Maxwell's equation Definition and 25 Threads

Starting from the microscopic form of Maxwell's equations and following standard mathematical procedure outlined in Inhomogeneous electromagnetic wave equation - Wikipedia we can have as end result the following equations: $$(\nabla^2-\frac{1}{c^2}\frac{\partial^2}{\partial...

While going through an article titled "Reflections in Maxwell's treatise" a misunderstanding popped out at page 227 and 228. Consider the following equations ##(23\ a)## and ##(23\ c)## in the article (avoiding the surface integral): ##\displaystyle \psi_m (\mathbf{r})=-\dfrac{1}{4 \pi} \int_V...

In a certain region for which σ=0, μ=2μ0, and ε=10ε0, J= 60sin(109t - βz). Determine D, H, and β.

I recently saw that in the solution of a problem the following assumption was made - "there are no free charges in the problem, therefore the D field must be equal to 0 ". however if we use that logic to calculate the field of a polaraized sphere we get a wrong result (E=-P/e0 instead of E =...

The first page of this short pdf from MIT sums the starting point to formulate my question: https://ocw.mit.edu/courses/physics/8-022-physics-ii-electricity-and-magnetism-fall-2006/lecture-notes/lecture29.pdf We can see that ∇xH = Jfree and ∇xB =μo (Jfree +∇xM) ∇xB =μo (Jfree +JB) And now my...

Hello all, I have a question regarding Maxwell's Equations and Faraday's unipolar induction equation. If we study the case of a cylindrical magnet with a radius of r which is rotating about its axis with angular velocity w. The electrons within the magnet collide with the moving atoms, causing...

Hi. Here, somebody apparently derives Maxwell's equations using only symmetry of second derivatives and the Lorenz gauge condition. Unfortunately it's in German, but I think the basic ideas are clear from the maths only. In this derivation, the magnetic field turns out to be divergence-free...

Homework Statement How to I explain that maxwell's equation has well defined divergence Homework Equations All four EM Maxwell's equation The Attempt at a Solution I discussed it by showing one of the property of Maxwell's equation that is the Divergence of a Gradient is always zero (With...

Hi guys!Im doing a Project about maxwell equations and need help with something. Let's say you have a current going through a copper wire with an insolation on, and ofcourse there is a magnetic field. I've wondering if the magnetic field have a temperatur impact on the cabelinsolation. I want...

So I believe I understand Maxwell's equation in vacuum pretty well and I feel like I understand them in different medium when I read in a textbook, but when I have to apply it to exercises I get thrown off quite a bit. For example, I cam across a PhD qualifying exam that had split Euclidean...

I found this http://people.sissa.it/~benassi/capitolo1/node2.html in the vacuum the equations would be q B = q E = 0 ##q \times E = (\omega / c) B## ##q \times B = -(\omega / c) E## Is there a typo? there is no t derivative. If E = 0 B would have to be null. Has B to be allways orthogonal to E...

Homework Statement Homework Equations http://esclab.tw/wiki/images/math/0/a/2/0a24f9d68ba8fd1a1a8e6c6b36a00be3.png The Attempt at a Solution [/B] Hello As you see the answers of 19 and 20 problems we should try to find K or B(wave number) in wave equation.both of equations are in air...

http://arxiv.org/pdf/physics/0511103.pdf I was wondering what people thought of this paper. Please read up to at least page 3 before responding. I find it to be pretty convincing up to page 4. Thanks for any response.

Problem: I'm trying to crudely prove the following: \frac{{\partial}B}{{\partial}x}=-\mu_{o}\epsilon_{o}\frac{{\partial}E}{{\partial}t} Solution (so far): I can get the derivation, but the minus sign eludes me somehow... Integrating over a thing rectangular loop of length l and width dx...

Homework Statement This is not actually a homework but a personal work. Here it is: Using the differential forms: F=\tfrac{1}{2!}{{F}_{\mu \nu }}d{{x}^{\mu }}\wedge d{{x}^{\nu }} and J=\tfrac{1}{3!}{{J}^{\mu }}{{\varepsilon }_{\mu \alpha \beta \gamma }}d{{x}^{\alpha }}\wedge d{{x}^{\beta...

One of Maxwell's equations says that \nabla\cdot\vec{B}{=0} where B is any magnetic field. Then using the divergence theore, we find \int\int_S \vec{B}\cdot\hat{n}dS=\int\int\int_V \nabla\cdot\vec{B}dV=0 . Because B has zero divergence, there must exist a vector function, say A...

I've got a couple of question about Maxwell's Equation and its relation to Special Relativity. 1. Why do we think that free space has permittivity and permeability? For me, due to quantum effects free space should have permittivity and permeability, but how did Maxwell accept that the free...

Homework Statement A sinusoidally-varying voltage V(t) = Vosinωt with amplitude Vo = 10 V and frequency of f = ω/(2π) = 100 Hz is impressed across the plates of a circular-shaped parallel plate air-gap capacitor of radius a = 1.0 cm and plate separation d= 0.01 mm. The amplitude of Maxwell's...

I've seen one derivation on Feynman Lectures on Physics, but the derivation is not really rigorous(he took a very special case for the derivation),I googled about the topic and couldn't find a satisfactory one. So can anybody give me a rigorous one? Thanks in advance

I am trying to find the magnetic field around a moving point particle. I have already found the curl. The only step remaining is to use Helmholtz's theorem. I am using http://farside.ph.utexas.edu/teaching/em/lectures/node37.html" . I am going to use equation 300, but I am not sure what to...

Maxwell's Equation HELP! This is one of the Maxwell's Equations that I can't understand: \oint E.dl = -\int dB/dt .dS From what I understand, \intE.dl gives the potential difference along the line. Therefore \ointE.dl should always equal to zero because it is the potential difference of a...

Hi, I'm new here. I have a question. How do you verify that: E = E(max)cos(kx-wt) is a solution to Maxwell's derived equation: ((d^2)E/dx^2) = e(epsilon nought)u(permitivity of free space) x (d^2)E/dx^2. Thanks. What I first did was to substitute k = 2pi/lambda, w = 2pi(f). Then I set 2pi(f)...

hi everyone can anyone explain to me or show me some site that explain Maxwell's equation in simple language... i have been reading most of my teacher's books but i still don't get it. (my teacher doesn't want to teach me... sigh) and where can i find a good introduction of E&M? thx a lot!

Hi everyone, I now have difficulties in using formula for gradient of tensor. The following is tensor for field strength Fsubscripts_alpha_beta = [ 0 -Ex -Ey -Ez Ex 0 Bz -By Ey -Bz 0 Bx Ez By -Bx 0 ] My question is, how do we derive the Maxwell equations...

How exactly did Maxwell prove speed of light is \frac{1}{\sqrt{\mu\epsilon}}