Field Definition and 1000 Threads

I am very confused, all i have thought about right now is that, in that isolated branch connecting A, B and C, the net charge would be conserved. Not sure how to proceed. I feel that, if there is a charge ## -Q ##at A, and a charge ##-Q_1 ## at B, then the charge at C MUST be ## Q+Q_1 ## maybe...

Definition. Let ##F## be a field and ##G## be a group. An ##FG##-module is a finite-dimensional vector space ##V## on which ##G## acts (from the right: ##V \times G \to V, (v,g)\mapsto v\cdot g##) such that the next conditions hold: 1) ##(v \cdot g)\cdot h = v \cdot (g \cdot h)## 2) ##v \cdot e...

Why in this derivation both the perpendicular electric field immediately above and below the boundary are pointing upwards? Why do we make this assumption and would it work if they are pointing in different directions?

Hi, While reading griffith introduction to electrodynamic I have stumbled upon this: I don't understand why when the pillbox hight goes to zero we have a discontinuity of electric field. On the figure 2.36 we can see the electric field penetrates the surface from below the plane and exits...

I don't know why, but I purchased Quantum Field Theory As Simple As Possible by Andrew Zee. I actually like it (not so much his other book Quantum Field Theory In A Nutshell). The purpose of this post is to mention that while math is required, it is nothing beyond a HS or even advanced middle...

Here a little document I'd like to have comments on it Electromagnetic Field from another perspective Analogy between the Electromagnetic Field and a Field Defined by the Constant k Definition of the Field: We have defined a scalar field A and...

Just a thought ... Given that the earths magnetic field has a stream of small changes, would a power transmission line forming a loop around the equator generate useful power ? Not exactly economic of course. Maybe just circumnavigating the arctic circle would be enough ?

I'm not asking for a solution, but for one of my homework problems, it is asking about a circular surface and a positive charge to the right of the surface. I just wanted to check if the net electric flux through the loop would be zero, as the charge is not enclosed by the loop. Is there...

Griffith's keeps mentioning the case r<R and r>R blah blah blah. Ok. But what if r = R? My attempt at an answer: when I take the limit from outside the sphere, I get the case when r > R. When I take the limit from inside the sphere, I get the case when r < R. Left and side hand side limits do...

It is clear in case K is a prime field, because then s(x) is just an identity. If K is not prime, s(x) is identity on its prime subfield. But how to show the automorphism of s() for the rest of the field, when it's not prime?

My calculations: ##2a = (2a)^4 = 16a^4 = 16a## ##14a=0## This allows for the characteristic to be 2 or 7. But, e.g., ##3^4 = 81 = 4 ~(mod~ 7)## rather than ##3##. So, the only answer is ##2##. 1. Is this derivation correct? 2. The hint in the textbook says to show that ##2a=0##. How to do that?

For part a) we have $$ E = \frac{Qy}{4 \pi \epsilon_0 (x^2 + y^2)^{3/2} } = \text{constant} $$ I am stuck on part b). What should the shape of the volume?...

I am watching this lecture by Richard E Borcherds on Galois theory: Field extensions and the following "easy example" is not easy for me to understand. Here it is screen-by-screen: How should I notice that x is transcendental?

Homework Statement: TE and TM polarization parralel question Relevant Equations: its a photo Hello, In the photo on the left bellow E-field is not parralel not to X nor to Z direction. to what exactly is it parralel? Thanks.

Hi I'm not sure if I calculated the magnetic field from task a) correct? for calculatin ##\vec{B}## i used, the formular ##\vec{B}=\vec{\nabla} x \vec{A}## $$\vec{B}=\left(\begin{array}{c} \frac{\partial}{\partial x_1} \\ \frac{\partial}{\partial x_2} \\ \frac{\partial}{\partial x_3}...

In Peskin's textbook, the coupling factor is given by a constant in the interacting field theory. The scattering matrix ##S## is given by the time-evolution operator, ##\exp(-iHt)##, in the limit of very large t, i.e., ##t\rightarrow \infty##, as expressed in Eq. (4.71). In my mind, the...

A few years ago I took a course on QC from the mathematics department. But I didn't see a direct connection to QFT, it seems QC is more connected to QM than to QFT. But I may be wrong I am just a novice here. Maybe a good title for a PhD dissertation... (now just to fill the details) so much...

Hi, I don't know if I have calculated the electric field correctly in task a, because I get different values for the Poisson equation from task b The flow of the electric field only passes through the lateral surface, so ##A=2\pi \varrho L## I calculated the enclosed charge as follows...

Suppose two orthogonal neighbouring orbitals ##|\phi _1 \rangle## and ##|\phi _2 \rangle## so that ##\langle \phi_1|\phi _2 \rangle =0##. Applying an electric field adds a new term ##u (c_1^{\dagger}c_1-c_2^{\dagger}c_2)## to the Hamiltonian which u is a constant potential. Obviously, we still...

In the standard model fermion field components collect quite a few labels. The basic fermion field has 4 components that obey anti commutation relations. If one has two types of fermions, say electrons and muons. Do these commute or anti commute? Same question for other labels like gauge group...

Source: https://tutorial.math.lamar.edu/Problems/CalcIII/SurfIntVectorField.aspx Alright so my confusion lies in the following step: Consider the side x = 0. Okay, from the formula (I am just going to insert an image here) Okay, so gradient of f would just be <1, 0, 0>, which is simply i...

Hi, I am reading Griffiths Introduction to electrodynamics. Currently I am solving problem 2.11 which asks to find an electric field inside and outside a spherical shell of radius R. Inside: $$\int{E \cdot da} = \frac{Q}{e_0} = |E|4\pi r^2 = \frac{Q}{e_0} = 0$$ The result is $$0$$ because we...

https://www.amazon.com/Student-Friendly-Quantum-Field-Theory/dp/0984513957?tag=pfamazon01-20

It is a giveaway. https://www.amazon.com/Quantum-Field-Theory-Standard-Model/dp/1107034736/?tag=pfamazon01-20

Cost me a fortune when the dollar was so high in the eighties :rolleyes: ##\ ##

My question is why the direction of gravitational field doesn't change relative to moving observer take for example gravitational field in the y direction relative to stationary observer but relative to an observer moving with velocity v in the x direction the field should have x component

How does QFT treat the Young’s DSE? Is there a wave function (wave packet) attached (and created at the moment of launching of the photon) or the modes of the EM quantum field are pre-existing due to experimental configuration (including the screen) and do they play the role the wave function is...

My understanding of this question is that, if you have a proton standing against a positive electric field, and move it in the opposite direction of the field, you're putting in work and therefore should have greater electric potential energy. But that idea breaks down when you consider a...

My attempt at a solution: Cylindrical coordinate system with ##r##, ##\theta##, ##z##. Conductivity ##\sigma## and permeability ##\mu_0##. Inner radius ##a## and outer radius ##b##. (##b>a##) The external field is spatially uniform and driven at sinusoidally at frequency ##f##. The external...

Hi there, The settling velocity is terminal velocity at which drag force is equal to the gravity. When the sphere is in rotating field the terminal settling velocity is reduced. What will be the expression for it in rotating field?

I did make the problem simpler by looking at the the part from d/2 down the upper plate here are my initial parameters I am making my size step be h since lowering it may make calculating harder I am especially getting weird results for the field and capacitance R = 0.1; % Radius of the...

I have come across the following paper (arxiv preprint link, it looks like it is published in Phys Rev D) that claims to have found a consistent quantum field theory of tachyons, overcoming three issues which have been said in previous literature to make such a theory impossible...

I took a point P on the conductor with charge Q. We know that the field inside a conductor is zero in electrostatic equilibrium Therefore I took induced charge on the neutral conductor to be x and gave the respective charges to the others. On the side facing conductor with charge Q the neutral...

My teacher said that gauss law may not accounts for the field due to the outside charges in the LHS in this expression ##\int E.ds## = ##\frac{q}{\epsilon}## as field lines coming in the surface leave it as well. Hence the total flux is 0 However i dont think thats very consistent with the...

Where can I find detailed derivation of Field Equation of Teleparallel Gravity from variation of Action ?

First astrophotography was black and white. So then we colored it in. Then the light got filtered so people can see the universe better. When I ask why are there no photographs of magnetic field lines in space, or anywhere; I read that it's because our eyes cannot see them, but we can't see...

here is my attempted solution. ## d^2 = z^2 + \frac {L^2} {3} ## ## C ## is coulomb constant since the point is symmetric, only the vertical component of the electric field remains. So, $$ E = 3 E_y =3 \frac {C Q cos \theta} {d^2} $$ $$ E= 3 \frac {C Q z} {d^3} $$ thus part (a) is done ( i...

https://www.space.com/sun-magnetic-field-flip-solar-maximum-2024 I know theyre not the same physics. I just wondered if the the Suns 11 year polarity flip has any analogy to the flipping T-wrench effect.

The solenoid can be assumed to be a stack of rings of width ##dz## each where ##z:0\to-\infty## . $$i=nIdz$$ $$\sin\theta=\frac{R-r}{l}$$ $$\cos\theta=\frac{z+x}{l}$$ $$dB=\frac{\mu_{\circ}nIR d\varphi dz}{4\pi l^2}$$ Call ##\frac{\mu_{\circ}nIR}{4\pi}=\alpha## $$ B_y =\int dB\cos\theta ...

I understand the following .a conductor is made of atoms and atoms always strive to be at equilibrium and that's why the electric field inside a conductor is zero because the electros distribute themselves in such a way so that they are in equilibrium , yet they do produce an electric field...

q encolsed =0 Second case q enclosed q by gauss law At 2r

If gravity is not a force, but rather curvature of spacetime, are gravitons necessary to couple with gravitational field?

There is a magnet in the shape of a hollow sphere. And the inner surfaces are all n-poles, and the outer surfaces are all s-poles. At this time, how is the magnetic field formed in the empty space of the sphere? There is no s pole for the magnetic force lines from the n pole to enter, so can...

If a vector ##V(x)## being transported down a path ##l##, The vector field is described with equation: $$\partial_\mu V(x)=\Gamma_\mu V(x)$$ The solution of the equation can be described with parallel propagator ##P(x, x_0)##(in mathematics it is also called product integration): $$V(x)=P(x...

I tried resolving the semi infinite rods into arcs of 90 degree each placed on the three axes but that doesnt take me anywhere.... Alternatively I tried finding out the field at the point due to each rod but im unable to find the perpendicular distance from the point to the rod...I dont think...

Lambda = charge density I tried first taking out the field due to the circular arc and I got $$ (lambda / 4π (epsilon knot) ) (2 sin (theta)) $$ For reference this is the arc that was provided in the question of angle 2(theta) and the tangent What I dont understand is how can the fields be...