Maxwell's equations Definition and 237 Threads

In Feyman's lectures on physics, he said Maxwell's first 2 equations in electrostatics, namely curl E =0 and div E=rho/epsilon, is equivalent to Coulomb's law and superposition principle, But for a particular charge distribution, we can always use Coulomb's law and superposition principle to...

Homework Statement Help to fully appreciate Maxwell's Equations Homework Equations Maxwell's Equations (Differential Form): \nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0} \nabla \cdot \vec{B} = 0 \nabla \times \vec{E} = \frac{\partial \vec{B}}{\partial t} \nabla \times...

Hello, I was tempted to put this in the math section but it is more of a visualization problem though it is most likley due to my lack of understanding the divergence and curl operators fully. I am comfortable with the closed loop integral of E dot dA and can visualize it as a solid closed...

Let respectively b = (b1, b2, b3) and e = (e1, e2, e3) denote the magnetic and electric field in some medium. They are governed by Maxwell’s equations which look as follows: (0.1) \partialte = curl b (0.2) \partialtb = − curl e (0.3) div e = 0 (0.4) div b = 0. Show that each bi and each ei...

Homework Statement What conditions need to be imposed on \vec{E}0, \vec{B}0, \vec{k} and ω to ensure the following equations solve Maxwell's equations in a region with permittivity ε and permeability µ, where the charge density and the current density vanish: \vec{E} = Re{ \vec{E}0...

Maxwell's Equations say about the velocity of electromagnetic wave..Does Maxwell's equations also say about path of the electromagnetic wave i.e. light? I want to know how to find the path of light from Maxwell's equations? Or it says only about velocity? One more question, what is the path...

Basic electrostatics (as I've seen it presented) usually starts off with an implicit \mathbf{F} = q q_2 \hat{\mathbf{r}}/r^2 = q \mathbf{E} definition of the electric field. Then with a limiting volume argument, you can then show that this can be expressed div \mathbf{E} = \rho. Eventually one...

Easy question for those who know, I expect. It would help me understand though. Generally, wherever I look for information the equation curl E = - dB/dt is given, but in some areas I see the equation curl E(r,t) = j*omega*u0*H(r,t) where j is the imaginary unit, omega is angular...

One author states that "the usual Maxwell field is the quantum wave function for a single photon" - see http://arxiv.org/ftp/quant-ph/papers/0604/0604169.pdf Is it correct that a single photon can be described using Maxwell's equations - or do the Maxwell equations only describe the behaviour...

I've seen two references to magnetic charge density as something that Dirac said would explain charge quantization. The first is in Schwartz's "Principles of Electrodyanamics" (Dover) where the author comments how it is unaesthetic that the two maxwell's equations aren't symmetric in form...

Let's say you're in a very fast car that can accelerate from zero to, eventually, 0.7c. I understand that as the car moves faster and faster, the driver will observe the light that hits him in the face to be of higher and higher frequency. This seems consistent with things becoming narrower in...

Homework Statement It is often said that Maxwell's equations in differential form hold in special relativity while Maxwell's equations in integral form don't hold. Consider one of equations: \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t} \oint_{\partial S} \mathbf{E}...

Are Maxwell's equations thought to be exact? I realize this question is very open-ended and loosely-phrased.

Maxwell's equations give that the electric and magnetic fields in E-M radiation are orthogonal. This is a classic equation, but can it be related to the orthogonality of, for example, the momentum and position operators which lead to non-commutivity?

[SOLVED] invariance of maxwell's equations under Gauge transformation Homework Statement Show that the source-free Maxwell equations \partial_{\mu} F^{\mu\nu}=0 are left invariant under the local gauge transformation A_{\mu}(x^{\nu})\rightarrow...

Homework Statement http://en.wikipedia.org/wiki/Maxwell_relations I am confused about the subscripts next to the partial derivatives. \left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial p}{\partial S}\right)_V\qquad= \frac{\partial^2 U }{\partial S \partial V} What does the...

Can Maxwell's equations (the usual 4 equations) be summarized in the form of one equation?

I am having trouble going about proving the Lorentz invariance and non-Galilean invariance of Maxwell's equations. Can someone help me find a simple way to do it? I've looked online and in textbooks, but they hardly give any explicit examples.

I'm not sure if this should go here, or in electrodynamics, or in relativity, but never mind. I'm given to understand that Maxwell's equations are completely compatible with the theory of relativity, and apply over all distance scales. I've also heard of Kaluza-Klein theories in which adding a...

I've put quick intros to these subjects on my web site, and I'd like to invite readers to comment. The goal of the tutorials is to give as quick an introduction as possible with the miminum of unnecessary technicalities, and yet to get to the essence of the matter . No doubt improvment is...

Hi, I'm just someone trying to learn a bit more about quantum. I was wondering what the relationship between maxwell's equations and quantum electrodynamics is? Are they compatible? Are maxwell's equations for solving macroscopic problems only? How do you determine the E field...

I have a question regarding two electric lines running parallel to each other with their current running in opposite direction. Under this set up the electric field points up vertically on the page and the magnetic field points out from the page. I am to show that Maxwell's equations reduce to...

Is it possible to derive Faraday's Law from the other three Maxwell equations plus the conservation of charge? If so, how? Any help would be greatly appreciated. Thank You in Advance.

The skepticism thread reminded me of a question I had for the professionals here. A lot of Electrodynamics (especially the idea of displacement current) was developed by Maxwell with the idea of Ether in mind. I'm not trying to argue that the ether-as-we-know-it actually exists, but the...

Is the fact that there could be no E-field inside a conductor purely experimental? I don't see any way to apply Maxwell's equations to prove this fact.

maxwells third equations states that the curl(electric field)=-rate of change of magnetic field intensity... does it have any other physical significance other than being derived from faradays laws of electromagnetic induction... does curl(electric field) indicate the curling or rotational...

Folks, I believe the direction of the circulation in the curl equations must always be considered counterclockwise (positive), because of Stokes' theorem and the right-hand rule. Right? (I'm asking because my books do not have a direction specified in the circulation integral) Thanks.

Maxwell's Equations: \nabla \cdot D= \rho \nabla \cdot B=0 \nabla \times E=- \partial B/ \partial t \nabla \times H=J+ \partial D/ \partial t Together with the continuity eq: \nabla \cdot J=- \partial \rho / \partial t There are 9 scalar equations and 16 scalar unknowns (B, E, D, H, J...

Here are some thoughts; if you have a different opinion, I'd be glad to hear it. In the real world, on a small enough scale, linear charge distribution and surface charge distributions do not exist. It all comes down to \rho. Same for the currents; there are only current densities \vec{J}. So...

Right or wrong? Specifically, an equation is said to be Galilean invariant if a substitution x \rightarrow x \pm v_x t y \rightarrow y \pm v_y t z \rightarrow z \pm v_z t t \rightarrow t doesn't change the equation. If right, would simply showing that x \rightarrow x \pm vt y...

Are Maxwell's equations deterministic in the sense that e.g. if given free space with H and E defined for any point at time t0, then Maxwell's equations are sufficient to determine H and E for any t>t0?

I'm trying to understand the physical meaning of Maxwell's Equation, but I'm confused about what generates what. According to Gauss's Law, electric charge placed somewhere generates electric flux, whereas Gauss's Law for Magnetism says that charge itself doesn't generate magnetic field...

hey i need help explaining this... I am really lost... What is the further condition on the charges and the currents, which is necessary for the Maxwell Equations? Explain how it relates to the existence of the displacement current.

I want to make sure that I understand this good. Given E and B are possible in a region of free space (J=0) only if \triangledown \times E=0 and \triangledown \cdot B = 0

I've never understood how the aether was dispensed with. It is said that Maxwell's equations don't require it. If that is the case, then where do the x, y and z axes come from if not from an aether.

Having some problems with my Electromag Unit again. Heres the questions I'm having problems with, any help would be appreciated 1 For plane electromagnetic waves in a homogeneous, linear, uncharged non conductor Formulate the Maxwell equations for the electromagnetic fields E and B...

the final equation ∇XB(x) = μ0j(x) But this means that the curl of the magnetic field at any point is proportional to the current density at that point. But take the case of a long straight wire carrying current. The magnetic field surrounding the wire is circular and...