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 I derive the potential from a homogeneous time dependent electric field?

As the title says how can I derive the potential $V(t)$ from the following electric field given as $$ E(t) = \frac{A}{\sqrt{\pi}\tau}e^{-(\frac{t}{\tau})^2} $$ Where $A$ and $\tau$ are constants.
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Free and bound current- and charge density in Maxwell equations

The first and fourth Maxwell equations are often denotet in vaccum: $$ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} $$ $$ \nabla \times \mathbf{B} = \mu_0\left( \mathbf{j}+\epsilon_0 \frac{\...
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383 views

Is it possible to derive Maxwells equations from geometrical optics?

Geometrical/Hamiltonian optics can be derived as short wavelength limit of Maxwells equation. In doing so one approximates the relativistic wave theory of light with a non-relativistic single particle ...
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Similar to Dirac Equation, could Maxwell Equations be derived by (first) quantization of energy-momentum relation (for describing a single photon)?

First I ask this because of similar (mathematical) structures of these relativistic wave equations. In addition, by quantization definitely I don't mean a canonical (or second) quantization. ...
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Do Maxwell's equations predict light instantaneously reaches a point one light-year away from the source? [duplicate]

Maxwell's equations don't seem to have any delay between changes in electric field and changes in the magnetic field. So, do Maxwell's equations predict light instantaneously reaches a point one ...
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Intuition differential ampere's law

Ampere's differential law states that - $$\nabla \times {\bf B} = \frac{4 \pi \, {\bf J}}{c}$$ I know to derive amperes integral form from special relativity, and to use stokes theorem in order to ...
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Derivatives involving four vectors [closed]

The Schrödinger lagrangian for complex fields is $$L=\frac{1}{2m}(D_i \psi)^* Di \psi - \frac{i}{2} \left[\psi ^* D_0 \psi - (D_o \psi)^* \right] - \frac{1}{4}F^{\mu \nu}F_{\mu \nu}$$ Where $D_\...
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Does the magnetic flux spin in the same direction when the electric field is growing and collapsing?

I have three concentric iron pipes, stacked inside each other. It looks like a bulls-eye when viewed from above. To the innermost and outermost pipes I have connected a battery through a switch. ...
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109 views

Does Gauss flux theorem hold in relativity?

Does the Gauss flux theorem, stated in the classical electrostatics as $\iint{\vec{E}}\cdot{\vec{dS}}=q/\epsilon_0,$ hold in the case of relative motions. For instance if we observe a charged body ...
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About curious form of Maxwell's Equations for a monochromatic field [closed]

In a review paper of Whispering-gallery waves from A.N. Oraevsky, he writes the source-free monochromatic Maxwell's Equations as $\nabla\times E = ikH$ $\nabla\times H = -ikE$ and he defines $k = (\...
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Relation between displacement current, dielectric and time varying Electric field

I know that displacement current is produced in dielectric material due to dipole moment. I also know that displacement current is produced by time varying electric field (according to maxwell ...
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derivation of the electic displacement D

I've been revising Maxwell equations recently and tried to prove that the electric displacement $ \mathrm{\nabla \cdot D = 0}$ in the electrostatic approximation ($\mathrm{E = - \nabla} f$). My steps ...
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In magnetostatics, is there any relation between flux and current?

I have noted while trying to find analogy between electrostatics and magnetostatics, for the equation, flux = charge/epsilon, is there any corresponding equation in magnetostatics, relating magnetic ...
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Two equal charges accelerating parallel to each other

Let's say constant acceleration for simplicity. Ignore possible logistic concerns, such as what is accelerating them or how they stay in path. Lets just assume they are in a conduit made of a solid ...
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Books on Faraday, Maxwell

Can you recommend a/some good book(s) on Faraday for the lay person? In particular, in relation to his 'Experimental Researches in Electricity'. Also, any books explaining how Maxwell explained ...
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Bobbin with $I=I_{0}\sin(\Omega t)$

If I have an infinite bobbin with $I=I_{0}\sin(\Omega t), \mu$ and $n=N/L$ using Ampère and supposing that $d\vec{D}/dt=\vec{0}$ I have found that $$\vec{B}=n\mu I_{0}\sin(\Omega t)\vec{e_{z}}$$ But ...
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Why wouldn't any Emission Theory work?

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/origins_pathway/#Emission Here, at the Emission theories of light, I loved the discussed theory. There seems to be a contradiction right ...
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Isn't there a loop in maxwell's equations? [duplicate]

I am curious about the following case: Consider the electrical field in a particular point just changed for some reason. Then by the maxwell's equations, there will be magnetic field generated ...
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Does displacement current occur in an inductor?

We have learned in school that displacement current comes about due to a change in electric field flux per time in a capacitor (Ampere-Maxwell Law). Does the same displacement current come about in an ...
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Interpretation of the displacement current

From Maxwell's equations, why is the displacement current viewed as a source for a magnetic field? If the displacement current were moved to the other side of the equation it would like like a current ...
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Why does charge build up at the boundary surface of two media?

On a homework problem, we are asked to to use the first two Maxwell equations, $$\nabla\cdot \mathbf{B} = 0$$ $$\nabla \cdot \mathbf{D} = \rho$$ to show that along the boundary surface of two ...
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Obtain the same Maxwell's equation after a change of coordinates

In the usual $(x,y,z)$ system of coordinates, if we expand the Maxwell's curls equations for phasors $$\nabla \times \mathbf{E} = - \mathbf{J}_m - j \omega \mu \mathbf{H}$$ $$\nabla \times \mathbf{H} ...
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E and B field from Time Varying Current

How would I go about calculating the B field and E field from a time varying current charging a capacitor. Theoretically I feel like a solution should exist, but there seems to be a dependence between ...
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Deduce magnetic field based on electric field

I'm learning Maxwell's electromagnetic equations and i can't wrap my head around this problem: Given the volume $x\in [0,1], y\in [0,1], z\in [0,1]$, electric field $\vec E(x,y,z,t)$ and material ...
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How to do this index notation differentiation?

I am studying classical Maxwell fields and I am stuck on this differentiating part. How can I derive the result given below ? $$\dfrac{\partial}{\partial(\partial A_{\mu}/\partial x_{\nu})} \left(2\...
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Are Lorentz force and maxwell's equations independent? [duplicate]

The Lorentz force and Maxwell's Equations gives answers to many physics problems, and the answers given by both methods are consistent. For example, consider the problem of a conducting rod of ...
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669 views

Solving the source free Maxwell equations for plane waves

I've been trying to solve the maxwell equations: $$\nabla\cdot\vec{D}=0,\quad \nabla\cdot\vec{B}=0$$ $$\nabla\times\vec{E}=-\frac{\partial \vec{B}}{\partial t},\quad \nabla\times\vec{H}=\frac{\partial ...
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An Electromagnetic Paradox?

The above diagram represents an isolated system with two masses $M$, at position $X$, and $m$, at position $x$, connected together by an extended spring. Each mass is connected by rigid rods to ...
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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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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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The wave function of the photon and electron are probability waves, does this mean the Maxwell are some time correct some time wrong? [closed]

The wave is probability wave, it is seams that the wave function some time is correct, the energy is sent out. Some time it is wrong the energy is not sent out. Hence we can obtained the conclusion ...
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The use of Helmholtz decomposition

Examining the article on Wikipedia Helmholtz decomposition, compatible with the explanations of the book Introduction to Electrodynamics $4^{\mathrm{th}}$ edition David J. Griffiths §1.6 the theory of ...
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Is Quantization implied in Maxwell's theory? [closed]

So as per Maxwell an electric charge oscillating at a certain frequency emits and absorbs radiations only of that frequency. So is quantization somehow implied here.? And I think Max Plank used the ...
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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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Solving Third Maxwell Equation [closed]

Suppose I want to solve the third Maxwell equation: $$\nabla\cdot\mathbf{B} = 0$$ The first assumption is that we could write the magnetic field as: $$\mathbf{B} \equiv B(x,y,z) \equiv b(x)\beta(y)Z(z)...
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What is the visualization of light according to Maxwell's theory of Electromagnetic wave? [closed]

The theory must imply a visualization. I am not being able to think or find any. I know the sine wave representation. But light obviously not goes like a physical string. right?
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Interpreting $\hat{e}_z$ in Maxwell's equations

I'm trying to interpret a form of Maxwell's equations, but I can't seem to figure out where the term $\hat{e}_z$ comes from in the following equation: $ \frac{\partial{\vec{E}_t}}{\partial{z}}+i\frac{\...
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Is there any property of a neutrino that prevents it from being considered the missing monopole that will make Maxwell's equations symetric

The zero in Gauss's magnetic law, is it an approximation? Could it be in reality be a really tiny number like the magnetic field strength of a neutrino? Neutrinos are members of the Lepton family ...
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Maxwell's Equation [duplicate]

I was reading a book and I found the following equation. I'm not good at physics and I couldn't understand where does it come from, can anyone explain me why is it valid? $$ \mathbf E = -\nabla\phi - \...
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How far will a 1Hz EM Wave propagate if it's source oscillator is running for exactly one second? [closed]

If you have an Oscillator set on 1Hz and you let it run for exactly one second connected to an Antenna , how far will the generated EM Wave travel ?
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Application of Displacement Current

I'm reasonably happy with the derivation and results of displacement current, however, I'd like to be aware of a few practical applications of this idea. So far, the only one I'm aware of is when ...
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Preference of right oriented Cartesian coordinates for the EM radiation in Maxwells equation [closed]

After fixing the conventions on north and south and plus and minus for the directions of magnetic and electric fields, the Maxwell equations describe the directions of the electric and magnetic ...
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Does the state of curl of the $E$-Field at a point adjust itself instantaneously as soon as $B$ begins changing at a fixed rate, or is there delay? [duplicate]

Faraday’s Law () states that a time-changing magnetic field vector induces a curl of the Electric field around that point. However it does not specify how quickly the necessary spatial gradient is ...
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How quickly is the desired state of curl of the Electric Field around a point achieved where a Magnetic Field Vector has just begun changing?

My question and context with explanation are given below. Thank you in advance. Faraday’s Law () states that a time-changing magnetic field vector induces a curl of the Electric field around that ...
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187 views

Is electric field independent of electric charge?

We have Poisson's equation , ${ \nabla }^{ 2 }\varphi =\frac { \rho }{ { \varepsilon }_{ 0 } } $ Which reduces to Laplace's Equation, ${ \nabla }^{ 2 }\varphi =0$ And we see that there are ...
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350 views

How does the Lorentz force work for all velocities

At small velocities, the lorentz force in the boosted frame is approximately $F' = q(E + 2v \times B)$, where the one for the rest frame is $F = q(E + v \times B)$. How is this invariant if the two ...
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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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About the closed line integral of electric field intensity

In electrostatics, we know that the closed line integral of electric field is zero : \begin{equation} \oint\limits_{C} \mathbf{E}\left(\mathbf{x}\right) \boldsymbol{\cdot} \mathrm{d}\mathbf{x}=\;\;...
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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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Feynman Lectures Vol II-18 A travelling field: I'm not getting Feynman's result

I may just need to sleep on this, but I am not able to make sense of section 4 of The Feynman Lectures Vol II 18 The Maxwell Equations. After explaining the origin and meaning of the displacement ...