Magnetic Definition and 1000 Threads

In the picture below, the direction of the magnetic field lines can be determined by using the right-hand rule with the thumb pointing in the direction of the current. If we use the right hand rule in the picture below, thinking of the yellow arrow as the current, we would not get the correct...

Summary:: I am trying to derive that the divergence of a magnetic field is 0. One of the moves is to take the curl out of an integral. Can someone prove that this is addressable Biot Savart's law is $$B(r)=\frac{\mu _0}{4\pi} \int \frac{I(r') \times (r-r')}{|r-r|^3}dl'=\frac{\mu _0}{4\pi}...

I have nearly finished my homework, but am blocking at one of the simplest questions... I'm going to let ##\rho=0.094\,\Omega/m## Since the magnetic flux is increasing, then, by Lenz's law, the current in both loops is counter-clockwise. If we only look at the left loop, then...

I'm trying to understand how the Lorentz force can explain why magnets attract and repel. The explanations that I have found have mostly involved the magnets moving in a way that decreases the forces between them ( ) but I have not been able to find any intuitive explanation involving the...

The direction of the magnetic potential, ##\vec A##, must be in the direction of the current, which is in ##\hat z## direction in cylindrical coordinates. It is obvious that the potential only varies with ##s##. Therefore, $$\vec A = A(s) \hat z$$ Therefore, $$\nabla \times \vec A = \vec B$$...

Hi there, I approached this problem by making use of the fact that a dipole can be modeled as a small current loop with the magnetic field ##\vec B_1 = \mu_0 \frac {m_1}{4\pi r^2} (2\cos \theta \hat r + \sin \theta \hat \theta)## which is the far-field approximation for a regular circular...

I am analyzing the rotor magnetic field, i feel i understand the basic concept but have few clarifications. At pt1, the net mmf due to currents ##i_a = i_{max}; i_b = -\frac{i_{max}} 2 ; i_c = -\frac{i_{max}} 2## is ##\frac {3F_{max}} 2## Similarly i can do for Pt2. But my confusion is the...

The Thompson jumping ring experiment consists in an AC supply connected to a coil with a metal steel core inside. A metal ring is placed around the core. When the AC supply is turned on, the ring suddenly jumps and after a time it starts levitating in a fixed height. I'm a little confused about...

Hello! The magnetic force is to the right. ##I_c## is the moment of inertia of the cylinder. For the net force on the centre of mass, I have the frictional and magnetic forces ##F=F_B-f##. I know that ##F_B## is ##IdB##. I also know that ##rf=I_c\alpha=I_c\frac ar##, so that...

My answer will be no for both (a) and (b) because there is no change in magnetic flux experienced by the circular coil. Am I correct? Thanks

Hello, I am looking for some information on how 2 different types of magnetic fields interfere with each other. And i don't mean, 2 magnets, but let me be specifically: Lets say that you have a very strong static magnetic field, from a huge magnet. (for instance, the strength of the magnet of...

This is supposed to be very basic, where the loop is held there is a declining magnetic field in direction (-z), therefore the current is supposed to be clockwise. However in the answers it is said the the current is anti clockwise. That doesn't make sense to me. Is there a mistake in the answers?

I was reading somethings about magnetic monopoles, and how, if it were discovered its existence, it would changes the Maxwell equations, in summarizing, is not the first time i see this: It is the consequences of the existence of a magnetic monopole? That is, IF it exist, SO the imagem is true...

p=Bqr and del p = p del theta

If I understand correctly, the concept of electric and magnetic fields originated with Faraday and was developed by reconceptualizing forces acting at-a-distance. For example, the electric field concept was developed by looking at the force on a test charge in the presence of a source charge...

The current direction is as follows I think so much and do the right hand rule i get 0 at the center, but not sure why the answer is non zero. I have shown the directions of the magnetic fields, i have not shown the magnitudes of equal length but they all are equal. Why the answer is non zero...

It is not a direct home work problem, i was thinking if a sine wave current passes through the straight current carrying conductor, what will be the magnetic field. For the DC current I know the formula as below. ##B = \frac {\mu_0 I 2a} {4\pi x\sqrt{x^2 + a^2}}## Let the current be ##I =...

Hi, can anyone provide literature that explains nuclear magnetic resonance spectroscopy in terms of a quantum mechanical theory? Could QED explain NMR in its entire phenomenon?

If you take copper wire and wrap it tightly around a bolt will that alone create and hold a magnetic field? I add an image for clarification

qvB=mv^2/R R=mv/qB= p/qB ! As you can see, the difference between this relation and the relation in question is in 'c'. Maybe my way is wrong. Maybe I should get help from relativity because the speed of light is involved here. Please help. Thankful

I am reading up on quasars because I am interested in the magnetic beams that emanate from their poles, accelerating material. I read that the magnetic beams are generated by the orbiting debris the quasar is consuming. Sorry, that doesn't sound right to me. I assumed the black hole core is...

Hello! I want to make sure I understand (mainly qualitatively) what happens to an atom in a magnetic field. Assume we have an atom with an even number of protons and electrons. This means that all proton (electrons) are paired up, except for one of them (I am not totally sure if this pairing is...

Everywhere I look online I see the formula for the magnetic field of a uniformly moving charge is, $$\frac{\mu_0 q \vec v \times \vec r}{4\pi r^3}$$ but when I calculate it by transforming the electrostatic field (taking the motion along x) I get, $$\frac{\gamma \mu_0 q \vec v \times \vec...

I am reading a book on fusion and just went over a paragraph of magnetic mirror confinement. What I want to understand is this. So all charged particles gyrate around magnetic field lines and if they have also a velocity parallel to the field they form helical paths. The gyroradius is...

I want to know how to calculate the braking force acting on a magnet falling through a copper tube. The setup can be seen in this video (YouTube, @ 1:49 - 3:12): Copper's Surprising Reaction to Strong Magnets. Note that it's not a copper tube in the video but a plastic tube surrounded by a...

The problem is simple, but have one confusion, if i substitute the values given, I get ## B = \frac {10^{-7}(6*10^{-6})[(8*10^6 \vec j) \times (-0.5\vec j + 0.5 \vec k)]} {r^2} ## ## B = 48\mu T\vec i## First thing the answer does not match. I don't see the angle in calculations between ##\vec...

Dear mechanical expert I have to realize a linear displacement system for a Hall sensor that has to slide along the central axis of a narrow cylinder and with which high intensity magnetic field measurements (1-14 Tesla) have to be made. The field is produced by a commercial vertical magnet...

Surely a tough one, I am doing it from the basics. This is the diagram i tried to draw showing the Force and current I The Length L is the tangent to the circle. The Force F is pointing upwards at ##90 Deg## to the ##\vec B## and also perpendicular to ##\vec L##. I am considering a small...

Can anyone explain the above answer to me? What does the "change in area" mean?

Homework Statement:: n/a Relevant Equations:: n/a These are the answers diagrams, with my questions in red. 1. In arrangement 1, I was wondering why there isn't any magnetic lines inside the magnet. While it seems that vector addition would make the field go outside the magnetic-less...

i tried to draw the directions of the parameters The direction of B is clear since then the Force will be in the positive X direction. I am bit confused with the direction of Force, how would i draw it and the components. Is the gravitational force i have drawn is correct? Do we have better...

I am confused with the concept of Torque handled differently in books, Concept1: If a loop is placed in a magnetic field and the current flowing in the loop is ##I## there will be force and torque acting on the loop given by ##F = I \vec l \times \vec B ##. The torque is given by ##\tau =\vec...

The attached file is the coordinate system I've used a) $$\vec{E}=\dfrac{\vec{F_e}}{q}=\dfrac{1,10\cdot{10^{-13}}\hat{j}\;N}{1,6\cdot{10^{-19}}\;C}=6,88\cdot{10^5}\hat{j}\;N/C$$ b) $$\sum{\vec{F_{net}}}=\vec{0}=\vec{F_e}+\vec{F_m}$$...

Is Peskin and Schroeder book, page 187 when they try to connect the electron form factors to its magnetic moment they get the expression $$\bar{u}(p')\left(\gamma^i F_1(q^2)+\frac{i \sigma^{i\nu}q_\nu}{2m}F_2(q^2)\right)u(p)$$ Where ##p##, ##p'## are the momenta on on-shell electrons and...

I have been reading Griffith's Introduction to Electodynamics and i am currently at the chapter about magnetostatics. There is an example about a long solenoid with n units per length and radius R that shows a way of finding the magnetic vector potential. The magnetic field inside the solenoid...

Ok, so I have long been fascinated with magnetic fields and their mysterious nature. I've been wondering what would happen when the magnetic field of Earth gets bent/disturbed/rippled by some extraneous force. I am aware the extent of effects that magnetic fields have on a planet is great, but I...

A classic example in textbooks is calculating the magnetic field inside a solenoid of length ##l## with ##N## turns and making the assumption that the magnetic field inside the solenoid is pretty uniform and outside it is 0. Using Ampere's law ## \oint_C \vec B \cdot d \vec l = \mu_0 I_{through}...

The beam of protons are directed towards the axis of the cylinder, perpendicular to the direction of the field. While traveling through the cross-section of the cylinder, the proton beam experiences a magnetic force, which tends to move the beam in a circular orbit of the radius given by: r =...

Hello. I was wondering if diamagnetic materials only repel varying electric field? By Ampere law only a variable flux can cause an electromotive force, so, and by what I understood diamagnetism is explained exclusively by Ampere law. Am I wrong?

The magnetic energy of a current carrying spring, with ##N## turns, length ##x## and cross sectional area ##A##, is $$E_m = \frac{\mu_0 N^2 I^2 A}{2x}$$The (negated) spatial derivative of this yields a quantity with dimensions of force,$$F = - \frac{dE_m}{dx} = \frac{\mu_0 N^2 I^2 A}{2x^2}$$How...

I first found the Lorentz force on the ball as a whole$$\vec{F}_m = \iiint_V \rho(\omega \times \vec{r} + \vec{V})\times \vec{B} dV = \rho \vec{\omega} \times \left( \iint_V \vec{r} dV \right) \times \vec{B} + \rho \iiint_V \vec{V} \times \vec{B} dV = Q\vec{V} \times \vec{B}$$due to the...

Recently I have encountered the following expression for the potential energy of a magnetic dipole of moment ##\boldsymbol{\mu}## placed in an external magnetostatic field B: $$U=-\boldsymbol{\mu} \cdot \textbf{B}$$. However, I was told that magnetic fields are non-conservative, so we can't...

I know that the problem of magnetic mirrors is that they leak out the tight ends of the mirror, on the other hand the main problem of toroids is that magnetic field line curvature creates a better confinement on the inner diameter and lesser on the outer diameter so needs a strong plasma current...

-------------------------------------------------------------------------------------------------------------------------------------------------- This was a problem introduced during my classical electrodynamics course. I am not 100% sure, but I think I've solved up to problems (a) and (b) as...

Suppose you are analyzing this image. The question to answer is: Explain why the alpha particle's path has a larger radius than either of the beta particle paths. Justify your answer using either momentum or charge-to-mass ratio. When you are answering this, suppose you know that , in...

Similar to what is shown here, except the south side would be the weak side of the array. A link to purchase one of these or at least the magnetic field arrangement would be very helpful. Thanks in advance.

My solution is making an analogy of the ##\text{Relevant equations}## as shown above, starting from the equation ##\vec \omega = \frac{1}{2} \vec \nabla \times \vec v##. We have ##\vec B = \vec \nabla \times \vec A = \frac{1}{2} \vec \nabla \times 2\vec A \Rightarrow 2\vec A = \vec B \times...

I'm reading about the Stern–Gerlach experiment and the only part that confuses me is how a magnetic field would deflect particles with magnetic dipoles instead of just rotating them. In this case the magnetic field is non-uniform, but it still seems intuitively strange to me since magnetic...

Say I've got a magnet flying through empty space in a homogenous magnetic field. The magnet precesses and flies in a straight path. Now make that magnetic field inhomogenous. The magnet precesses and flies in a curved path. What I can't figure out is why the path is curved. It is because...

I am new to this forum, and this is my first post. Please bear with me if my query has any inaccuracies. In the attached figure, a coil is wrapped around the central arm of a flat H-shaped thin metallic plate (such as iron). DC current flows through the coil and magnetizes the arm. At the...