Fields Definition and 1000 Threads

I am reading Dummit and Foote Section 13.4 Splitting Fields and Algebraic Closures In particular, I am trying to understand D&F's example on page 541 - namely "Splitting Field of x^p - 2, p a prime - see attached. I follow the example down to the following statement: " ... ... ... so...

The photon field has two physical degrees of freedom (dof): its two transverse polarization directions. But what about non-abelian gauge theories? What about N massless spin-1 particles that transfom under SU(N), how do I count their degrees of freedom? Gluons, for example, are massless spin-1...

Dummit and Foote Exercise 1 on page 545 reads as follows: Determine the splitting field and its degree over \mathbb{Q} for x^4 - 2 . ------------------------------------------------------------------------------------------------------ I have started on the solution to this exercise as...

Hi everyone, :) Thought this might sound interesting to all you people. The Fields Medal Symposium is broadcasted live today. Here's the link. Fields Medal Symposium - Arithmetic Dynamics - Home

Homework Statement The permittivity of a given medium is given by the equation ε = \begin{pmatrix} ε_1 & 0 & 0\\ 0 & ε_1 & 0\\ 0 & 0 & ε_2 \end{pmatrix} A wave is traveling in the \hat{k} direction in this medium where the unit vector \hat{k} is defined as \hat{k} =...

Homework Statement The differential equation is y' = y^2 Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t →∞. If this behavior depends on the initial value of y at t =0, describe this dependency.Homework Equations The...

Homework Statement Let K be the closure of Qu{i}, that is, K is the set of all numbers that can be obtained by (repeatedly) adding and multiplying rational numbers and i, where i is the complex square root of 1. Show that K is a Field. Homework Equations The Attempt at a...

Hi, upon studying vector calculus and more precisely about the curl I stumbled upon a question : why is it that there is always a potential function of a vector field when the curl of this vector field is equal to 0?

Hi folks! I've considered a career as a technical writer for the mechatronics/electronics fields for a while now (yes I have engineering education), but I'm wondering if I'd want to work in a European country like Netherlands, Germany...do they need technical writers in English? Or, do they...

Can an electromagnetic wave be deflected by electric or magnetic field.

reading this page : http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potsph.html it says "The electric field inside a conducting sphere is zero, so the potential remains constant at the value it reaches at the surface:" if the electric field inside the sphere is 0, then wouldn't that...

Homework Statement Consider two “circulating” electric field configurations. Expressed in polar coordinates (s,φ,z) they are: (these expressions are not dimensionally correct) 1. E = (0,s,0) 2. E = (0,1/s,0) a. Calculate ∇×E for both configurations. b. Note that ∫E⋅dl≠ 0 in either...

Homework Statement An infinitely long, uniformly charged straight line has linear charge density λ1 coul/m. A straight rod of length 'b' lies in the plane of the straight line and perpendicular to it, with its enared end at distance 'a' from the line. The charge density on the rod varies...

Hi guys! I need help on a problem from one of my GR texts. Suppose that ##\xi^a## is a killing vector field and consider its twist ##\omega_a = \epsilon_{abcd}\xi^b \nabla^c \xi^d##. I must show that ##\omega_a = \nabla_a \omega## for some scalar field ##\omega##, which is equivalent to showing...

I wasn't sure where to post this question, so I posted it here. As the title suggests, I want to know how to calculate (at least roughly) the electric field induced by excitation and ionization of a material (such as a metal) using a high intensity laser. My final goal is to compare the...

I started working for a multinational FMCG after graduating in Mechanical Engineering. With one year as of now in it, I somehow feel this is not a path to take for lifetime. I am paid well and my work is mix of management and engineering (Since it's the maintenance and I am the process owner)...

Whenever I ask someone what an electromagnetic field is exactly, they say that science does how questions, not why questions (which doesn't really make sense in this context, maybe i worded my question differently). We say that there are four fundamental forces that create the universe we live...

hi i know what is coherent state, but i read this text in an article and i don't understand this " if we wish to describe long range macroscopic forces, only bosonic fields will do, since fermionic fields cannot build up classical coherent states. " can you explain it for me, how...

In the absence of external forces, the electric field inside a conductor is supposed to go to zero. This is because if any field were to exist, then the charges in the conductor would experience force and continue moving until they canceled the field. However, is it true that for any system a...

To keep it simpler let take the electromagnetic (EM) field. A photon, in one perspective, can be described as an excitation of the EM field. Is the EM field omnipresent in all (time-space) the universe? or Does the photon creates/emit an EM field around it?

Basically my question is this: could we, in principle, formulate all of classical electromagnetic theory purely in terms of the force one charge exerts on another, or do we need to include the electromagnetic fields in order to arrive at a complete theory? ("complete" as in equivalent to...

It is well known that all sorts of systems tend towards minimal potential energy. I was wondering if this applies to static electric fields also, i.e. is an electric field such that it's energy integrated over all space is minimal? For example if we have a bounded source free region and if the...

So I've been simulating a really simple geometry using ANSYS Maxwell. It is a cylinder only and I am looking at the \overrightarrow{B} and \overrightarrow{H} fields in order to see their relationship between them when the material is magnetized in the circumferential direction. I used a...

when we say , electron acts like a wave ,does we mean to say that it produces electric and magnetic field or em waves varying with distance and time

In Srednicki's textbook (chpt 5) he has an expression: \int d^3k f(k) \int d^4x (\partial^2 e^{ikx}) \phi(x) and he wants to integrate by parts in order put the Laplacian on the field \int d^3k f(k) \int d^4x (e^{ikx})\partial^2 \phi(x) instead of the the exponential. He says that...

Hi. I am researching magnetic fields and getting no where. I am writing a computer programs to calculate Magnetic force between 2 magnets that can act both + to + and + to -. Given the movement of the magnets, the program will be calculating minute movements and compensating for changes in...

I did some research on Wikipedia, and I quote from the write up on Real Particles: "The term(Virtual Particles) is somewhat loose and vaguely defined, in that it refers to the view that the world is made up of "real particles": it is not; rather, "real particles" are better understood to be...

If a body was between two gravitational fields, would it feel a tension force like the two gravitational forces were pulling it apart, or would the two fields cancel each other out and the body wouldn't feel anything? I'm assuming in this scenario that both fields are big enough so that there...

Homework Statement Let w be a primitive n-th root of unity in some finite field. Let 0 < k < n. My question is how to rationalize [\tex]\dfrac{1}{1 + w^k}[\tex]. That is, can we get rid of the denominator somehow? I know what to do in the case of complex numbers but here I'm at a loss...

Homework Statement A,B,C,D are four 'thin',similar metallic parallel plates,equally separated by distance d,and connected to a cell of potential difference(V) as shown in the attachement. Write the potentials of A,B,C,D. If B and C be connected by a wire,then what will be the potentials...

What impact will a extremely high frequency of ultrasound have on a electromagnet? Will the magnetic field also oscillate at that frequency? What about a conductive wire transmitting electrical current? Will ultrasound on the wire cause the magnetic field to oscillate?

Hi, I'm done with my second year of electrical engineering and am interning at nVidia. So far all I see is people in cubicles debugging code and compiling kernels. Of course there's nothing wrong with it but I was disappointed because I chose electrical over computer science in the hope of...

I have seen on several books that the expression for the E field generated by an accelerated charge, at enough distance and in the non-relativistic aproximation, is something like that (taken from Jackson): where "β with the dot above" is the acceleration divided by c, n is a vector...

Hello all, I am in need of understanding of magnetic fields. More specifically i was wondering exactly why there is a magnetic field around a wire with current moving through it. Where i am going with this is.. if i had plasma contained, and i managed to get it moving in the container, would...

Homework Statement There is a magnetic field given by the equation \overrightarrow{B}=B_{0} \hat{x} \sin\left(2\pi z/L\right). If there is a 10^7 eV electron going in the \hat{z} direction (moving at a relativistic velocity), a mag. field strength of 0.1T, and a mag. period of 0.01m, what...

Hi guys, brand-new simpleton here. Quick question: would it be possible to stop ice formation on a cold surface with an electromagnetic field? How strong should it be (if possible)? Thank you!

Hi, just reviewing some of my physics material, and realized I had a question that has never been answered for me. I know that charged particles, traveling parallel to a magnetic field, feel no force either forwards or backwards, but feel a force perpendicular that causes them to spiral...

Do the $\mathrm{SU(2)}$ gauge fields takes the same value in the Lie subalgebra spanned by the $\mathrm{SU(2)}$ field strength tensor? I will try to clarify my questions. Define the Lie algebra as: \begin{equation} [t^a,t^b] = \varepsilon_{abc}t^c \end{equation} where $\varepsilon$ is the...

Two infinite sheets of current flow parallel to the y-z plane as shown. The sheets are equally spaced from the origin by xo = 7.5 cm. Each sheet consists of an infinite array of wires with a density n = 19 wires/cm. Each wire in the left sheet carries a current I1 = 3.5 A in the negative...

I wanted to know if there is a mathematical model to know the force with which a source of a magnetic field attracts or repels another source of magnetic field. For example, the mathematical model for the electrostatic force a charged particle exerts over another charged particle is: F =...

I am reading Dummit and Foote Section 9.5 Polynomial Rings Over Fields II. I am trying to understand the proof of Proposition 16 which reads as follows: --------------------------------------------------------------------------------- Proposition 16. Let F be a field. Let g(x) be a...

I am reading Dummit and Foote Section 9.5 Polynomial Rings Over Fields II and need some help and guidance with the proof of Proposition 15. Proposition 15 reads as follow: Proposition 15. The maximal ideals in F[x] are the ideals (f(x)) generated by irreducible polynomials. In particular...

hello , could someone please remind me I have forgotten a few things. So the electric field is perpendicular to the conductor and the flow of charge. So if i have a pipe and in the pipe flows a conducting gas or a plasma , now around the pipe I have a simple copper wire wound in many many...

Hey. Let's say you have an infinitely wide and long disk with a thickness h. Inside the disk, there is a constant charge density ρ0. Why would the electric field lines be perpendicular to the disk? Can somebody explain how symmetry and such generally affect electric field distribution of a...

edit: Nevermind, I found the answer myself :X

Hi everyone, next year i'll get a Bachelor in Computer Engineering , then i should choose a Master course... I really like electronics, electronics projects, robotics and controls, physics and photonics. The doubt is that in my university there are masters (relatively to my interests) in : -...

Homework Statement Two point charges are placed at the opposite corners of a rectangle as shown. What is the Electrical Field magnitude at each point due to the charges?Homework Equations Pythagorean theorem, E=kq/r^2The Attempt at a Solution r= square root of .8^2 +.4^2 =.89 E= 8.99x10^9 X...

Homework Statement I need to find all the intermediate fields between Q(\zeta_7) and Q. Homework Equations The Attempt at a Solution For the group Q(\zeta_7). I found all the permutations that are possible for \zeta_7. Here is what I have: Since Aut(<\zeta_7>) = Z^{\times}_7 = \{1, 2, 3...

How is it that the electric and magnetic fields in unpolarized light are not canceled out? The simplest example would be two photons of the same energy traveling coherently in time along exactly the same path in space, differing only by a rotation of 180 degrees around the axis of travel...

Hey guys, just got a question at school and the last part makes no sense. I replicated it almost exactly, except for the diagram. Just imagine the dotted line is a solid line indicating the electric field lines. Ignore the 4 dots around X, it was just to keep the field lines in line.Question 4...