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 Maxwell-Boltzmann distribution, or the thermodynamical equations known as Maxwell's relations.

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51 views

Recipe for finding non-conservative electric field in general case

I know that Faraday's law gives a recipe for finding the EMF over a closed loop. But, other than through symmetry arguments, I have not found a way discussed in my textbooks on how to find explicit ...
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How strong an electric field is needed to violate electrostatic equilibrium of usual conductor?

As is told by almost all textbooks, a conductor reach electrostatic equilibrium in an elctric field. My quetion is that, is there any kind of conductor, which has so few electrons and eletron-like ...
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How to model radiative transfer of incoherent light through packed spheres?

If you have an unpolarized radiation from a broadband light/thermal source propagating through a medium packed with spheres (inter-sphere distance less than wavelength), do you need to account for ...
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Maxwell's action with differential geometry formalism

I'm having problems in showing that the following identity, regarding Maxwell's action, holds true: $$ S_{Maxwell}=-\frac{1}{2}\int F\wedge\star F=-\frac{1}{4}\int \sqrt{-g}\,F_{\mu\nu}F^{\mu\nu}\...
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Covariant Maxwell equations

As we know, the covariant form of Maxwell's equations (there are 2 equations in this formulation) are covariant under Lorentz transformation. Are these equations covariant under general transformation,...
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Using magnetic field of plane polarized standing EM wave for Faraday's law?

Is it possible to use the undulating magnetic field of a plane-polarized standing EM wave as the source of changing magnetic flux for Faraday's law? Why or why not? I assume that if it's possible, ...
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EM-wave equation in matter from Lagrangian

Setup Let's suppose a homogeneous dielectric with a (spatially) local dielectric response function $\underline{\underline{\epsilon}} (\omega)$ (in general a tensor), such that we have the linear ...
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Using Maxwell's equations to find $\mathbf{B}$

The $\mathbf{E}$ component of an electromagnetic wave in free space is: $$\mathbf{E}(x, t) = E_0 \cos{(kx-\omega t)} \hat{\bf y}$$ How do I find the corresponding $\mathbf{B}$ component using one of ...
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Is it possible to unify Maxwell's four equations into one single equation? [closed]

The ultimate goal of physics is to unify all the four fundamental forces together. These forces basically are laws of nature. This makes me ask if it is possible or not to unify Maxwell's four laws?
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Faraday law, derivative that enter in the integral?

In the Faraday law derivation written below there is a passage that I don't understand (the one in bold). My professor gave us just a short comment about it that it's not enough for me to understand, ...
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In relation to General Relativity, Invariant form of Lorentz force

I am a High school student, so am new to this topic. Using my own understanding I want to come up with the covariant(or invariant) form of Lorentz force. But I am unable to do it. MY IDEA: Let $\...
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Light from Maxwell's equations

According to Maxwell's equations, an accelerating electron emits light. My question is, does Maxwell's equations explain the emission of all electromagnetic waves in the universe including, say, light ...
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Maxwell equations in Feynman's lectures

I read the FLP vol. 2 and in the chapter 1, section 1.4 Feynman states from the physical point of view to form the intuition $$c^2(\text{circulation of B around the curve} \ C)=\frac{d}{dt}(\text{Flux ...
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Are moving charges and changing electric fields different causes?

Question Are moving charges and time-varying electric fields really distinct causes of magnetic fields?? Various EM Phenomena Two larger purposes are providing some Background to make sure I follow ...
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Is it true that Maxwell equations are interpreted by taking right side of formula as the "origin" and the left part as "consequence"?

When books or various references interpret the meaning of Maxwell equations, they typically state that the source (origin of the phenomena) is the right part of the formula, and the resulting effect ...
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Non-conservative electromagnetic fields $ \displaystyle \nabla \times \vec{E} = - \frac {\partial \vec{B} }{\partial t}. $ [closed]

While studying electromagnetism, I came across the statement $$ \displaystyle \oint_{\delta S} \vec{E} \cdot \mathrm{d}\vec{l} = \frac {\mathrm{d}}{\mathrm{d}t} \iint _{S} \vec{B} \cdot \mathrm{d}\...
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Simple **Unsolvable** electric field problem

Cannot be integrated w Coulomb, Maxwell doesn’t work. Impossible situation? So then what would really happen? Large sheet of charge (assume infinite or far from edges, and even assume low but nonzero ...
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Using Faraday's law twice

I have trouble understanding Faraday's law when there is an induced current which in turn induces another current in the same circuit. I shall illustrate my confusion with an homework problem and I ...
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Magnetic Charge through conducting loop

There's a problem in Griffith's book that I don't understand his solution : Here's the solution : What's the justification for $\varepsilon = -L\frac{\mathrm{d} I}{\mathrm{d} t}$ ? $$$$ This ...
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Does the divergence of the electric potential in the event horizon describe a singularity?

A possible way to analyze the presence of spacetime singularities deals with divergent invariants of the curvature tensor. For example, in the Schwarzschild black hole the scalar quantity defined from ...
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Uniform Convergence of the Electric Field Integral - Proving Gauss' Law

I'm working on mathematically proving the Gauss' Law, and I'm having proving the approximations of the electric field integral converge uniformly. The steps are: First I take discrete charges $q_i$ at ...
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Deriving $E=mc^2$ from relativity and the Maxwell equations [duplicate]

I've heard that Einstein derived $E=mc^2$ from applying the relativity principle to the Maxwell equations. Is this true? If so, could someone derive it and show me how this is and why it's true?
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How to deduce existence of photons by applying quantum mechanics to Maxwell's equations

Watching this video lecture of Peter Higgs https://youtu.be/QtudlGHoBQ8?t=372, he says (roughly) at one point that Paul Dirac applied quantum mechanics to Maxwell's field equations and deduced the ...
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Macroscopic Maxwell Lagrangian

We know that the microscopic Maxwell Lagrangian (density) with source $J^\mu$ $$ \mathcal{L} = -\frac{1}{4} F_{\mu\nu}F^{\mu\nu} + A_\mu J^\mu $$ with the antisymmetric field-strength tensor $$ F^{\mu\...
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Apparent inconsistency in wave-optics

$\renewcommand{\vec}[1]{\boldsymbol{#1}}$ $\renewcommand{\hvec}[1]{\hat{\boldsymbol{#1}}}$ In Optics f2f, the author solves for the phase of the a plane wave of frequency $\omega$ propagating along $\...
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Area of reference to find magnetic field inside a (dis)charging capacitor

Faraday's law of induction can be expanded:$$V=-N\frac{d(BA)}{dt}$$ and for a circuit which creates an area between the wires if that area doesn't change then it becomes $$V=-N\frac{dB}{dt}A$$ The ...
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Can we predict harmonic generation from Maxwell's equations?

One typical experimental setup to generate harmonics from a laser pulse is to irradiate some plasma stab with a laser, register both reflected and transmitted waves, and the spectrum of those waves ...
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Faraday's Law of induction with battery emf

Faraday's Law of induction stays that the induced emf is equal to negative rate of change of magnetic field connected with the circuit. Now let us consider a closed circuit made of wire with a ...
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Refractive index and light-matter interaction Hamiltonian

I am wondering if the light-matter Hamiltonian obtains a dependency on the refractive index if we insert our system into a homogeneous medium that can be characterized by a scalar refractive index $n$....
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What does scale invariance or non-invariance of electromagnetism physically imply?

According to Wikipedia, classical electromagnetism is scale-invariant. I understand what it means mathematically as explained in Wikipedia. But what does it really imply physically? Next, here it ...
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On the domain of applicability of Maxwell's equations [duplicate]

We know that different physical laws have their own domains of applicability. For example, Newton's law of Gravitation is valid when the gravitational field is weak and Einstein's theory takes over ...
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Causal relationships in solutions of Maxwell's equations

Both sides of Maxwell's equations are equal to each other, so each of these equations connects quantities simultaneous in time, and as a consequence none of these equations can represent a causal ...
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Boundary condition of magnetic field intensity when one of the mediums is a perfect conductor

i'm studying boundary conditions of maxwell's equations at the interface of two mediums, for the case of the magnetic field intensity $\boldsymbol{H}$ one can obtain using the ampere-maxwell law that \...
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Far field of accelerating charge

What are the differences between the far field of an accelerating charge in a periodic motion compared to that of a uniformly accelerating charge. As the periodic motiom has omega in it. which is ...
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131 views

Do the Lienard Wiechert Potentials satisfy the wave equation?

The Lienard Wiechert potential (leaving out the vector potential for simplicity), $$\left.\phi(\vec{r},t)=\frac{e}{4\pi\epsilon_0R\,(1-\hat{n}\cdot\vec{\beta})} \right|_{t'=t_{\rm ret}},$$ where the ...
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Derive ultraviolet catastrophe from first principles

Relativity is derived from Maxwell's equations, which yield a constant speed of light - a counterintuitive conclusion. Likewise, which equations and their counterintuitive results yield QM? I am not ...
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Four vector for dual field-strength tensor

To generate the electromagnetic field strength tensor, one can use the electromagnetic four-vector using by $F_{\alpha\beta}=\partial_{\alpha}A_{\beta}-\partial_{\beta}A_{\alpha}$. Is there a similar ...
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Calculating drift velocity/number of charge carriers [duplicate]

You know current and voltage of a circuit. how would you calculate number of charge carriers or drift velocity of electron? through experiments/theoretically
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What does the minus sign in Maxwell's third equation imply?

If we write out Maxwell's equations with magnetic charges, we get $$ \begin{align} \nabla \cdot \mathbf{E} &= 4 \pi \rho_e \tag{1}\\ \nabla \cdot \mathbf{B} &= 4 \pi \rho_m \tag{2}\\ -\nabla \...
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Galilean transformation of magnetic and electric field with magnetic monopole

Starting from the lorentz force in presence of a magnetic charge: $$\vec{F} = q_e(\vec E+\vec v\times \vec B)+q_m(\vec B - \vec v\times\vec E)\tag 1$$ by galilean invariance, we should have $\vec F =...
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What is the role of the magnetic moment on wave particle duality

An electron, travelling at high speed relative to an observer, does not radiate unless it undergoes some form of acceleration. Yet we can observe wave like properties under certain measurement ...
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Vector identity and Electric Field Screening in Tinkham's

I'm going through Tinkham's "Introduction to Superconductivity" Second Edition. In Chapter 2, the author states that "we obtain \begin{align} -\nabla \times \nabla \times {\bf E} = \...
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Equations of Motion for Hidden Photon

I was reading a paper called Parametrically enhanced hidden photon search by Peter Graham et al. In the paper, a Lagrangian that describes the theory of the hidden photon is $$\mathcal{L}=-\frac{1}{4}(...
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What is the right version of Faraday's Law of Induction for a moving integration contour?

In Electrodynamics the law of induction for a moving integration contour (not necessarily a conducting wire) is, according to my books, e.g. Jackson, Classical Electrodynamics $\oint_C \vec E' \cdot ...
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Why Faraday's law works with coils?

I always wondering why faraday's law works with coils Faraday's law only works with closed loops An the coil could be open. So the coil here doesn't form a closed loop so that we can apply faraday's ...
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Conversion of Maxwell's Equations to Ohm's Law

I am working on electric currents in Comsol and have the following set of simplified equations: $$ \nabla \cdot \mathbf{J} = Q_{j,v} \\ \mathbf{E} = -\nabla V \\ \mathbf{J} = \sigma \mathbf{E} + \frac{...
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Finding the surface from the electric potential [closed]

I am stuck on a request from this problem: I have the electrostatic potential $$V(x, y, z) = -\alpha \ln\dfrac{x^2+z^2}{R^2}$$ for $x^2+z^2 > R^2$ (otherwise it's zero), where $\alpha, R$ are ...
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Calculate the absorption of light using time averaged pointing vector (from RCWA simulation)

GOAL: I would like to compute the local absorption of light in material from an RCWA simulation. The RCWA tool can output the time-averaged (and input-normalized) Poynting vector. The time-averaged ...
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Lorentz invariance and SR postulate

Probably a ridiculous question - why do we need to express Maxwell's equations in covariant form to show Lorentz invariance? I mean, first SR postulate States that physical laws are same in inertial ...
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The role of the separation constant when solving the wave equation for electromagnetic waves & Cut off wave number

I have the following wave equation that I need help to solve via separation of variables: $$\nabla^2 \mathbf{E} + k^2 \mathbf{E} = 0$$ Where E is the electric field and k is the wave number Using ...

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