Field Definition and 1000 Threads

I have a vector field which is originallly written as $$ \mathbf A = \frac{\mu_0~n~I~r}{2} ~\hat \phi$$ and I translated it like this $$\mathbf A = 0 ~\hat{r},~~ \frac{\mu_0 ~n~I~r}{2} ~\hat{\phi} , ~~0 ~\hat{\theta}$$(##r## is the distance from origin, ##\phi## is azimuthal angle and ##\theta##...

Hi everyone, I'm new to PF and this is my second post, I'm taking a QFT course this semester and my teacher asked us to obtain: $$[\Phi(x,t), \dot{\Phi}(y,t) = iZ\delta^3(x-y)]$$ We're using the Otto Nachtman: Elementary Particle Physics but I've seen other books use this notation: $$[\Phi(x,t)...

Hi everyone, I'm taking a QFT course this semester and we're studying from the Otto Nachtman: Texts and Monographs in Physics textbook, today our teacher asked us to get to the equation: [Φ(x,t),∂/∂tΦ(y,t)]=iZ∂3(x-y) But I am unsure of how to get to this, does anyone have any advice or any...

My first impression was the electric field is 0 at the center of the sphere, but it turned out not the case. My understanding when problems refer surface charge density, is that the charge exists only on the surface and it is hollow inside the sphere. Am i correct? Using the electric field...

I am trying to solve the following problem from my textbook: Formulate the vector field $$ \mathbf{\overrightarrow{a}} = x_{3}\mathbf{\hat{e_{1}}} + 2x_{1}\mathbf{\hat{e_{2}}} + x_{2}\mathbf{\hat{e_{3}}} $$ in spherical coordinates.My solution is the following: For the unit vectors I use the...

My guess is that the force per volume is: $$ \vec F_V = \rho \alpha x \hat x + \vec J \times \beta x \hat y$$ but I'm not sure where to go after that. I'm not given a value for either the charge density or the current density, so I can't simplify the relation much. Further, I'm not sure if my...

I have drawn a picture of what the induced electric field will look like, and I have determined its magnitude both within and outside of the magnetic field. I was able to get the right answer for part (b) with this information, but I don't understand why the answer for part (c) is 0 J. It...

The net electric field is ## 2dE \cos\theta ## ## dE = \lambda dx/(4\pi\epsilon (x^2 +r^2)) \\ 2dE \cos\theta = 2r\lambda dx /(4\pi\epsilon (x^2 +r^2)^\frac 3 2) \\ E_{net} = 2\lambda r /(4\pi\epsilon) \int_0^a dx /( (x^2 +r^2)^\frac 3 2) \\ E_{net} = 2\lambda r /(4\pi\epsilon) [\frac x...

I tried getting E by dividing volts and distance since I know the distance between the two plates is .352 m but it did not work

I thought it was easy but i am not getting the correct answer The electric field due the point charge q is ## E1 = q/(4\pi\epsilon x^2) ## The electric field due to the thin ring of radius R is considering the electric field due to the element charge dq (dS) ## dE2 = dq/4\pi\epsilon (x^2 + R^2)...

Thank you very much

Isn't the superposition principle of electric field just force being addable? Jackson's electrodynamics says it's based on the premise of linear Maxwell's equations. Which support(s) the superposition principle?

I understand how do 3 no. equation come from 1 & 2 no. equation. But I am struggling to understand how do 4 no. equation come from 3 no. equation. Will anyone do the steps between 3 no. equation and 4 no. equation, please ?

The movement in the z-direction is easy to solve for, as it's only affected by the gravitational force. However, if there's a magnetic field pointing down along the z-axis, the particle is going to be accelerated along the y-axis (F=q*v *B). The force is always going to be perpendicular to the...

Homework statement: Find the electric field a distance z from the center of a spherical shell of radius R that carries a uniform charge density σ. Relevant Equations: Gauss' Law $$\vec{E}=k\int\frac{\sigma}{r^2}\hat{r}da$$ My Attempt: By using the spherical symmetry, it is fairly obvious...

Hello, in this problem I'm supposed to calculate de magnetic field due to a bent wire at any point of the x-axis after the bending of the wires. It is obvious that the part of the wire that is parallel to the x-axis makes no contribution to the field so we can focus on the other part of the...

Once I know the Hamiltonian, I know to take the determinant ##\left| \vec H-\lambda \vec I \right| = 0 ## and solve for ##\lambda## which are the eigenvalues/eigenenergies. My problem is, I'm unsure how to formulate the Hamiltonian. Is my potential ##U(r)## my scalar field ##\phi##? I've seen...

Please help. Thank you.

Hello everyone ! I'm getting into General relativity. I wonder know how we find the Einstein's field equation. Maybe we can have an intuition with the strong equivalence principle. So if you can enlight me ☺️☺️ please Regards

Magnetic fields are sometimes measured by balancing magnetic forces against known mechanical forces. Your task is to measure the strength of a horizontal magnetic field using a 12-cm-long rigid metal rod that hangs from two nonmagnetic springs, one at each end, with spring constants 1.3 N/m ...

What I've done so far: From the problem we know that the curve c is a half-circle with radius 1 with its center at (x,y) = (0, 1). We can rewrite x = r cos t and y = 1 + r sin t, where r = 1 and 0<t<pi. z stays the same, so z=z. We can then write l(t) = [x(t), y(t), z ] and solve for dl/dt...

If I put a very long steel plate above a coil with DC, the magnetic field above the plate will decrease because of the shielding of the steel plate. However, from the perspective of magnetci domain, some domains will be magnetized to turn to the direction of the magnetic field from the coil...

Hello, I am still trying to fully grasp the general idea of the EM field, which always travels at the speed of light regardless of the reference frame, and is represented by a tensor with 16 components in relativity theory. My understanding is that, depending on the observer's frame of...

Is the intensity of a general electromagnetic wave always the norm of its Poyinting vector? Or are there other notions of intensity?

This is my homework. And we don't have online lessons. But my teacher gave this for homework. I couldn't solve this problem. Can you help me?

I have been following the book called "Conformal Field Theories" by Francesco, also known as "the yellow pages". I do this for fun but, of course, sometimes it gets rather technical. Do there exist solutions to the problems in this book? I haven't found a solutions manual available. Many...

But yet again my text says that option 4 is correct.

Hello, I'm searching for how magnetic field affects the thermal conductivity of the metal (such as steel in solid form). If someone suggests any article about it will be very helpful.

a. For the question a the solution is If the uniform charge density is ρ then the charge of the sphere up to radius r is q = ρ * (4/3)*π * r3; Hence the electric field is E = (ρ *4π*r^3)/(3*εο*r^2); E = (ρ*r)/(3εο); b. I don't understand what is superposition? How to proceed? Please advise.

If the magnetic field is constant then no change in flux will bring no induced emf nor any induced current. With the loop is in rest position the external magnetic field will exert a force but to calculate that force with the help of magnetic field isn't obvious. If this were a charged loop, the...

Suppose ##f## is reducible over ##F##. Then there exists ##g, h \in F## such that ##g, h## are not units and ##f = gh##. If there exists ##b \in F## such that ##b^p = a##, then ##(x - b)^p = x^p - b^p = x^p - a##, using the fact that ##F## has characteristic ##p##. So, if such a ##b \in F##...

What is the electrostatic field of a non-conductive sphere (it's radius is R) which has a density charge distribution inside? ρ0 and R are parameters. I started solving this with Gauss's law: then: Solving the integral: This means the electrostatic field of the sphere in r is: Can you...

If we look to the figure, in several articles they mentioned that the part of the mode field, the tail of the mode field diameter, travel in the cladding, this maybe I can understand that because of a little change between the refractive indices of the core and the cladding, then the transverse...

I'm going through the "Advanced Lectures on General Relativity" by G. Compère and got stuck with solving one set of conditions on the subject of asymptotic flatness. Let ##(M,g)## be ##4##-dimensional spacetime and ##(u,r,x^A)## be a chart such that the coordinate expression of ##g## is in Bondi...

Silly question but could someone explain why a real, 'observable' particle is said to be 'off-shell' in an external field? @A. Neumaier 's excellent FAQ notes that the mass shell constraints ceases to have meaning in this case. I'm just not fully clear on why (probably obvious) given that energy...

I'm just going to skip some of the step since I only need help with understanding the last part. After rearranging the equation stated at "Relevant equation" (and skipping some steps) we will get: E * 4*pi*e0*R^2 = integral pv * 4*pi*R^2 dR E = 1/(4*pi*e0*R^2) * 4*pi * integral pv*R^2 dR E =...

As for Laguerre-Gaussian beams, the direction of wave vector is helical, and how about the direction of electric field? I found that there was little literature mentioned this.

Unsure about this, but here is my attempt: B from the first wire: ##\dfrac {\mu _{0}I}{2\pi r} ## B from the second wire: ##\dfrac {\mu _{0}I}{2\pi r} ## Let the point be (x,y) Can I state that: ##\dfrac {\mu _{0}I}{2\pi y}+\dfrac {\mu _{i}\left( I/3\right) }{2\pi x}=0## Hence the magnetic...

Hi everyone, I have abit of trouble with this question. Please help! Given charges +q, +2q, −5q and +2q are placed at the four corners ABCD of a square of side a, taken in cylic order from the bottom left corner. Find the electric field E and the potential V at the centre and verify that they...

So this was a section taken out from a question which I am trying to do shown below I have drawn a sketch to help me visualise of what is going on I have used Fleming's left hand rule to help me determine what direction the force is facing on each side of the coil. For the last part in...

If we are in a cabine in a gravitational field and inside, we have a racket and a ball. We put strings in each side of the racket and we connect the racket to the ceiling of the cabine. This strings only allows us to keep the weight of the racket. Then, we drop a ball to the racket. We do this...

I am required to find the direction of the electric field on the surface of a grounded conducting sphere in the proximity of a point charge ##+q##. The distance between the center of the sphere and the point charge is ##d## and using the method of images we find that the charge of the sphere is...

This page claims that "[t]he electric field outside the sphere is given by: ##{E} = {{kQ} \over {r^2}}##, just like a point charge". I would like to know the reason we should treat the sphere as a point charge, even if the charges are uniformly distributed throughout the surface of the...

This is my attempt at this question, and I'm probably wrong, will need some help/guidance from the experts here :/ i) (ii) Since energy band given by ##6.67x^2##, can I assume that electric field is simply the energy difference from 0-3m divided by 3m? In this case, would the answer simply be...

Here i tried this way (see picture) Please tell me am i right or wrong. Also they says find the change in magnetic field with time using Faraday's law in a rectangular loop. How can i solve that??

Hi. In videos online the kink is explained as a delay in the electric field when charges accelerate. Does this mean we can deduce the existence of kinks from coloumb law. Does the simple form of plane electromagnetic waves which is well treated in most books really exist. What is the...

The moving magnet and conductor problem is an intriguing early 20th century electromagnetics scenario famously cited by Einstein in his seminal 1905 special relativity paper. In the magnet's frame, there's the vector field (v × B), the velocity of the ring conductor crossed with the B-field of...

Suppose we have a hollow metallic conductor, just a thin metallic shell forming a large hollow cavity. It is then polarized by electric charges placed nearby externally. The equilibrium electric field must be parallel to the surface normals of the shell, there must be no tangential component...

I am getting started in applying the quantization of the harmonic oscillator to the free scalar field. After studying section 2.2. of Tong Lecture notes (I attach the PDF, which comes from 2.Canonical quantization here https://www.damtp.cam.ac.uk/user/tong/qft.html), I went through my notes...