). Now, one could argue that since ...
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Why are 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 about his explanation of divergence and curl. I don't understand how divergence is the dot product of a gradient ...
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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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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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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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Magnetic fields and closed loop

It is well known that there don't appear to be magnetic poles. In Maxwell's equations this has the implication $$ \nabla \cdot \mathbf{B} = 0 $$ and results in the statement "the magnetic field forms ...
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How to derive $c=1/\sqrt{\varepsilon_0\,\mu_0}$ from integral form of Maxwell equations? [closed]

I've read similar questions and answers given thereto but find them unsatisfactory. So please don't mark my question as "duplicate". The question may as well be a duplicate, but it's still waiting for ...
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Divergence of non conservative electric field

I'm looking for the proof that the 1st Maxwell equation is valid also on non conservative electric field. When we are talking about a electrostatic field, the equation is ok. We can apply the Gauss (...
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Electric field for point charge in a smoothly-varying dielectric?

A classic textbook E&M problem is to calculate the electric field produced by a point charge $Q$ located at $(\mathbf{r}_0,z_0)$ inside a medium with two semi-infinite dielectric constants defined ...
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How to derive the expression for the electric field in terms of the potential?

How can I derive that $$\vec{E}=-\vec{\nabla}\phi-\frac{\partial \vec{A}}{\partial t}$$ where $\phi$ is the scalar potential and $\vec{A}$ the vector potential?
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How much of Maxwell's equations is recoverable from the zero divergence of the stress-energy tensor?

As a motivating example, consider the static electromagnetic field defined by $\textbf{E}=(\text{const})x\hat{\textbf{y}}$, $\textbf{B}=0$. The stress-energy tensor for this field is $T=\operatorname{...
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Why should gluons move at a speed determined by $\mu_0$ and $\varepsilon_0$?

I understand that the speed of light can be derived from Maxwell's equations, giving $c=\frac{1}{\sqrt{\mu_0\varepsilon_0}}$ I furthermore understand how the principle of invariance of laws w.r.t. ...
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Maxwell equations in absence of magnetic field

I always thought that a change in electric field induces a magnetic field and vice-versa. Moreover, I imagined that any current distribution will give rise to a magnetic field. But then I wrote this ...
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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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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 this ...
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Is there a more elementary example of the holographic principle?

Someone was telling me about the holographic principle, basically he said that the state of a system is determined entirely by the values of various physical quantities on its boundary. This is not ...
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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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Electron model under Maxwell's theory

I was not able to recall my memories, so: What is the formula that states the frequency of electrons revolving around nucleus is equal to the frequency of light (or photon) emitted (or radiated)? (I ...
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Laser beam in terms of maxwell's equations

It is my understanding that a laser creates a beam of light which is contained in a cylinder. Maxwell's equations speak of the partial derivatives of the electric and magnetic fields. If the ...
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Physical implication of $\textbf{E}\rightarrow\textbf{B},~~\textbf{B}\rightarrow -\textbf{E}$ invariance of the Maxwell's equations

An interesting observation to consider about the Maxwell's equation is that in absence of the sources, the equations are symmetric under the interchange $$\textbf{E}\rightarrow\textbf{B},~~\textbf{B}\...
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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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The truest/most general Maxwell's equations in isotropic, linear, inhomogeneous media with sources

Sources use $\mu H=B$ and $\epsilon E= D$, assuming homogeneous media. Obviously if $\mu$ is space varying, $\nabla . (\mu H)$ need not be equal to $\nabla . B$ What is the most general form for ...
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Electromagnetism - Proof of the Uniqueness theorem for an external problem

In the electromagnetic Uniqueness theorem, we consider a volume $V$ enclosed by a surface $S$. It is initially assumed that two different fields are valid solutions for the Maxwell's equations with ...
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How to show with Maxwells Equations that nonaccelerating charges don't radiate? [closed]

How to show with Maxwells Equations that nonaccelerating charges don't radiate?
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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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A question on Andrew Strominger's lecture

(I now use the same conventions) (I think the notations are clear enough if you are familiar with differential geometry. Further, I tagged this post as homework-and-excercises. What is the problem ...
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Is curl of a vector a scalar quantity in 2 spatial dimensions? If it is so, then somebody help me understanding Maxwell's equations in 2+1 D

I have seen on wikipedia that in 2 spatial dimensions, Green's theorem, Gauss's divergence and Stokes theorems are equivalent and it makes sense. When I tried to write Maxwell's equations in 2+1 ...
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The curious case of parallel $E$ and $B$ fields and inertial frames

In a comment to this Physics SE question, @MichaelSeifert stated, For the more general case, IIRC there's always a frame in which $\vec{E}$ and $\vec{B}$ are parallel when $\vec{E}\cdot \vec{B}\...
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KVL for non- conservative E-field

Can we use KVL in a circuit having non-conservative field. I mean if its true then it denies the Maxwell equations which says that closed loop integral of E.dl is not zero in non-conservative fields.
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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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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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Are Maxwell's equations valid in a rotating frame?

Maxwell's equations are covariant under Lorentz transformations. Are they covariant under going to a rotating frame and if not how do they look?
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Does the Meissner effect preclude currents from the bulk of superconductors?

The Meissner effect means that superconductors will spontaneously set up currents that expel magnetic fields from them. The Ampere-Maxwell law, $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \...
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Once introduced will an electric and/or magnetic field live for ever?

So if generate an electric field or magnteic field, will it live for ever? because whenever you get rid of that field for example getting rid of electric field by discharging a capacitor, it will ...
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Ensuring Lorenz Gauge condition in Green Function solution

In the Lorenz Gauge, we can write Maxwell's equations as: $$\tag1 \Box A^\beta=\mu_0j^\beta.$$ We then go on to solve this by treating each component $A^\beta$ as an independent solution of the ...
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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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Question about units of mass, $M = (L^{3})(T^{-2})$?

In section 5 of the "Preliminary: On the measurement of quantities" chapter (page 3) in "A treatise on electricity and magnetism" Maxwell uses, total length, $s=mt^{2}/{2r^{2}}$to show that $m=2sr^{2}/...
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In plasma physics, why are the motional electric field and the frozen-in-flux condition represented by the same equation? ($E = -u \times B$)

I'm trying to refine my understanding of space plasmas, and feel like there's an intuitive understanding here that I'm just missing. We commonly refer to a motional electric field in the solar wind. ...