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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115 views

Is there differential form notation for Maxwell's equation in curved spacetime?

In special relativity, Maxwell's equations may be written as \begin{align*} dF = 0, \\ \star\, d\star F = J. \end{align*} In four-vector notation, this translates to $\partial_{\mu}F^{\mu\nu} = J^{\nu}...
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Single frequency solutions to wave equation - Two forms? Whats the difference?

I've seen these two forms from multiple sources for solutions to Maxwell's equations: $$ \cos(kz - \omega t) $$ and $$ \cos(\omega t - \vec{k} \cdot \vec{r}) $$ The first one shows a wave travelling ...
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Derivation: (lossless case) Plane waves have no electric field component in the direction of propagation

Set up Assume that a wave is propagating in the $\hat{z}$ direction with the $E$-field polarized along the $\hat{x}$ direction. In the lossless case, $$0 = \nabla \cdot E = \frac{\partial E_x}{\...
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Biot-Savart law from Ampère's with multivariate calculus

Let us assume the validity of Ampère's circuital law $$\oint_{\gamma}\mathbf{B}\cdot d\mathbf{x}=\mu_0 I_{\text{linked}}$$where $\mathbf{B}$ is the magnetic field, $\gamma$ a closed path linking the ...
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206 views

Compact expression of Maxwell's equations: is there a miss minus sign?

The compact form of Maxwell's equations: $$\boxed{\square\, \boldsymbol{\mathsf{F}}=\mu_0 \boldsymbol{\mathcal{J}}} \tag{1}$$ where the current density quadrivector is given by the relation $\...
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122 views

Derivation of Ampere's Law from Biot-Savart

Our aim is to derive $\nabla\times \mathbf B=\mu_0(\mathbf J+\epsilon_0\frac{\partial E}{\partial t})$. To begin with, let $ \mathbf A=\frac{\mu_0}{4\pi}\int_{\mathbb R^3}\frac{\mathbf J(\mathbf r')}{...
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Can a charge moving in an open trajectory qualify as current?

It is sometimes said that a point charge is equivalent to an electric current. If it were a steady current, I should be able to find it from Ampere’s law or Biot-Savart’s law. Even if the current is ...
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Does the technology exist to generate AC current with a frequency high enough such that when used in a circuit, could generate visible light? [duplicate]

The rapidly fluctuating magnetic field should generate a rapidly fluctuating electric field which propagates away from the wire at the speed of light. I'm not sure how rapidly current can be switched ...
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Constructing an equation for the induced EMF, in terms of the radius of a circular loop

In order to calculate for the curl of the induced electric field for a loop moving in a uniform magnetic field, and using the cylindrical coordinate system for a curl, it's my understanding that since ...
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Importance of the equations of Clebsh-Helmholtz: doubts

Reading the book Introduction to Electrodynamics 4th edition David J. Griffiths §1.6 the theory of vector fields (subparagraph 1.6.1 The Helmholtz Theorem), I have these doubts: Why I should to have ...
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Are there sources for potential wave solutions for which the electromagnetic far-field is zero?

Are there sources for electromagnetic potential propagating wave solutions for $\phi$ and $\overrightarrow{A}$ for which the electromagnetic far-field $\,>\!\lambda\,$ in vacuum is zero $\...
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Where does the energy go to for a charged sphere with pulsing radius?

In the question A charged sphere with pulsing radius the answer says that the charged sphere does not radiate. However, compressing a sphere of charge to a smaller radius requires work, so where does ...
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Non-relativistic vector first integral

In this paper the author discusses the Poincaré vector $\vec D$, and he wrote the Lorentz equation when magnetic charge is present. Do you have any suggested reading for this and how he derived the ...
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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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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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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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How to acquire the individual components of electric field (x,y,z) for a EMF induced in a circular loop?

I am trying to calculate the curl of the electric field induced in circular loop of wire. In order to do the actual cross the product, I would require the x,y,z component of the electric field induced ...
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76 views

How to compute the curl of the electric field, experimentally?

In order to experimentally verify Faraday's law and express the curl of the induced electric field, is there any other way to compute the curl without directly working on the cross product (ie working ...
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Is there a way to express the curl of the electric field in the integral form?

In order to experimentally measure the curl of the electric field from faraday's law... is there a way to equate the curl of the electric field to some integral that are measurable in a practical ...
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1answer
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Electromagnetic field of a spinning cylinder

Let us consider an infinite cylinder of axis $(Oz)$ and radius $R$ spinning at a constant radial velocity $\omega$. We assume that this cylinder is made of a metal that is assumed to be a conductor (...
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27 views

Investigating the relationship between a changing B field and the curl of the electric field induced

I am currently working on a 12 page lab report on Faraday's law, essentially investigating, how for different magnetic field strength through a stationary loop of wire with N number of turns, effects ...
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Experimentally defining Faraday's law [on hold]

I am a highschool student, and I currently writing a lab on the how the curl of the electric field (with respect to the induced emf) is effected by changing the strength of the magnetic field for each ...
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Confusion with representing the negative rate of change of magnetic flux in Faraday's law

So Faraday's law states in differential form that $$ \nabla \times \vec{E} = -\frac{\delta H}{\delta t} $$ Using Stoke's theorem, the right hand side (the magnetic flux rate of change) is expressed as ...
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The meaning of the 4-divergence of the 4-magnetic field?

In special and general relativity, the magnetic field is defined as $$B^\mu = F^{*\mu\nu}u_\nu, \label{tag1}\tag{1}$$ where $F^{*\mu\nu} = \frac12 \varepsilon^{\mu\nu\rho\sigma}F_{\sigma\rho}$, and $...
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How can I show that the speed of light in vacuum is the same in all reference frames?

I have regularly heard that the Michelson-Morley experiment demonstrates that the speed of light is constant in all reference frames. By doing some research I have found that it actually demonstrated ...
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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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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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How is it possible for the induced emf to take negative values in Faraday's Law of induction?

Faraday's Law of induction states that the work done per unit charge by the (induced) electric force along a loop of wire, or the emf, is minus the rate of change of magnetic flux through the loop/...
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Maxwell equation similar to a solution for a standing wave in a box [closed]

From Nature Of Photon: Electromagnetic field The set of Maxwell equations [2] for vacuum is: $$\begin{align} \mathrm{rot} \mathbf{E} &= -∂\mathbf{B}/c∂t, \tag{1} \\ \mathrm{rot} \mathbf{...
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Intuition of Maxwell's Equations [duplicate]

Is there an intuitive explanation for Maxwell's equations? I know they are axioms but is there a logical understanding of why instead of mathematical. Both forms don't explicate the scientific ...
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Maxwell equations in curved spacetime with cosmological constant

I am aware of Maxwell Equations in Curved Spacetime. But how do these equations change if the cosmological constant is not assumed to vanish?
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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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What is 'velocity' in classical electrodynamics?

I have recently noticed that unless the objects in question are conducting, neutral wires, the Lorentz force law along with Maxwell's equations will give you anything and everything as a solution for ...
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57 views

An electrodinamic identity: starting point [closed]

With this request, I would like to ask you kindly how you can prove this identity. I thank you for those who can help me. \begin{equation} \overline{\nabla} \times (\overline{\nabla} \times \...
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118 views

Electromagnetic waves according to Maxwell

If a variable Electric field creates a variable magnetic field and VICE VERSA (according to Maxwell's equations), then why don't we enter a loop where E vector and B vector keep creating one another ...
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What's the difference between conduction current density and source (impressed) current density in an RC circuit?

My electromagnetics textbook has a picture of an RC circuit with a current source. As you can see, there are three current density vectors, $J_i$, $J_c$, and $J_d$. The book labels them as follows: $...
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1answer
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Maxwell Laws Summary Diagram - Suggestions that I am missing? [closed]

I have been going through a summary book of Maxwell's equations and hope I have organised this correctly but I think perhaps I am missing things important prompts that I could add? Image below Thanks ...
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178 views

Cause of induced EMF in a loop

Len'z law states that the change of magnetic field in a loop of wire produced current in a wire as the magnetic field in and out the loop.Although it just true experimentally, but i) What happened ...
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180 views

Does electric field generated by changing magnetic flux generate an opposing magnetic field?

According to Faraday's law a changing flux through a loop will create an Electric-field curling around that loop. And if the loop is a conducting wire the current looping will create an opposing ...
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Maxwell's equations UPML in FDTD with inhomogeneous media

I'm looking at matching the UPML (uniaxial perfectly matched layer) defined in Taflove&Hagness' Computational electrodynamics to an inhomogeneous media (inhomogeneous w.r.t. both $\varepsilon$ and ...
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How can changing magnetic field produce instantaneously the electric field and vice versa? [duplicate]

Maxwell's curl equation for electric field says that time varying magnetic field produces electric field instantaneously but nothing can happen instantaneously according to special relativity. What is ...
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Why maxwells speed distribution law doesn’t violet special theory if relativity [duplicate]

As per maxwells distribution law the molecule of gas will have speed across zero to infinity with some probability function. I want to know that why the speed above speed of light is possible (i know ...
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Colors of the Earth from space, an “average” of particular emitters?

When we're say about 100 km above Earth's ground and look down to it and see the Amazonian region as green, is this green color a sort of "average" of greens from trees from that forest or is the "...
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Helmholtz equation and sources

it is known that starting from the Maxwell equations it is possible to get the following Helmholtz equations: In time domain it corresponds to a sinusoidal EM field, according to the wave equation: ...
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How can the first Maxwell equation be valid in non-static cases?

I am thinking in the framework of Classical Gravity, where the speed of the interaction is infinite. Now it is also known that there is a correspondence between Classical gravity and electrostatics, ...
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How does charge movement vary between insulators and conductors?

I've been reading A Student's Guide to Maxwell's Equations by Daniel Fleisch, and he states: in nonconducting materials (called "insulators" or "dielectrics"), charge does not move freely, but may ...
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190 views

Does a Static E-field Increase the Gauge Invariant Vector Potential Without Bound?

The gauge invariant formulation of Maxwell's Laws (7.13): Indicates that the transverse electric field is the time derivative of the transverse vector potential. This gauge invariant vector ...
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Magnetic field in a capacitor

If in a flat capacitor, formed by two circular armatures of radius $R$, placed at a distance $d$, where $R$ and $d$ are expressed in metres (m), a variable potential difference is applied to the ...
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Why Is Abelian Gauge Theory So Special?

I have a perhaps stupid question about Maxwell equations. Let $G$ be a generic Lie group. We consider a $G$-gauge theory. Let $A$ be the associated connection $1$-form, and $F=dA+A\wedge A$ be the ...
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How can I define the phase out of a Mach–Zehnder interferometer?

currently I am trying to learn more about integrated photonics, more specifically about optical processing (Matrix multiplication, for instance). I have read different books regarding classical ...