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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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 equation similar to a solution for a standing wave in a box [on hold]

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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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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Importance of the equations of Clebsh-Helmholtz

Why we use also the Clebsh-Helmholtz equations into the Maxwell equations and into delayed potentials? Why are they used? What is their usefulness? See §2.3.4 The Potential of a Localized Charge ...
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An electrodinamic identity: starting point

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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Compact expression of Maxwell's equations: missed minus sign

With much courtesy I ask a simple explanation to be able to obtain a minus sign missing from the compact form of Maxwell's equations: $$\boxed{\square \overleftrightarrow F=\mu_0 \boldsymbol{\mathcal{...
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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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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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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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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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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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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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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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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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Tensor Notation - David Tongs Notes [duplicate]

I'm trying to understand the Maxwell's Equation example from David Tongs QFT notes. He uses the Lagrangian: $$ L = -\frac{1}{2}(\partial_{\mu}A_{\nu})(\partial^{\mu}A^{\nu})+\frac{1}{2}(\partial_{\mu}...
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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 ...
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Magnetic field on a super conductor cylinder

Suppose that i have a cylinder of the z axis. I'll put this cylinder on a uniform magnetic field with magnitude of B0 along de y axis. Since we have B = 0 inside the superconductor, this will ...
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Understanding gauss's law for magnetism using classical concepts

How to show with the help of diagrams that magnetic lines of force, whatever their origin have no divergence?
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Why is light moving transversal?

This question will be in some way complicated for different reasons - I am no physicist, I know about things like wave-particle duality, that the tranversal wave motion comes from change in electric ...
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Klein-Gordon/Maxwell Equation: dissipative or dispersive?

In Aspects of Symmetry, Coleman says (p. 185) ''Most of the simple field theories with which we are familiar have the property that all of their non-singular solutions of finite total energy are ...
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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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What happens with the divergence of maxwell stress tensor when EM fields in vacuum?

The conservation momentum can be derived from the total electromagnetic force on the charges in volume $V$ and is written in this way: $$ \frac{d\vec{p}_{mech}}{dt} + \frac{d}{dt} \int_V (\vec{E}\...
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Do Maxwell's equations predict that electrons have no internal structure?

As far as I know, Maxwell's equations can't be derived from anything more fundamental. Does this indicate that electrons have no internal structure? I mean to say that, in my view, the entire nature ...
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Derivation of Maxwell's Equations using the Energy-Momentum tensor [duplicate]

If the energy momentum tensor is related to the EM field tensor by $$ T^{\mu v}=F^{\mu \sigma}F^v_\sigma-\frac{1}{4}\eta^{\mu v}F^{\sigma \tau}F_{\sigma \tau} $$ Is it possible to derive Maxwell's ...
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Physical Relation in Maxwells Equations of quantity between as well as fundamental forces

Recently learnt about Maxwells Equations, am wondering what is the physical relation between electric field E and magnetic field B. It would help if the physical meanings are related to the ...
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What is the relation between the frequency of the light produced and the acceleration of the charged particle

We know that accelerating charges produce EM radiation. Can we derive a relation between frequency of the light produced and the accelaration of the charge ?
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Why using an imaginary surface is allowed when applying Faraday's law?

In a lot of problems, like a rod rotating in a constant magnetic field $B$, we find the EMF induced by the movement by defining an imaginary surface in which the rod is a part of it. Then we apply ...
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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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$* d * $ operator — Digest the (differential/geometry) meaning

I like to digest better: the $* d * $ operator in Maxwell differential form equation the $* D * $ operator in Yang-Mills differential form equation We already knew that in Maxwell differential ...
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How to show $z$-component of EM plane wave in free space is 0?

I know that for a uniform plane wave propagating in the z-direction in free space, there should be no z-component, however, I am having trouble proving this. Assuming $\vec{E} = E_x (z,t) \hat{x} + ...
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Where am I going wrong in deriving Maxwell's first equation in differential form?

By denoting the source coordinates with prime, I get flux through a closed surface: $$\Phi= \displaystyle\oint_{A} \mathbf{E}(x,y,z) \cdot \mathbf{\hat{n}}\ dA =q (x',y',z')$$ And now using the ...
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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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How did Maxwell figure out the speed of light?

The Wiki article is about 2 graduate years of physics beyond my understanding. What is a good high-school rendition of his thought process: regarding his use of the "distributed capacitance and ...
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What does Maxwell's equations predict for the propagation of EM waves converging to a point?

Maxwell's equations model EM radiation as propagating away from an accelerating charge. Suppose instead the propagation of this EM radiation is reversed and presented as a source-free boundary ...
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Lagrangian of Phonon-photon

A quite interesting but also hard problem are Polaritons. As far as I have understand the concept it's about phonons coupling to light. The Lagrangian function should therefore have a term for the ...
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Electromotive force in the presence of non-steady currents

Griffiths's Introduction to Electrodynamics states $$\mathcal E = \oint \mathbf f \cdot d\mathbf l$$ In which $$\mathbf f = \mathbf f_s + \mathbf E$$ Where Griffiths describes the summation as ...
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Electromagnetism and differential forms

I am currently writing a Bachelor's thesis in theoretical physics, and since I like the interplay between mathematics and theoretical physics, I am writing about Maxwell's law in terms of differential ...
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Does a homogeneous oscillating electric field produce a magnetic field?

I am working on a homework problem that says an electron in a continuous laser field can be modeled as experiencing a homogeneous oscillating electric field $\vec{E}(\vec{r},t)=\cos \omega t \ \hat {z}...
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Is the speed of Magnetic field infinite?

My real question is: From Amperes law we know that there is no magnetic field outside of the coaxial cable because the magnetic field generated by the inner wire and outer shell are equal but in ...
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What is the formula that gives the EMF

I have been recently studying Maxwell Equations, and I wasn't able to understand properly the EMF $\zeta$. Mathematically we have $\zeta=-\dfrac{d\Phi_B}{dt}$ where $\Phi_B$ is the magnetic flux of a ...
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Variational formulation of Maxwell equations with interface/boundary conditions

Consider $\Omega = \Omega_1 \cup \Omega_2$, where $\Omega _1$ and $\Omega_2$ are two different media with conductivity and permeability \begin{equation} \sigma= \begin{cases} \sigma _1 & \text{in ...
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Differentiability of electric field due to bounded volume charge distribution

In books on electromagnetism, one often sees expressions of Maxwell's equations like $\nabla \cdot \mathbf{E}$ and $\nabla \times \mathbf{E}$. These expressions make sense if $\mathbf{E}$ (which is ...
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Is tangential component of $\mathbf{B}$ undefined at the boundary of two media?

Tangential component of $\mathbf{B}$ is discontinuous at the boundary of two media. Does this mean that tangential component of $\mathbf{B}$ is undefined at the boundary of two media? If yes, then: $...
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How to connect Maxwell's equations to quantum anomalous Hall effect?

The quantum anomalous Hall effect (QAHE) describes the response of a material resulting from topological properties of its band structure. These topological properties are often characterized by the ...
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Doubt on why magnetic flux density is solenoidal

The $\mathbf{H}$ field can be derived from the potential $\psi$: $$\mathbf{H}=\dfrac{\mu_0}{4 \pi} \int_{V'} \rho \dfrac{\mathbf{r}-\mathbf{r'}}{|\mathbf{r}-\mathbf{r'}|^3} dV' + \dfrac{\mu_0}{4 \pi}...
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A simple proof covariance of Maxwell equations

I read that Maxwell equations are covariant under Lorentz transformations, but I can't find a proof. Or at least a proof understandable by someone that doesn't know higher mathematics (please don't ...
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Static electric field which admits no potential

Conservative condition for (static) electric field $\mathcal{E}$ is usually defined as $\mathcal{E}$ being closed (curl-free). Now this clearly holds when for the given manifold $X$ we have $H_\text{...
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Current sources and conservative electric fields

Suppose a current density ${\bf J}({\bf r},t)$, for which $\nabla \cdot {\bf J} =0$, is compactly supported on a 3D region $R_1$ in vacuum. In general it can produce a nonzero electric field ${\bf E}({...