Maxwell equations Definition and 144 Threads

Homework Statement Hi, I can't seem to understand the following formula in my professor's lecture notes: F_αβ = g_αγ*g_βδ*F^(γδ) Homework Equations Where g_αβ is the diagonal matrix in 4 dimensions with g_00 = 1 and g_11 = g_22 = g_33 = -1 and F^(γδ) is the electromagnetic tensor with c=1...

According to Faraday's Law, Time-Changing magnetic field creates an induced current in a closed conducting loop. This is the equation: ##\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}## 1-) Does this current (##\nabla \times \mathbf{E} ##) have to be an alternate...

Homework Statement Show whether or not the following functions satisfies Maxwell's Equations in free space. (That is, show whether or not they represent a valid electromagnetic wave). E(x,y,t)=(0,0,E_0 sin(kx-ky+\omega t)) B(x,y,t)=B_0 (sin(kx-ky+\omega t),sin(kx-ky+\omega t),0) Homework...

Hi! My high school physics tells me using right hand grip rule to determine the direction of magnetic field induced by a current carrying wire, but I wonder whether I can deduce the direction merely from Maxwell's Equations? Suppose now we have a current density in cylindrical...

Maxwell's equations reveal an interdependency between electric and magnetic fields, inasmuch as a time varying magnetic field generates a rotating electric field and vice versa. Furthermore, the equations predict that even in the absence of any sources one can have self propagating electric and...

Hello everyone, There is something that has been bugging me for a long time about the meaning of Lorentz Transformations when looked at in the context of tensor analysis. I will try to be as clear as possible while at the same time remaining faithful to the train of thought that brought me...

Homework Statement I am studying for an Optics exam and in one of the practise tests is the following question: "Over what frequency range are Maxwell's equations valid?" Homework Equations Maxwell's Equations The Attempt at a Solution I've searched through my Griffiths Intro to...

Homework Statement Verify that ##\partial_{\mu}F_{\nu\lambda}+\partial_{\nu}F_{\lambda\mu}+\partial_{\lambda}F_{\mu\nu}## is equivalent to ##\partial_{[\mu}F_{\nu\lambda]}=0##, and that they are both equivalent to ##\tilde{\epsilon}^{ijk}\partial_{j}E_{k}+\partial_{0}B^{i}=0## and...

These are Maxwell´s equations in potential formulation: ∇2φ = DIV(grad(φ)) . Am I right? ∇2A = ROT(ROT(A))=ROT(B)=grad(DIV(A))-Laplace(A) . Am I right? In coulomb gauge in every point and at any time DIV(A)=[PLAIN]https://upload.wikimedia.org/math/4/4/1/44131cc26bd9db464d0edb7459ccca84.png...

Homework Statement A harmonic EM-wave is propagating in glass in the +x-direction. The refractive index of the glass ##n = 1.4##. The wave number of the wave ##k = 30 \ rad/m##. The magnetic portion of the wave is parallel to the y-axis and its amplitude ##H_0 = 0.10A/m##. At ##t=0## and ##x =...

I don't know why I was persuaded that in the free space, the electric field of an EM wave is always orthogonal to the direction of propagation. I've recently read my old textbook, and found that this is true only when the wave is far from the emitting source. But if I've understood right the...

In a vacuum, the plane wave solutions to Maxwell's Equations are... E=E0*cos(wt-kr) B=B0*cos(wt-kr) ie they are in phase. (See for example https://www.physics.wisc.edu/undergrads/courses/spring08/208/Lectures/lect20.pdf http://hyperphysics.phy-astr.gsu.edu/hbase/waves/emwv.html ) I don't...

Hello! In this thread, in this answer, my statement "A time-varying electric field creates a magnetic field which is time-varying itself" was refuted. Because I never observed this before, I would like to discuss about it. As far as I know, Maxwell's equations are valid always together, that...

Hi there! It looks like you are trying to prove that the second derivatives of the magnetic potential function ##\mathbf{A}## belong to the class ##C(\mathbb{R}^3)##. This is a great question and involves some advanced mathematical techniques. One approach you can take is to use the dominated...

Hi, friends! I have been able to understand, thanks to Hawkeye18, whom I thank again, that, if ##\mathbf{J}## is measurable according to the usual ##\mathbb{R}^3## Lebesgue measure ##\mu_{\mathbf{l}}## and bounded, a reasonable hypothesis if we consider it the density of current, if...

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 current of intensity ##I_{\text{linked}}##. All the derivations of the Biot-Savart law for a...

Hello! In this document a solution of Maxwell's equations in cylindrical coordinates is provided, in order to determine the electric and magnetic fields inside an optic fiber with a step-index variation. The interface between core and cladding is the cylindrical surface r = a. For example, the...

As we know, the Fermat's principle states: Light takes the path of least time. I wonder whether Fermat's principle can be derived from Maxwell equations. If it can, then Fermat's principle is included in Maxwell equations, or Fermat's principle is not an independent postulate.

In a source-free, isotropic, linear medium, Maxwell's equations can be rewritten as follows: \nabla \cdot \mathbf{E} = 0 \nabla \cdot \mathbf{H} = 0 \nabla \times \mathbf{E} = -j \omega \mu \mathbf{H} \nabla \times \mathbf{E} = j \omega \epsilon \mathbf{E} If we are looking for a wave...

hi, I have just encountered following Maxwell equation in cgs system ▽×H = (1/c)((∂D)/(∂t))+((4π)/c)j, ▽×E = -(1/c)((∂B)/(∂t)), ▽.D = 4πρ, ▽.B = 0, now , c is the speed of light in vacuum , my question is that we have studied earlier equation without this factor 'c' and 4pi in third...

I am having trouble with deducing the origin of Maxwell's Laws, especially Faraday's Law. Obviously some of the laws has to be originated by experiments and the rest should be mere deductions. I would guess that Lorentz force law is the empirical information where we just named some terms as...

Homework Statement I have to expand the following term: $$\dfrac{1}{4} F_{\mu\nu}F^{\mu\nu} = \dfrac{1}{4} \left(\partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu}\right) \left(\partial^{\mu}A^{\nu} - \partial^{\nu}A^{\mu}\right)$$ to get in the end this form...

I have been studying the Maxwell equations recently (namely the integral forms of them). Of course I had to study line integrals before that. Well, I went to a hyperphysics page to look up the equations: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq.html I noticed that the...

If magnetic charge exists, it can flow. Would the flow of magnetic charge produce a current that would be a source for the curl of B, in Ampere's law? Ever yours Bob Eisenberg Chairman emeritus Dept of Molecular Biophysics Rush University Medical Center

Homework Statement This isn't necessarily a problem, but a question I have about a certain step taken in showing that the electric and magnetic fields are transverse. In Jackson, Griffiths, and my professor's written notes, each claims the following. Considering plane wave solutions of the...

The flat-space source-free Maxwell equations can be written in terms of differential forms as $$d F = 0; \ \ d \star F = 0.$$ And in the theory of gauge fields, one can introduce a connection one-from A from which one can formulate general Maxwell equations (for Yang-Mills fields) by $$ dF + A...

Homework Statement I am currently in quantum chemistry, and in class one day my professor spent some time talking about Maxwell's equations. I am looking at my notes, trying to piece together Maxwell's equations, differential equations, and the principle of superposition, since this is not in...

Hello, I have a three dimensional FDTD code. The problem I have for simulation is one dimensional. How can I use this 3D FDTD code for the 1D problem. The 1D problem is like this: in one-dimension half of the problem space is filled with a dielectric medium and the other half is free-space. A...

Hello, I have been attempting to reduce Maxwell's equations to the forms shown in the image, by substituting the plane wave solutions for E and B of the wave equations back into Maxwell's equations, but I cannot find a way. Anybody know how to do this?

Hello Physics forum, I have come here seeking for some experienced help about a doubt that to some extent is not letting me advance on my studies of electromagnetism. Basically is about the magnetic (B) field, and more specifically, about the force at each point of the vector field (The lorentz...

In Einstein's paper section 6 (I'm reading an English version online: https://www.fourmilab.ch/etexts/einstein/specrel/www/), it's said that one of the Maxwell Equations in frame K \frac{1}{c}\frac{\partial X}{\partial t} = \frac{\partial N}{\partial y} - \frac{\partial M}{\partial z}, where <X...

For example, it could be said that the equation ∇*B= 0 is based on the observation that there are no magnetic monopoles. But for Faraday's law of induction, it is easy to derive it from other equations but it's hard to say on what empirical law it is based. Could it be said that it is itself...

Homework Statement Part (a): Show wave equation for E can be reduced to that. Part (b): Show impendance of material is: Part (c): Find skin depth. Homework Equations The Attempt at a Solution I've got parts (a) and (b) solved, part (c) I've worked it out, but I'm not sure...

Homework Statement Derive the 2 divergence equations from the 2 curl equations and the equation of continuity. Homework Equations ∇°D=ρ ∇°B = 0 ∇xE = -∂B/∂t ∇xH = J + ∂D/∂t ∇°J = -∂ρ/∂t (equation of continuity) The Attempt at a Solution 1)∇xE = -∂B/∂t ∇°(∇xE) = ∇°(-∂B/∂t)...

hello, Help me to answer these questions: Give the physical meaning of Maxwell equations (equations in the general case). div D=ρ div B=0 rotE=-∂B/∂t rotH=∂D/∂t+J i have second question: What is the difference between conduction current and displacement current? thankyou

Guys, Let me ask you the silliest question of the year. I am looking at the Maxwell equations in their standard form. No 4-dim potential A, no Faraday tensor F, no mentioning of special relativity - just the standard form from a college-level textbook. I know that the eqns are NOT...

[This is mostly about notation] I was working on a problem where I had to prove that div(B) remains invariant under lorentz transformations. That was not too hard, so I came up with div(B) = \partial_{\mu} B^{\mu} must equal div(B) = \partial'_{\mu} B'^{\mu} so I did a...

I'm starting my study in eletromagnetism and I would like to know how do you deduce the eletric field produced by a single particle of charge q placed in the origin. The magnetic field is constant so by Maxwell equations, the rotacional is 0 and the divergence is constant. Is this enough to...

Homework Statement The field E(r,t) can be written as a Fourier expansion of plane waves E(r,t)=∫E(k,w)e^{i(kr-wt)}d^{3}kdw with similar expansions for other fields. Need to show the derivation of kXE(k,w)=wB(k,w) from Faraday's law ∇XE(r,t)=-∂B(r,t)/∂t and also the derivation of...

Dear fellow physicists, looking at the derivation for the maxwell equations into k-space, I've stumbled upon something that seems not so logical to me. It is concerning the two parts where they transform \nabla \times E and \nabla \bullet E on page 27 (on the sheets 14)...

So I keep hearing that the maxwell equations are variant under Galilean transform. Tired of simply accepting it without seeing the maths, I decided to do the transformation on my own. To make things easy, I only tried Gauss' law, furthermore I constricted the field to the x-axis only. So I have...

Dear all, I'm studying a paper on coupled magneto-mechanical problems. Suppose we have a "deformable" ferromagnetic bar placed in an initially uniform magnetic field. Both ends of the bar are clamped. The bar has magnetostriction property, so it may expand or contract depending on the the...

Hello, I'm trying to make a sort of "system theory approach" to dynamic Maxwell's equations for a linear, isotropic, time-invariant, spacely homogeneous medium. The frequency-domain uniqueness theorem states that the solution to an interior electromagnetic problem is unique for a lossy...

2A\mu=-\muoJ\mu Griffith's Introduction to Electrodynamics refers to this 4-vector equation as "the most elegant (and the simplest) formulation of Maxwell's equations." But does this encapsulate the homogeneous Maxwell Equations? I see how the temporal components lead to Gauss' Law, and I'm...

In the Lorenz gauge, the Maxwell equations reduce to four inhomogenous wave equations, with the charge density acting as the source for V, and the current density for A. For now, just take a static charge distribution -- say, a point charge at the origin. It is well known that a static...

How does todays "modern" form of Maxwells equations differ from the original equations Maxwell developed and why? If this should be in the physics section...please move it...

I have a question here about Maxwell's equations: according to faraday's law at some point in space changing magnetic field with time creates the curl of electric field at that point and according to Ampere's law with Maxwell's correction changing with time electric field or electric current...

The differiantial form of faraday's law tells that at a any point in space changing with time magnetic field creates the rotor of electric field (let's say circular electric field at that point), but in the centre of the circular field there is no E vector, it's zero, there only is it's rotor...

yo ok progress on the electromagnetic wave front is progressing nicely...finally, but i have stumbled on a area that i need some help with. see below when maxwell took amperes law, he added what's known locally ! as the current term, this was done because he realized that a changing...

yo ! quick question on jc maxwell, got an exam comming up and was wondering see attached these are the equations for free space (vacuum) and i was wondering if these will still hold for simple media such as plain old atmosphere (the breathable kind). following this can simple medium be...