Maxwell's equations Definition and 237 Threads

Hello all... I have been working on this problem that I just am not being able to solve. I've been spending my spare time learning some vector calculus and non-euclidean geometry (my aim is to be able to finally tackle relativity). After learning some basic things about the del function, I...

Homework Statement Write Maxwell's equations for electromagnetism in differential form: in matter, for a linear material, using the vectors D and H The Attempt at a Solution div D= ro (Gauss' law) div H*mu*mu0=0 gauss' law in magnetism curl (D/(epsilon*epsilon0))=-dB/dt(partial...

Why is eqn 34.16 B(x,t)•l - B(x+dx,t)•l instead of B(x+dx,t)•l - B(x,t)•l ? Thanks!

The first thing you learn about the Dirac equation is that it provides a relativistically-correct quantum-mechanical description of spin-1/2 charged particles, e.g. the electron. Then, it seems that it's at least implied that the Dirac equation completely describes the interaction between...

what is the connection between maxwell's equations and relativity?

Which form do you prefer, the integral form or differential form? EDIT: Forgot to say I prefer the integral form.

Homework Statement Derive equation (1) from equation (2): (1) \nabla \cdot D = \rho_f (2) \nabla \times H = J + \frac{\partial D}{\partial t}Homework Equations [PLAIN]http://img198.imageshack.us/img198/4645/maxwell.png The Attempt at a Solution \nabla \times H = J + \frac{\partial...

According to Dyson, Feynman in 1948 related to him a derivation, which, from 1) Newton's: m\ddot{x}_i=F_i(x,\dot{x},t) 2) the commutator relations: [x_i,x_j]=0m[x_i,\dot{x}_j]=i\hbar\delta_{ij} deduces: 1) the 'Lorentz force': F_i(x,\dot{x},t)=E_i(x,t)+\epsilon_{ijk}\dot{x}_j B_k(x,t) 2)...

I know I may be in the wrong place, but I think I'll get a quicker and better response here. My question is: How do \nabla \cdot \textbf{B} = 0 and \nabla \times \textbf{E} + \frac{\partial \textbf{B}}{\partial t} = 0 derive from \Box^2 A^\mu -\partial^\mu(\partial_\nu A^\nu) = j^\mu?

Hello! I am very interested in learning Maxwells equations, and learn it good. I need a recommendations for books where electrodynamics is presented from scratch and Maxwell's equations are used to explain most examples. I need examples like direct current, alternating current, and...

Homework Statement Parallel plate capacitor with circular plates with radius of 26mm and a plate separation of 6mm. A sinusiodal potential difference is applied across the capacitors plates with Vmax = 170V at a frequency of 60Hz. 170sin(2*pi*60Hz*t) Homework Equations V = ∫E∙dl = El (l...

According to the Wikipedia article on Gravitomagnetism: http://en.wikipedia.org/wiki/Gravitomagnetism There is a gravitational analog of maxwell's field equations that is valid for weak gravitational fields. Basically all you have to do is replace eps_0 in maxwell's equations with -1/4...

Hello, First of all, I have no objections against Faraday's Law in differential form, i.e. \vec \nabla \times \vec E = - \frac{\partial \vec B}{\partial t}. But in integral form, I usually encounter it in the form \oint \vec E \cdot \mathrm d \vec l = - \frac{\partial \Phi_B}{\partial...

If I understood well my professor, he showed that "playing" mathematically with Maxwell's equation \frac{\partial \vec E}{\partial t} = c \vec \nabla \times \vec B can lead to the result that \frac{\partial \vec E}{\partial t} satisfies the wave equation (only in vacuum). So what does this...

Every textbook I read seems to follow the same logic/derivation of physics: -Gauss' Law is observed experimentally, shows us there's this thing E -Biot-Savart's Law is observed experimentally, shows us there's this thing B -Ampere's Law (after fixed by Maxwell) observed experimentally, along...

Hey there is something that I don't really understand In Landau Lifgarbagez"Classical Theory of Fields" it is said that one of the Maxwell's equations in the presence of a gravitational field is: div E= \frac{\rho}{\epsilon_0}\sqrt{g_{00}} So I thought that if you have a hydrogen...

In deriving the plane wave solutions of Maxwell's equations in vacuum, one assumes from the very start that the E and B field oscillate with the same frequency omega (cf. Jackson). This is a starting point for all further properties of plane waves. Can one start from two different frequencies...

Homework Statement A region in space without any charges or current has a timevariable magnetic field given by \vec{B}(t) = B_0 e^{-at} \vec{e_x} where a and B_0 are constant. a) Use Farraday's law to show that there has to exist an electric field in this region. Find this field. b)...

I'm wondering where to start for the proof of Snell's Law using Maxwell's equations. Any help in the proper direction would help!

Homework Statement This question is closely related to physics but it's in a maths assignment paper i have so here it is: By taking curls of the following equations: \nabla \times \bf{E} = -\frac{1}{c}\frac{\partial\bf{B}}{\partial t} \nabla \times \bf{B} =...

Homework Statement Suppose Maxwell's displacement current was left out of the Maxwell equations. Show that , in a vacuum, the magnetic field has to have the form B = grad f(r,t), where f is any function which satisfies the Laplace equation. Homework Equations curl E = - dB/dt curl B = 0...

Let us consider Maxwell's equations in a homogeneous isotropic medium. We may look for a set of transformations for which the form of the equations remain unchanged[in accordance with the first postulate of Relativity].Of course we get the same Lorentz transformations but with a different value...

I did more than one course of classical electromagnetism in college. Recently, however, after reading "How Relativity Connects Electric and Magnetic Fields" (http://galileo.phys.virginia.edu/classes/252/rel_el_mag.html) I was astounded to realize how little I knew about it! In college (if I...

Homework Statement The problem statement is in the attached .png file. There are a few equations involved which would have taken a decent amount of time to type out. Homework Equations The Attempt at a Solution I understand Maxwell's equations, and wrote out all 4 assuming there are no...

Maxwell's equations in curved spacetime can be written as \nabla^a F_{ab} = -4\pi j_b, \nabla_{[a} F_{bc] = 0 or as d*F = 4\pi*j, dF = 0, where F is a two-form, j is a one-form and * is the Hodge star. How do you show that these two sets of equations are equivalent (basically, that the first...

In the realm of General Relativity one must use Maxwell's Equations in their covariant form[the ordinary derivatives in the traditional form should be replaced by the covariant derivatives]. Now we select a point, A ,on the 4D spacetime surface and setup a "local inertial frame" on it by some...

Hi I would like to know what your thoughts are on books that make an attempt to discuss quantum electromagnetism without using any of Maxwell's equations. I came across a text written by an author who decided not to use Maxwell's equations because Maxwell and others "didn't have access" to...

What conditions are necessary to use the constitutive relations for Maxwell's equations? I am working in a nonlinear media, but am a little confused about whether I can assume isotropy or not. If I am assuming the media is nonlinear is it necessarily anisotropic? Or, is it possible to have...

The no. of unknowns in the Maxwell's Equations is 6- the components of E and B. But there are 8 partial differential equations if we separate them out component- wise. So when we find the solution to them how do we ensure their mutual consistency?

"Maxwell's equations explain all electromagnetic phenomena." ...What does this mean exactly? How do these equations represent the unification of electricity and magnetism? What's really an unification? And how can you see it from the equations? Aren't his equations only applicable to EM waves?

Q1) The amplitude of an electromagnetic wave is E0 = 471.0 V/m. Find the following values. (a) Erms 333.047 V/m (b) Brms __ nT (c) the intensity I __W/m2 (d) the radiation pressure Pr __nPa Q2)(a) For a given distance from a radiating electric dipole, at what angle (expressed...

Homework Statement Suppose we know that B(\vec x ,t) is a solution to Maxwell's equations in vacuum and furthermore we know that E(\vec x , 0)=E_0. How do we find E(\vec x , t)? Homework Equations \nabla \cdot E = 0. \nabla \cdot B =0. \vec \nabla \times \vec B = \left ( \frac{-1}{c}...

P | | r | ----------------A------------------wire W---> Q: Wire positioned along x-axis has steady current of 1 ampere, solve for E(r) and B(r). What Maxwell's equations are supposed to apply here...

I'm confused about Maxwell's Equations. 1) does an electrical charge (say, an electron) traveling with a constant velocity (say, in the x-direction) travel as an electromagnetic wave? I'm thinking of an analogy with flowing mass. Suppose you have massive particles, evenly distributed...

I'm learning electrodynamics and one of the speakers I'm learning from said that when faced with the incompatibility of retaining both Newton's equations (based on mass, distance and time) and Maxwell's equations (based on charge, E and B) unchanged, Einstein had to choose one or the other. The...

Maxwell's equations with charges can be written as the following (in the cgs system): \frac{\partial \vec E}{\partial t} =c \vec \nabla \wedge \vec B-4\pi \vec J. \frac{\partial \vec B}{\partial t} =-c \vec \nabla \wedge \vec E. \vec \nabla \cdot \vec E =4 \pi \rho. \vec \nabla \cdot \vec...

The maxwell's equations in vacuum are satisfied by a non trivial solution involving \vec E (t,\vec x) and \vec B (t, \vec x). Correct me if I'm wrong. I don't really understand the physical interpretation of the solution. I know that if I'm given an initial condition then I can know the...

I find Maxwell's equations insufficient and superfluous having the Lorentz & Coulomb's force equations. As far as I see magnetic (Lorentz force) and electric (Coulomb's force) interaction is best defined by these two equations themselves, and although Maxwell's equations can describe quite a few...

I just finished the first week of the term. It was very loaded I must say. I also ended my introductory courses and I'm now taking upper level undergraduate physics courses. My professor wrote notes for us because he doesn't really like Jackson's book, but I'm having a very hard time to...

Homework Statement For a particular Dieletric it is observed that over a range of frequencies, the group velocity varies exponetinally with wave number: v_{g}=ae^{bk} , where a,b are constants. *(PLease not that the superscript g on v on the LHS side is meant to be subscript, however it...

It is a well-known fact that Maxwell's Equations, along with Lorentz's Force Law, form a complete description of classical electromagnetism. But why is that? I mean, I can understand that Lorentz's Law is necessary for describing the interaction between matter and electromagnetic fields, and I...

Excuse me if this is a stupid question. I'm now studying Electricity and Magnetism, and I'm coming toward the end of the course. The thought has been crossing my mind recently of what a shame it is that Maxwell's Equations turned out not to be correct, seeing as they are so beautiful and...

Homework Statement Draw the state of polarization of the electromagnetic (EM) wave defined by *****PLEASE NOTE EQUATION SHOWN IN NEXT POST****** (For some reason can't change it in this post... with Eo real. Use a sentence to describe in words the state...

Homework Statement For a harmonic uniform plane wave propagating in a simple medium, both \vec{E} and \vec{H} vary in accordance with the factor exp(-i \vec{k}.\vec{R}) Show that the four Maxwell’s equations for a uniform plane wave in a source-free region reduce to the following: \vec{k}...

Homework Statement # Everyone knows that a time varying magnetic field produces an electric field and vice versa. But are the fields produced, static or dynamic? From Maxwell's equations(Faradays and Ampere's law), it seems like they are static. Moreover, Faraday's law of electromagnetic...

I'm new to these equations but let's see if I have the talk down. 1. The electric field surrounding a charge will go thru a surface and not come back into the surface. It's strength is proportional to the charge and inversely proportional to the perm of free space. 2. The magnetic field...

Could someone point me in the direction of the derviation of each of Maxwell's equations? I'm working on a presentation and can't find a good one that starts with primitive assumptions (i.e. to help explain to a non physics audience).

I was reading Michio Kaku's book Prallel Worlds recently and I believe I saw it say that Maxwell's equations for electricity and magnetism become the same for electricity and magnetism when monopoles are introduced. My question is, if the equations become the same then why don't we say that...

Homework Statement The question is simple, I want to obtain Eq.5 from Eq.2 using Eq.1. Homework Equationshttp://img150.imageshack.us/img150/1108/question.png The Attempt at a Solution Can anybody explain how Eq.4 becomes Eq.5, what does happen to Re (Real part)?

Homework Statement Show that any charge distribution in a conductor of conductivity σ and relative permittivity κ vanishes in time as ρ = ρ0exp(−t/ζ) where ζ = κǫ0 σ Homework Equations Maxwell's equation ∇ · D = ρfree equation of continuity for a free charge density ∇ · Jfree =...