Maxwell's equations Definition and 237 Threads

are maxwells equations theoretically accurate? do they describe electromagnetism? its basically a series of differential equations for describing the electric, and magnetic fields. including particle motion and the field it creates? the electric field makes a lot of sense. but what is...

I am attempting to understand a question posed to me by an acquaintance, who asked me if I could refer him to literature freely available on the Internet on "self-dual solutions to Maxwell's equations on Euclidean space, or pseudo-Euclidean space, not Minkowski space (where there are none)" and...

A Student's Guide to Maxwell's Equations by Daniel Fleisch is the best physics book I've ever read. I just love the way it analyzes each equation. I'm looking for other books/supplements similar to it for the other branches of physics (Quantum Mechanics, Thermodynamics/Statistical Mechanics...

Can anyone please explain me some uses of maxwell's on my REAL life? REAL life = weapons, propulsion, tech, radio frequency and microwaves,nuclear physics(maybe); no REAL life = monopoles, origin of the universe, space bull, particle physics( muons,pions etc.); PS. I am 14 years old so don't...

Homework Statement Show how the given physical magnetic field is consistent with a monochromatic plane wave solution to Maxwell equation Homework Equations [/B] Physical: > Bphys(t) = B0 sin (2πft) ex Maxwells: > B = iB0 exp[i(kz − ωt)] ex.The Attempt at a Solution I know that field is the...

I have recently finished an extensive review of vector calculus. I need to connect the exhaustive techniques of Surface Integrals and line integrals to quite a few problems involving Maxwell's Equations before I really feel certain that I am on board with both the math and the physics. I feel...

For example, if I have a magnetic field perpendicular to some surface and I change this magnetic field with constant speed, how do I calculate the Electric field at any point on this surface, since ∫E⋅ds=k, where k is some constant, could be done with many different vector fields.

Hello. I would like to ask one simple question. Do we need to distinguish E-field (Electric field) in Gauss's law from those in Maxwell-Faraday equation and Ampere's circuit law? I firstly thought that E-field in Gauss's law is only for electrostatics so I need to distinguish it from E-field in...

Newtonian mechanics is considered an extremely valid "approximation" for large objects whose speed relatively small (compared to the speed of light). But, we generally acknowledge that they aren't "true," even though they are still useful. My question is are Maxwell's equations similar in this...

I need some help in defining what are the assumptions needed to derive a constant speed of light from Maxwell equations. Is it correct to say that this result applies to a sinusoidal wave as an assumption? In my understanding that is (more or less) equivalent to planar waves in vacuum: is it...

Homework Statement I'd like to know how to convert Maxwell's Equations from Differencial form to Integral form. Homework Equations Gauss' Law Gauss' Law for Magnetism Faraday's Law The Ampere-Maxwell Law The Attempt at a Solution Convert using properties of vector analysis (as Divergence and...

The standard way of writing Maxwell's equations is by assuming a vector potential ## A^\mu ## and then defining ## F_{\mu \nu}=\partial_\mu A_\nu-\partial_\nu A_\mu ##. Then by considering the action ## \displaystyle \mathcal S=-\int d^4 x \left[ \frac 1 {16 \pi} F_{\mu \nu}F^{\mu\nu}+\frac 1 c...

In one of our lectures we wrote Maxwell's equations as (with ##c=1##) ##\partial_\mu F^{\mu \nu} = 4\pi J^\nu## ##\partial_\mu F_{\nu \rho} + \partial_\nu F_{\rho \mu} + \partial_\rho F_{\mu \nu} = 0## where the E.M. tensor is ## F^{\mu \nu} = \begin{pmatrix} 0 & -B_3 & B_2 & E_1\\ B_3 & 0 &...

Hi PF I am reading Feynman's lectures on gravitation. The equivalence principle says that no local measurement (it includes measurement of the electromagnetic field) can tell you if you are accelerated or in gravity. Feynman agrees and writes that we have then a problem. Accelerated charges are...

Hi guys! First, I'm a high school student. A senior! We don't study maxwell equations yet so when I'm doing a research about E=mc^2 and especially ghe energy part I came across electromagnetism and of course these bizarre equations for me ! I tried to understand them using internet but I failed...

There are a few good youtube videos that calculate c from Maxwell's Equations, but the jist of it still hasn't gelled with me. In other words, I'm still scratching my head. I wonder if anyone could (without using math) explain to me how a velocity can be calculated from magnetic and electric...

The electromagnetic action in the language of differential geometry is given by ##\displaystyle{S \sim \int F \wedge \star F},## where ##A## is the one-form potential and ##F={\rm d}A## is the two-form field strength. At the extremum of the action ##S##, ##F## is constrained by ##{\rm d}F=0##...

Consider the following Maxwell's equation in tensor notation: ##\partial_{k}F_{ij}=0## ##-\partial_{k}\epsilon_{ijm}B_{m}=0## ##\partial_{k}\epsilon_{ijm}B_{m}=0## ##\partial_{k}B_{k}=0## I wonder how you go from the third line to the fourth line.

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, A time-varying (sinusoidal) voltage source is applied to a parallel plate capacitor of length d. Then the E field will vary according to E(t) = V(t)/d. However, this suggests that, for any given time, the E field is constant with respect to spatial coordinates. Therefore, the curl of E is...

Homework Statement This is a general question that applies to many homework problems (and real world problems), but I will provide an example to help guide the discussion. I am hoping you all can give me some examples of particularly clever manipulations of Maxwell's equations to make a...

Homework Statement There's a uniform infinite line charge with the charge density λ. A point particle with charge q moves with a velocity v parellel to infinite line. What is force exerted on point particle? What is magnetic field seen in ths moving frame(particle frame)? Homework Equations...

So from what I seem to understand up until now, Maxwell's equations usually work while assuming that the fields are continuous and smooth instead of the actual complexity at the atomic scale. However, as we move more and more towards the microscopic realm, a point comes when we cannot ignore...

Hello, I have derived two Maxwell's equations from the electromagnetic field tensor but I have a problem understanding the second formula, which is: \partial_{\lambda} F_{\mu\nu} + \partial_{\mu} F_{\nu\lambda}+\partial_{\nu} F_{\lambda\mu} =0 I have a few questions to help me start: 1) Is...

Hi, I'm trying to interpret a form of Maxwell's equations, but I can't seem to figure out where the term $\^{e}_z$ comes from in the following equation: ## \frac{\partial{\vec{E}_t}}{\partial{z}}+i\frac{\omega}{c}\hat{e}_z\times \vec{B}_t=\vec{\nabla}_tE_z ##

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 Given the Maxwell Lagrangian ##\mathcal{L} = -\frac{1}{2} (\partial_{\mu}A_{\nu})(\partial^{\mu}A^{\nu}) + \frac{1}{2} (\partial_{\mu}A^{\mu})^{2}##, show that (a) ##\frac{\partial \mathcal{L}}{\partial (\partial_{\mu}A_{\nu})} = -...

I'm looking for an EM wave solution to Maxwell's equations that matches the Doppler diagram below. That is, circular wavefronts that are not concentric due to the motion of the source. Does a solution that accurately matches the Doppler diagram exist?

I have an understanding of Maxwell's equations and a vague grasp on potentials. I'm trying to do something different with the potentials. I'm using the Feynman Lectures on physics, http://www.feynmanlectures.caltech.edu/II_21.html#mjx-eqn-EqII2113, using the equations an potentials in a box...

Greetings all, Quick question. I know that all 4 Maxwell's equations are said to be first-order, coupled PDEs, where each equation has an unknown field. I see that with Faraday's and Ampere's law, because, E and H appear in each of those equations. But Gauss' laws, I'm not seeing that...

I couldn't finish it, so I paid $35 for Alan Macdonald's Vector and Geometric Calculus. This uses geometric algebra, where vectors may be multiplied together to form bivectors, trivectors, and so forth. They are added together with abandon. The electric field E is more or less 1D so it is...

Homework Statement The Lorenz gauge ∂Φ/∂t + ∇. A = 0 enables the Maxwell equations (in terms of potentials) to be written as two uncoupled equations; ∂2Φ/∂t2 - ∇2Φ = ρ 1 and ∂2A/∂t2 - ∇2A = j 2 The tensor version using the Lorenz gauge is, i am told, ∂μ∂μ Aα = jα 3 expanded this is...

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...

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...

Homework Statement A conducting square loop (L × L) moving with velocity vo ay m/s where the magnetic flux density is B=Bo ax Wb/m2 in 0 < y < 2L, and is equal to zero when 0 > y and y > L. Determine the current in the loop and plot its magnitude as a function in the loop's position in the...

there are no electromagnetic waves? All I know is that there is a modified version of the Maxwell equations (in differential form) for such a universe, such as (the arrows represent vector arrows): →∇x →B = μ0 →j + μ0 ε0 ∂→B/∂t instead of having ∂E/dt in the last term (which would be the case...

Zahid Iftikhar asked why charges get separated in a changing magnetic field over in the EE forum. I pointed him to Maxwell's equations and also pointed out we took them to be observational and axiomatic. Yet it occurred to me there might be an reason in quantum probability. So is there a...

So I've been wanting to build a particle accelerator for a while, and have kind of been brain storming ideas to make it work. I've been recently trying to figure out how to get the actual acceleration to happen. I have a few ideas, but the one that I like (assuming it's possible) is using a...

Hello all, While I understand the significance of natural units, I am wondering why, in SI units, we are able to assign μ0 an exact value. The speed of light is experimentally determined in m/s, and given the relationship derived from Maxwell's equations, we know that c^2 = 1/√(ε0μ0). Thus by...

I want to know how can i prove that Maxwell's equations for the propagation of electromagnetic wave are Lorentz invariant.

A parallel plate capacitor with circular plates of radius R is being discharged. The displacement current of discharge through a central circular area, parallel to the plates and with radius R/2, is 2.0 A. What is the discharging current?

Maxwell's equations are frequently solved numerically using deterministic methods such as finite difference time domain (FDTD) methods (https://en.wikipedia.org/wiki/Finite-difference_time-domain_method). The problem is that FDTD methods are known to be very computationally intensive. I'm...

opposites magnetic fields repel each others. How big of an magnetic would I need to lift mass ( 5g) 3 centimetre in the air. F = MA A = 9.81 m/s^2 M = mass of the object ( 5 g) F = 49.05 F = I L x B 49.05 = IL X B I = 3000 mA ( from a AA battery) µ = 4π E-7 T m/A Bsol = µ N/L I F = IL X...

we have that Ht1 (x,y,z) - Ht2 (x,y,z) = Js and for the special case Ht1 (x,y,z) - Ht2 (x,y,z) = 0 where there is no surface current. At a boundary with Js =0, which for simplicity let's asume is at at x = a, then knowing that Ht1 and Ht2 are the magnetic fields to the left and right of the...

According to Maxwell's equation, the speed of light, ##C_0 = \frac{1}{\sqrt{\epsilon_0\mu_0}}##, is a constant regarding to some form of medium, called luminiferous aether. Shortly after the death of Maxwell, Michelson-Morley Experiment shows that the speed of light is constant regarding to the...

Homework Statement I've not been able to do this question for years so I'd really appreciate some help. Light is normaly incident from a medium 1 with impedance Z1 through a layer of medium 2 of thickness L and impedance Z2 into medium 3 of impedance Z3. Obtain an expression for the total...

Homework Statement Given an electric field in a vacuum: E(t,r) = (E0/c) (0 , 0 , y/t2) use Maxwell's equations to determine B(t,r) which satisfies the boundary condition B -> 0 as t -> ∞ Homework Equations The problem is in a vacuum so in the conventional notation J = 0 and ρ = 0 (current...

Once we define energy and momentum carried by the field , is it possible to derive Maxwell's equations from conservation of momentum and conservation of energy (along perhaps with conservation of charge)?

Hi guys, I am having hard times in understanding whether or not the longitudinal electromagnetic waves are solutions to Maxwell's equations. In Cohen-Tannoudji "Introduction to QED" it's stated that by writing the fields as the sum of a longitudinal and transverse part one can show that waves...

Maxwell's equations seem overdetermined, in that they involve six unknowns (the three components of E and B) but eight equations (one for each of the two Gauss's laws, three vector components each for Faraday's and Ampere's laws). (The currents and charges are not unknowns, being freely...