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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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Can electric displacement field be zero if electric field is not?

The electric displacement field is defined as $$\mathbf{D}=\epsilon_0\mathbf{E}+\mathbf{P}$$ But these equalities hold as well: $$\mathbf{P}=\epsilon_0\chi \mathbf{E}$$ $$\mathbf{D}=\epsilon_0(1+\...
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Where does this form of the induction law come from?

I am currently studying a eddy current disk break and came across this promising paper (PDF, princeton.edu) from 1942. However, in the first formula a suspicious $4\pi$ appears before the current $U(...
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Prove that the electric field produce by a punctual charge is isotropic and radial

I would like to prove mathematically that the electric field produced by a punctual charge is isotropic and radial, i.e. $$\vec{E}(r,\phi,\theta)=E(r)\vec{e}_r\tag{1}$$ I think that this statement ...
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Simple explanation to the induction from the slowly changing $\vec B$ of a solenoid in the region of $0$ magnetic field

I would like to get some elementary intuition into the problem a solenoid fed with a time-dependent current, and the resulting current that such the solenoid field would induce in a loop completely ...
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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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How to choose the boundary condition for Maxwell's equations in the vacuum?

I need to solve the Maxwell's equations with sources in the vacuum numerically. The simplified problem is as following. A charged particle moving along the $z$ direction with speed $v_z$. Then, it ...
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How are the differential forms for Maxwell's Equations used?

I am currently reading up on Maxwell's Equations (specifically Ampere's Circuital Law- with Maxwell's Addition) for a presentation on differential equations. I chose the topic ignorant of how the ...
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Does superposition of all possible plane waves represent complete solution of Maxwell's equations in free space?

Consider the set of all possible superpositions of all possible "plane waves that satisfy Maxwell's equations in free space". Does this set represent all possible solutions of Maxwell's equations in ...
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Polarization on a spherical electromagnetic wave in free space using classical electromagnetism

The polarization of a plane wave traveling in free space is well defined and traverse to the direction of propagation from classical electromagnetic theory. Spherical waves are another type of ...
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Solution to Maxwell's equations in free space that are not plane waves [closed]

Are there solution to Maxwell's equations in free space that are not plane waves? I think there aren't. (Save trivial ones, i.e. E=const , B=const ) But i am not able to prove it. Please help. I would ...
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Derivations of Maxwell equations

In my book of electrodynamics, the Maxwell equations are always used for specific conditions (electrostatics, magnetostatics, …). But nowhere I see a complete derivation of the equations. Maybe it ...
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How to extract all information regarding electric and magnetic fields from Maxwell's equations in free space? [closed]

Is it possible to obtain some set of equations in E and B that have decoupled E and B , but are exactly equivalent to Maxwell's equations in free space? Exactly equivalent in the sense that the 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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Flux of Electric field non-zero through a surface for light in free space?

Consider an electromagnetic wave propagating through free space.The Electric and magnetic components of the fields, vary as sinusoids. If I construct a sphere of radius $\lambda/4$ at any location; i ...
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Are wave equations equivalent to Maxwell's equations in free space?

In free space, do Maxwell's equations contain the same amount of information regarding electric and magnetic fields as is contained in the wave equations derived from them? If so, how?
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How do we get a expression for speed of light $\frac{1}{\sqrt{\mu\epsilon}}$ using Maxwell's equation? [duplicate]

I am a $12^{th}$ class student in India. I am quite new to these interesting concepts. And, I think I've learnt about electrostatics, magnetism, Maxwell's equations very thoroughly. But, my books ...
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Maxwell stress tensor for electromagnetic wave

Sorry if this is a naive question but I've been struggling in trying to proof this for a week. Consider an electromagnetic wave with wave vector $\vec{k}=k\hat{n}$, the Maxwell stress tensor can be ...
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How can we prove the law of Ohm $V=I*R $ from Maxwell's equations [duplicate]

$$∇⋅E=ρϵ0$$ $$∇⋅B=0$$ $$∇×E=−∂B/∂t$$ $$∇×B=μ0(J+ϵ0 ∂E/∂t)$$
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Feynman-Heaviside formula and Mach's principle

I was wondering if the Feynman-Heaviside formula for the electric field of a moving charge could be used to write down the force/reaction force between charges $q_1$ and $q_2$ in a Machian purely ...
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Why dielectric polarization is not considered at boundary condition?

Consider the problem of reflection, transmission for incident light at the boundary of two dielectrics. From Ampere' law, $\vec\nabla\times \vec H = \vec J+\partial\vec D/\partial t $. Every text ...
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Reason why dot notation isn't used for time derivatives in Maxwell's equations [closed]

Maxwell's equations seem to be usually written: \begin{align} \nabla \cdot \mathbf{E} &= \rho/\epsilon_0,\\ \nabla \cdot \mathbf{B} &= 0,\\ \nabla \times \mathbf{E} &= -\frac{\partial \...
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Could magnetic fields really be completely substituted by relativity and electric fields?

In many textbooks (especially those for undergraduate level), magnetic fields are described merely as a relativistic side product of electric fields when considering frames in motion relative to ...
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TMZ TME modes, clarification

I'm refering here to Taflove's "computational electrodynamcis, 3rd ed." He says Let us assume that the structure being modeled extends to infinity in the z-direction with no change in the shape ...
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Questions about plane electromagnetic wave

A wavefront is defined to be the locus of all points on which the field oscillations are in phase, in the plane electromagnetic wavefront, it is said that all points on a plane perpendicular to the ...
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What is knotted in EM and GR?

I found this paper with beautiful illustrations: Helicity, Topology and Kelvin Waves in reconnecting quantum knots, and this one which seems to describe something closely analogous: New knotted ...
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Why Proca Term forbidden in Schwinger Model?

In my QFT Lecture we considered the Schwinger model with a Proca term. Solving the eom for the Stueckelberg field and plugging it back into the original Lagrangian, we receive an effective Lagrangian ...
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Ampere's Law, Interface conditions for magnetic field

I'm failing to understand the derivation of the interface conditions for the tangential components of the magnetic field given her (based on d.j,griffiths) Ampere's law in integral form is given as $$...
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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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Covariant Maxwell equations invariant under parity transformation

I tried to proof that the Maxwell equations are invariant under parity transformations. Therefore I used the covariant formulation of the Maxwell equations \begin{align} \partial_{\nu}F^{\nu\mu} &...
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Maxwell's equations in differential form in 2-space+1-time dimensions

How does one write maxwell's equation in 2+1 dimensions? It becomes particularly interesting as the components of 2 forms and 1 form are 3. Are there any sources for this?
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What is the formula for electromagnetic force on magnetic charge in condensed matter?

It is known that if we take into account the magnetic charges, Maxwell's equations acquire a symmetrical form (Jackson, 3rd edition, eq. 6.150): \begin{align} \begin{aligned} -\nabla \times \...
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Does the induced current in one wire affect the driven wire?

Let's say that we have two parallel, vertical wires with radii much smaller than lengths. The wire on the right is driven with an AC current. When the current is increasing in the upwards direction a ...
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Numerically Stable Light Absorption Density Calculation

I am reading through the documentation provided by Lumerical concerning light absorption per unit volume : https://kb.lumerical.com/layout_analysis_pabs_simple.html Lumerical says that: It can be ...
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Is there Electric Flux through a closed loop around a current wire?

In one of his lectures, Professor Walter Lewin is ammending Ampère's Law to include displacement current (i.e. It not only depends on the current that penetrates the loop, but also on the changing ...
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Difference between $\bf J$ and time derivative of $\bf E$ in Maxwells equations? [closed]

Maybe I am being confused. It was some years ago I did this. An electric current changes charge distribution which creates rotation in $\bf B$. So in Ampères / Biot-Savarts law what is the difference ...
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Maxwell-Chern-Simons equation: Translating from differential form to component form

I am trying to solve the scalar-coupled Maxwell-CS equations (which is one of the equation of motions in $N=2$ supergravity coupled to 3 vector multiplets), which is written in this form in the ...
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Field intensity for electric field and vector potential

In general, the intensity of an electric field is given by $$ I = \frac{c\epsilon_0}{2}E_0^2 $$ where $E_0$ is the peak amplitude of the electric field. Let's say we have an electric field $$ E(t) = ...
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Faraday's Induction Law Notation

I am confused as to the notation used in a course I'm taking on physical optics. I have presented 2 variants of Faraday's Law, combined with the full set of Maxwell's equations. The first ...
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Physical Interpretation of $\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0} $

The differential's form of Gauss' Law is $$\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}. $$ This suggests that at every point in space, the the electric field $\vec{E}$ is determined by the charge ...
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Electric field produced by a moving charged particle above a planar dielectric interface

The electrostatic field of a single charged particle above a planar dielectric interface is a standard example given in many books (see example 4.4 in Griffiths or https://en.wikipedia.org/wiki/...
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Current induced by permanent magnet moving along toroid coil

(It's not really shown in the pictures, but please assume that the coils are included in a closed circuit in both configurations. Maybe they could serve as a tension source in their respective circuit ...
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Ampère's circuital law in case of uniform current density in infinite space

Let's have an ideal conductor with current density $\mathbf{J}$. The ideal conductor takes up the entire space, effectively resulting in the entire space $\mathbb{R}^3$ being permeated with $\mathbf J$...
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Electrodynamics of inhomogeneous media

I'm interested in electromagnetic scattering and for that purpose I would like to write out Maxwell's equations for space-dependent permittivity (and permeability). Actually I only need them for ...
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Equivalence between Maxwell's equations and vector Helmholtz equations

When are equivalent the Maxwell's harmonic equations: $$ \nabla\times\left(\nabla\times\mathbf{E}\right)=\mu\epsilon\omega^2\mathbf{E} $$ and the vector Helmholtz equations: $$ \nabla^2\mathbf{E}=\mu\...
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Explanation of Lenz's Law phenomena

If we drop a magnet through a copper pipe (without it touching any of the sides), it would fall slower than it would if there were no pipe. Having the pipe otherwise accelerate the magnet would be in ...
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How was the value of vacuum permittivity originally found?

The vacuum permittivity appears originally in Maxwell's equations, used to describe electric fields. The permeability of vacuum was defined using Ampere's force law (itself derived from Biot-Savart ...
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How does Superposition principle follow from Maxwell's equation's linearity?

It is said that whole of electromagnetism can be completely described by the Maxwell's equations. The thing that intrigues me is that how does superposition principle follow? First, I take an ...
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are there changing magnetic and electric fields that are not EM radiation?

Let us consider these two Maxwell equations: $$\frac{\partial \vec{B}}{\partial t}=-\vec{\nabla}\times \vec{E}$$ and $$\frac{\partial \vec{E}}{\partial t}=\frac{1}{\epsilon_0}\left(-\vec{J}+\frac{1}{...
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Are Maxwell's equations “physical”?

The canonical Maxwell's equations are derivable from the Lagrangian $${\cal L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} $$ by solving the Euler-Lagrange equations. However: The Lagrangian above is ...
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Flattening Electrodynamics in a curved space

It is possible, apparently, to describe gravitational lensing as if gravitational potential induces an effective refractive index change in the vacuum, and spacetime is flat. As pointed out by @...