Field Definition and 1000 Threads

I am trying to derive radial and axial magnetic fields of a current carrying loop from its magnetic vector potential. So far, I have succeeded in deriving the radial field but axial field derivation gives me trouble. My derivation of radial field (eq 1) can be found here. Can anyone point out...

(1,1)or(2,0)or(0,2)?And does a dual vector field have gradient?

Mentors’ note: this thread is forked from https://www.physicsforums.com/threads/free-fall-in-curved-spacetime.1016510/ But what if the gravity field is homogeneous? Like that of an infinite massive plane? The objects in the ship will stay where they are. An infinite massive plane is quite...

If we define Laplacian of scalar field in some curvilinear coordinates ## \Delta U## could we then just say what ##\Delta## is in that orthogonal coordinates and then act with the same operator on the vector field ## \Delta \vec{A}##?

I got E. 13q as the answer. That is what i did: The electric field due to +q at origin 0 should equal the electric fields of charges -3q and the new charge placed at 2x. So applying the equation above like this; k*(q) / (2^2) = -3q*k + (k*C)/ 4 solving for C the new charge added, gives 13q. I...

If I have two separated and non-interacting molecules with different constants polarizabilities ##\alpha_1## and ##\alpha_2## and I send an EM field of frequency ##\omega## first on the molecule no.##1## and then on the molecule no.##2## so that the two molecules will have a dipole moment...

The Higgs mechanism is an ingenious mechanism inspired by condensed state physics. The famous Mexican hat potential ensures a VEV value of about two times the mass of the Higgs particle (which, as an aside, is of comparable order as the W and Z vector bosons, the difference though is that its a...

My attempt was to consider spherical shells of radius ##r## (##r\leq R##))and thickness ##dr## and then the potential energy of this shell would be in the field only of the "residual" sphere of radius ##r## (a result also known as shell theorem) $$U_{dr}=G\frac{\rho\frac{4}{3}\pi r^3 \rho 4\pi...

My attempt: We have 3 charges inside 2 +ve and 1 -ve so i just added them up. 4 + 5 +(-7) = 2q Then there is a -5q charge outside the sphere. I did 2q + (-5q)= -3q . The electric field flux formula is Flux= q/ E0 . So i got -3q/E0 which is obviously wrong : ) . After quick googling , I...

Is the electric field inside a sphere always 0? Even if we have charges on the surface?

I argue not. Let ##f:\mathbb{Q}\rightarrow\mathbb{R}## be defined s.t. ##f(r)=r^2##. Consider an increasing sequence of points, to be denoted as ##r_n##, that converges to ##\sqrt2##. It should be clear that ##\sqrt2\equiv\sup\{r_n\}_{n\in\mathbb{N}}##. Continuity defined in terms of sequences...

I've already tried to calculate the potential with respect to the 3 segments and then apply superposition (V1+V2+V3). However, I was not very successful. My error I think is in the calculation of the radii, mainly of the line segment that is on the z axis. Can anybody help me? I need some light...

I recently read a paper on using an electric field to drive water autoionizaton. I'm trying to figure out how to use the Laplace equation on pg 9; 4th paragraph; to solve for voltage. I'm also interested in how this equation would change if I replaced the hemispherical tip with a parallel plate...

The notation I think best describes it is ## F = \lVert\int^{space}_s|\vec{V}|ds\rVert ## So you have a vector field V in a 3d space. For each point you integrate over all of space (similar to a gravitational or electromagnetic field) *but* vectors in opposite directions do not cancel, they...

To solve this problem, we need to evaluate the following integral: $$\epsilon = \int_{P}^{C} (\vec v \times \vec B) \vec dl$$ The main problem is, in fact, how do we arrive at it! I can't see why a Electric field arises at the configuration here. The magnetic field of the rotating sphere is...

this paper postulating a minimum gravitational field strength postulating a minimum gravitational field strength (minimum curvature) and a minimum acceleration but otherwise leaving Gr could reproduce MOND [Submitted on 25 May 2022] MONG: An extension to galaxy...

Is there any approach in any books out there, where we consider that in universe exists only one field, let it be called the Unified Field (UF), in which all of the known fields (gravitational, EM field, quark field, gluon field, lepton field, Higgs Field, e.t.c.) are just components (pretty...

If a magnetar is a neutron star, how do the neutrons composing the star generate a magnetic field? A neutron has zero charge, so it generates no magnetic field.

My solution was as follows: $$\frac {d\overrightarrow p} {dt}=q \frac {\overrightarrow v} {c}\times \overrightarrow B_0$$ The movement is in the ##[yz]## plane so ##|\overrightarrow v\times \overrightarrow B_0|=vB_0##, therefore: $$\biggr |\frac {dp} {dt}\biggr |= \frac {qvB_0} {c}.$$ On the...

Hi alltogether, I have been confused about a certain topic of EM wave propagation: it´s clear to me that E and M field are perpendicular to each other (I know Maxwell´s equations well). But: sometimes you can find on the internet that both fields are in phase...

Hello, i need help with the S-matrix. From what i understand, with the S-matrix i would be able to compute the scattering amplitude of some processes, is that correct? If so, how would i be able to do that if i have some field ##\phi(x,t)## in hands? Is that possible?

Hi, here's a theoretical problem that I am trying to find a satisfactory answer for. Imagine a coil that is temporarily switched on an off and generates a magnetic field that permeates through space. Now imagine a charged particle passing through this field, at time that the coil is already...

Hi. I'm not sure where to put this question, it concerns particles, mass-energy equivalence and various things. Classical electromagnetism seems to be as sensible a place as any. There is energy stored in an E field. Energy density (at position r, time t) = \frac{1}{2}...

TBH I don't really understand the question that I am asking myself. I was inspired asking this from my textbook "Do you know". Can you make me understand why would not we require total length field? Here's a similar question-...

So, we have A, the magnetic vector potential, and its divergence is the Lorenz gauge condition. I want to solve for the two vector fields of F and G, and I'm wondering how I should begin##\nabla \cdot \mathbf{F}=-\nabla \cdot\frac{\partial}{\partial t}\mathbf{A} =-\frac{\partial}{\partial...

I've been researching water bridges and electrowetting to learn the effects of electric fields on water molecules but something continues to confuse me: if polar molecules can only rotate in an electric field, how is the water moving? Anyone familiar with this phenomenon? Any help is greatly...

If we increase the magnetic field, the radius of the particle's circular path will decrease which increases the tangential acceleration. How do I find the tangential acceleration. Do I use derivatives?

this formula in the picture is the average electrostatic field over a spherical volume of radius R. It is the same expression of the electrostatic field, at the (position) of the point charge, of a volume of charge of uniform density whole entire charge is equal to (negative)q. My question is...

If I'm correct then the maximum change in magnetic flux occurs when the semi circle crosses the point at which it's plane is parallel with the magnetic field and minimal when it crosses the point at which the magnetic flux is maximum ( perpendicular with the field). I'm having trouble writing a...

##B_0 = \frac{\mu_0(N)(I)}{2\pi r}## ##\frac{N}{2\pi r} = 200## ##B_{net} = B_0 + B_m = (1+X)\times B_0## Plugging in the numbers: ##B_0 = 4\pi\times 10^{-7}(200)(1.5) = 3.8\times 10^{-4}## ##B_{net} = (1+X)\times B_0 = (1+ 3\times 10^3)\times 3.8\times 10^{-4}## = 1.13 T But the answers says...

Is it correct that a salt bridge in a Galvanic cell makes that there is no electrical field between the solutions of the two hallf cells? Does that mean that the electrical potential (I do not write electrochemical potential) between both solutions is zero in an ideal world? Is it also possible...

At first I tried plugging everything in with 60Hz in the numerator but that did not work. I was told to think about sinusoidal waves and derivates but I'm not sure how that works. Any ideas? Thanks a lot

Can someone explain how there can be a radial magnetic field? I thought the magnetic field was always tangent to the circle using the right hand rule where you wrap your fingers around the current and point your thumb in the direction of the current.

if a sphere rotates, it's like multiple currents going around in a circle. I can find the magnetic field of each of those currents at the center point of the circle and add them together. We can integrate with respect to y and R. y ranges from 0 to 5 cm away from the center of the loop and the...

I am confused about this, do the black arrows represent the direction of magnetic force? The torque ##\tau = -IABsin\theta##, where I = current A is area of loop and B is magnetic field strength and I am a little confused how ##\theta## here is 45 degrees when the angle between the normal for...

Hi I am new to the forum. I am a investor, athlete, and a "field physicist." I got a bachelors in physics and Hopefully soon can get a phD. I like to do basic experiments that demonstrates physics.

I am a beginning graduate student and I've been assigned a paper which uses landau levels for 3d fermionic gas in uniform background magnetic field. I am having trouble finding a proper source which deals with solution of dirac equation in such a case. With the two papers that i have found which...

I was wondering if anyone could walk me though a better explanation on how to get the given results for these two questions. The solutions posted by my professor aren't really clear to me so if anyone is able to better explain how to get the solution it would be much appreciated!

What i don't understand is why we are able to replace the ring with 'two oppositely charged superposed disks'? Just trying to understand.. So we have a uniform charge which means that this'll just be a simplification of the problem than, correct? Thanks in advance.

If the question had been asking about the flux through the whole surface of the cylinder I would have said that the flux is 0, but since it is asking only about the lateral surfaces I am wondering how one could calculate such a flux not knowing how the cylinder is oriented in space. One could...

I joined an article by Davis and Onoochin. I have troubles to understanding his critic of the conventional field momentum interpretation (sec. 3). More precisely, while I am able to check that eq. (23) is true, and that the field is of the order ##1/r^5##, I don't understand in which way this...

I am building small, simple version of a railgun using 2 copper bars and a couple of neodymium magnets to increase the magnetic field. I have also been trying to mathematically describe the magnetic field created by the conducting rods themselves. I am coming across some trouble when trying to...

Hello friends, Is it a waste of time to get both a degree and certificate in the same field? If for example I received a graduate certificate and a masters degree in Mechanical Engineering, does having a flow blown masters degree sort of overwrite the certificate credential? While it's nice to...

Hi, I'd request you to keep it simple so it's accessible by a layman. Question 1: Is Higgs field made up of Higgs bosons? Higgs field has a positive value everywhere. Other fields such as electron field, hover around zero though virtual particles come into existence and decay almost...

Hello there, I am given a diagram of a Josephson Junction like so: With a magnetic field ##B = \mu_oH## in the z-direction. I'm reasonably sure ##d_x,d_y,d_z## are normal lengths, not infinitesimal lengths although that is up for debate. Using the above equations I rearrange the expression...

Hi everyone! I'm pretty new in this forum, I found the topics here very relevant to my physics course. And here is my question: Given the following drawing, two infinite sheets (in y and z axis) of ideal conductive material. their thickness is infinitesimal (dx->0). The electric field is...

I am confused with the solution. It says ##\vec E = \frac{\sigma}{\epsilon_0}##. Shouldn't E = ##2*\vec E = 2*\frac{\sigma}{\epsilon_0}##? Electric field of the positive plate and electric field of the negative plate.

I recently watched this video by David Tong on computer simulation of quantum fields on lattices, fermionic fields in particular. He said it was impossible to simulate a fermionic field on a lattice so that the action be local, Hermitian and translation-invariant unless extra fermions get...

Electric field is 0 in the center of a spherical conductor. At a point P (black dot), I do not understand how the electric field cancels and becomes 0. Electric field is in blue.