What is Magnetic moment: Definition and 181 Discussions

The magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current (such as electromagnets), permanent magnets, elementary particles (such as electrons), various molecules, and many astronomical objects (such as many planets, some moons, stars, etc).
More precisely, the term magnetic moment normally refers to a system's magnetic dipole moment, the component of the magnetic moment that can be represented by an equivalent magnetic dipole: a magnetic north and south pole separated by a very small distance. The magnetic dipole component is sufficient for small enough magnets or for large enough distances. Higher-order terms (such as the magnetic quadrupole moment) may be needed in addition to the dipole moment for extended objects.
The magnetic dipole moment of an object is readily defined in terms of the torque that object experiences in a given magnetic field. The same applied magnetic field creates larger torques on objects with larger magnetic moments. The strength (and direction) of this torque depends not only on the magnitude of the magnetic moment but also on its orientation relative to the direction of the magnetic field. The magnetic moment may be considered, therefore, to be a vector. The direction of the magnetic moment points from the south to north pole of the magnet (inside the magnet).
The magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse cube of the distance from the object.

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1. Calculate the magnetic moment of a rotating sphere

Ich wäre Ihnen sehr dankbar, wenn Sie sich meine Lösung der folgenden Übung ansehen: A sphere with radius ##R ## is spatially homogeneously loaded and rotates with constant angular velocity ##\vec{ \omega}## around the ##z ## axis running through the center of the sphere. Calculate the...
2. I Average magnetic moment of atom in magnetic field ##B##

from the partition function - am trying to show that ##\langle \mu \rangle = \beta^{-1} (\partial \log Z / \partial B)## where ##Z## is the canonical partition function for one atom, i.e. ##Z = \sum_{m=-j}^{j} \mathrm{exp}(\mu_0 \beta B m)##, and ##\mu = \mu_0 m##. The average...
3. I Is the magnetic moment of a hydrogen atom not equal to Bohr's magneton?

Can you cite experiments where, in some excited states of a hydrogen atom, magnetic moment significantly differs from Bohr's magneton was detected? Correction for magnetic moment of nucleus is insignificant. Only experimental data, not theoretical forecasts. Starting from the experiments of...
4. A First order electroweak correction to the g-2 magnetic moment

We know that we need to go to 5th order in perturbation theory to match 10 decimals of g-2 for electron, theory vs. experiment. But let us not assume QED is pure and independent, but it's a lower energy limit of GSW (not Green-Schwartz-Witten from superstrings) electroweak theory. Has anyone...
5. I Definition of magnetic moment in quantum mechanics

* The general formula for the magnetic moment of a charge configuration is defined as ##\vec{\mu} = \frac{1}{2} \int \vec{r} \times \vec{J} \,d^3r##* For an electron it's said that the correct equation relating it's spin and magnetic moment is is ##\vec{\mu} =g\frac{q}{2m}\vec{S}## * It's...
6. I Work Done in Changing Shape of Current Carrying Loop

How would you go about calculating the work done in morphing a square current-carrying loop into a circular current-carrying loop, without change in length while maintaining the same angular orientation with an external magnetic field. My book suggests defining P(potential energy) = M.B (dot...
7. Why the Stern-Gerlach experiment didn't detect the L?

i recently read about the stern-gerlach experiment and found out that they did it in the first place to verify the principle of the "space quantization " introduced by Bohr , and they thought they did detect the quantization of the orbital angular momentum of ( L = 1 , m = 1,-1 ) neglecting the...
8. I What is the effect of a magnetic field on an atom's magnetic moment?

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...
9. I Electron's magnetic moment

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...
10. How to get the magnetic moment for this loop?

About this figure, the current in the opposite wires are parallel (and not anti-parallel). So, for instance for the first option the torque is zero; but I wanted to know what is the magnetic moment of this loop. Since I rely only on formula I've have no idea how to compute for this one.
11. Derive an expression for the applied field of a superconducting wire

So far the best I've been able to come up with is to use ##\vec{B} = \mu_0 \vec{H}## which gives me i_c = H 2\pi r j_c = \frac{H 2\pi r}{\pi r^2} = \frac{2H}{r} \therefore B = \mu_0 \frac{r j_c}{2} I'm fairly confident this is just terrible math and physics on my behalf but I'm struggling to...
12. Finding a method to compute the magnetic moment of an even-odd nucleus

I am having difficulties computing the magnetic moment for an even-odd (proton-neutron) nucleus. The formula is: $$\mu_J=g_J\times j\times \mu_N$$ I checked this helpful post...
13. I A bar magnet and magnetic moment in a magnetic field

Why a magnet bar would become aligned with the external magnetic field while a magnetic moment would precess around the external magnetic field?
14. Electron anomalous magnetic moment

Hello there! I'm trying to check the first order (1 loop) correction to the electron magnetic moment. I'm following Schwartz and Peskin, but both of them have a point where they hide the calculations, and I'm not sure if my calculations are correct. The point is exactly this: I don't know...
15. Derivation: force on magnetic moment in magnetic field

I am trying to derive the equation ##\vec{\Gamma} = \vec{m} \times \vec{B}##, where ##\vec{m} = I \vec{A}## is the magnetic moment, and ##\vec{A}## is normal to surface ##A##, from the Lorentz force law ##\mathrm{d}\vec{F} = I \vec{dl} \times \vec{B}##. For an arbitrary closed current loop ##C##...
16. A Steps in an electron's magnetic moment derivation

Hello! I am reading Schwarz's book on QFT and in chapter 17 he introduces the anomalous magnetic moment. I am not sure I understand a step in the derivation (from a mathematical point of view), when going from 17.23 to 17.24 (I attached a SS of it). I was able to get certain terms, but I am not...
17. I Does a free electron have an orbital magnetic moment?

I know that total magnetic moment of an electron (I am not sure if it is magnetic moment of electron or atom, please clarify this) is sum of magnetic moment caused by orbital motion and spin angular momentum. So, Total magnetic moment = Orbital magnetic moment + spin magnetic moment Do I have...
18. Rotating speed of a proton ion

I tried to calculted the rotating speed fro a proton from the clasical point of view by using its magnetic moment and the moment of a rotating sphere uniformly charged as example here: https://ocw.mit.edu/courses/physics/8-07-electromagnetism-ii-fall-2012/exams/MIT8_07F12_quizsol2.pdf It is said...
19. I What are the magnetic states of nucleons?

Could I have hundred times the ground state or there is a limit? Is there a limit for excited magnetic momentum that if reached the nucleous explode or generate gammas? I suppose If I excite it it would spin faster but proportional to quantum values. Note: there is a "theory" to avoid electron...
20. Magnetic moment and magnetic field and dot product

Homework Statement a magnetic moment of U = 1 (i) + 2 (k) , surrounded by a magnetic uniform field of B= 3 (i) + 4 (j) - 1 (k) find the potential energy in mJ ? Homework Equations dot product of 2 vectors ( ui*bi)+(uj*bj)+(uk*bk) = or finding the module of both vector and doing AB...
21. Total magnetic moment of hydrogen in weak magnetic field

"Calculated the total magnetic moment of a hydrogen atom in the ground state in a weak magnetic field which arises from hyper fine splitting of the ground state. How many beams does hydrogen produce from a Stern-Gerlach analyzer with a weak magnetic field?" I've calculated the magnetic moments...
22. Finding Magnetic Moment from Pull Force

For an undergraduate project, I need a magnet with a magnetic dipole strength of 0.3 A*m^2. However, all distributors I can find only list their magnets in terms of "pull force" which appears to be defined as the force between a magnet and a steel plate. How do I find a magnet with the dipole I...
23. I Magnetic moment of a massless charged Fermion?

The spin magnetic moment of a charged, spin-1/2 particle is $$g \frac e {2m} \frac \hbar 2$$ where g is the g-factor (2 for any particle in tree-level approximation, 2.00231930436182 for electron), e is charge m is mass ##\frac \hbar 2## is spin But with zero mass this expression does not make...
24. N

Magnetic Moment and Spacing of Adjacent Magnetic Substates

Homework Statement [/B] Consider the hydrogen atom in the 42F5/2 state. Take into account the effects of finestructure (spin-orbit coupling). (a) Write down the spectroscopic notation of the state that the 42F5/2 is degenerate with, in the absence of an external magnetic field. (b) Calculate...
25. Relationship between magnetic moment and induced magnetism

How would you calculate the induced magnetic field B at some distance R from a bar magnet, given the magnetic moment of a magnet? (In general)
26. Magnetic Moment of a crystal

Homework Statement Find the magnetic moment of a crystal when placed (i) in a weak field at high temperature (ii) in a strong field at low temperature Homework Equations This is the last part of a question which I feel I have solved correctly up until this point. The mean magnetic moment I...
27. Average magnetic moment of the system

I was reading the statistical physics textbook and was really confused with the notation: I don't understand the last part of the section. Why is that \sum_{\sigma = \pm1} \sigma P(\sigma) equals to \left< \sigma \right>? And what does \left< \sigma \right> actually mean? Is it the average...
28. B Exploring the Mystery of Electron Magnetic Moments in Quantum Mechanics

If electrons have a magnetic moment (or behave like they have) why don't all orient North Up in a magnetic field (pointing down)? Plus, if thought as magnetic dipoles, like poles repel, therefore all should point the same direction. In a Stern-Gerlach apparattus shouldn't the magnetic moment...
29. Magnetic moment and Minimum energy

In exam we have a question like this , I said its false cause ##U=-\vec μ⋅\vec B## , ##U=-μBcosθ## when ##cosθ=1## it is in the most stable point.But when ##cosθ=-1## its not, since.In both cases ##\vec μ## and ##\vec B## are parallel ?
30. I Calculate the Dipole Moment of an object

How would I calculate the Dipole Moment of a piece of mild steel approximately 15cm in length?
31. Magnetic Moment of loop

Homework Statement A 15-turn rectangular loop of wire of width 10 cm and length 20 cm has a current of 2.5 A flowing through it. Two sides of the loop are oriented parallel to a uniform magnetic field of strength 0.037 T, and the other two sides are perpendicular to the magnetic field. (a) What...
32. I What does the magnetic moment of a particle depend on?

Every magnetic object has a magnetic moment. From electrons to molecules, to even planets. But my question is, what determines how much of a magnetic moment a quantum object has? I'm not sure if "how much" is the right word for it. What determines the "quantity" of a magnetic moment of a...
33. B Does an electron's position collapse when measuring g factor?

https://link.springer.com/chapter/10.1007/978-3-540-39664-2_1 http://iopscience.iop.org/article/10.1088/0031-8949/1988/T22/016/pdf In these two experiments done back in the 80's, electrons were trapped inside a penning trap for long periods of time. They were measuring the ratio of the magnetic...
34. Neutron scattering - determing the magnetic moment for MnO

I'm told that the MnO crystal resembles in structure that of NaCl (FCC) with lattice constant a, and am first asked to write a general expression for the position vector Rj of the ion j in the unit cell of MnO. I am then asked to find the vector K for MnO in order to use the relation...
35. A gyromagentic ratio for a cylinder

Homework Statement In classical physics, a system's magnetic moment can be written like so: \mu = g\frac{Q}{2M}L, where ##Q## is the total charge, ##M## is the total mass of the system and ##L## the angular momentum. a) Show, that for a cylinder (##I = \frac{1}{2}MR^2##) spinning around its...
36. Induced Magnetic Moment (vector) vs. Induced EMF (scalar)

When I induce magnetic flux through a closed loop, I should expect the lines of flux produced by current in that loop to oppose the change of flux through that loop. But what happens when that loop, say a rectangular loop, is curved into the shape of the letter J (like a candy cane) and my flux...
37. A Spin magnetic moment in half metals.

I read that the stoichiometric half-metallic compound has integer spin moment. For this, n(up)-n(down) should be integer. Since n(up) +n(down) is always integer, either n(up) or n(down) should be integer to make total spin moment integer. I could not understand how the presence of energy gap in...
38. Torque upon a rotating magnetized body

Hey there! I would really appreciate if someone could help me with the following problem. I didn't find it anywhere (textbooks, web...). Not only currents but also magnetized bodies possesses magnetic moment. I know that if the magnetized body is at rest in a constant external magnetic field...
39. A Calculation of magnetic moment of an atom in the compound

How is it calculated from magnetic susceptibility measurements using the mass of the sample? I know only this formula https://en.wikipedia.org/wiki/Magnetic_moment#Magnetic_moment_of_an_atom, but there is no mass, only quantum numbers.
40. Does a Magnetic Moment μ exist for any closed current loop?

I'm asking the above question as I imagined a current loop made out of a curving wire that cannot fit into a flat plane. Where does the direction of μ point then? Also, is there only one μ value for any current loop, independent of the chosen axis of tilting? Or can a current loop have...
41. Non-uniform magnetic fields and magnetic moment

Hey all, I'm having some issues with electromagnetism here. Let's say we have a particle with magnetic moment ##\vec{\mu} = \mu_0 \hat{x}## and magnetic field ##\vec{B(x)} = B_0 \frac{x}{a} \hat{x}## where ##\mu_0,B_0,a## are constants. If we assume that the magnetic field ##B_0## is far, far...
42. Relation between torque and magnetic moment

The magnetic moment ##\vec{M}## of a charged particle is defined as ##\vec{M}=\frac{1}{2}q\,(\,\vec{r}\times\vec{v})##. Starting with torque ##\vec{N}=\vec{M}\times\vec{B}##, I arrive at a contradiction. Consider a charge particle moving at a constant speed ##v## anticlockwise in a circle of...
43. Magnetic moment and current of permanant magnet

Every magnetic dipole has a magnetic moment associated to it. Magnetic moment of electromagnets could be found by ##M = iA##. But for permanant magnets how it is measured? If we use this formula it implies that there must be some internal current flowing in permanant magnet. Is it true? What...
44. Total magnetic moment of simple system.

Homework Statement If there's a current I flowing through the rectangular conductor and it's located in the magnetic field in such way that normal vector of the surface that this rectangle forms closes the angle of 60 degrees with magnetic induction vector find total magnetic moment of this...
45. Magnetization (M) / magnetic moment (m) of NdFeB?

Dear All, Hi, I am pretty new in the area of magnetism. Please pardon me for some questions that might be pretty fundamental and basic here. I am trying to understand the difference between magnetic moment and magnetization. I thought I understood magnetization as the degree to which a magnet...
46. What gives rise to a magnetic moment in a proton/neutron?

Homework Statement Describe, with examples, what is meant by magnetic moment. What gives rise to a magnetic moment in a proton/neutron? Homework Equations The Attempt at a Solution I know what a magnetic moment is, just struggling with the other parts of the question. So what I'm thinking is...
47. Magnetic field components of a circuit

Homework Statement A circle-formed circuit with an area A lies in the (xy)-plane. An electric current I runs clockwise through the circuit (figure 1). An external magnetic field B exerts a torque t = D(3i - 4j) on the circuit, where D is a positive constant, i is the x-axis unit vector and j is...
48. Magnetic moment between 2 bar magnets

Homework Statement A bar magnet floats above another bar magnet. The first has mass u1 and magnetic moment m1=m1k^ and is on the ground. The second has mass u2 and mag. moment m2=-m2k^ and is a distance z above the ground, find z 2. Homework Equations I assume I need to calculate the magnetic...
49. Deriving the magnetic moment of a specimen in a given magnetic field

Homework Statement I'm working on a problem that says that >If $\varepsilon_{\pm}=\mp (\mu \mu_0 H + k \theta \frac{M}{\mu N} )$ is the energy of the atom of a specimen that can orient itself either parallel or antiparallel in a magnetic field, show that \$ \frac{M}{\mu N}= tanh(\frac{1}{kT}(...
50. Find spin only magnetic moment of [Fe(H2O)5NO](2+)

Homework Statement Find spin only magnetic moment of ##[Fe(H2O)5NO]^{2+}## Homework Equations None The Attempt at a Solution When I used Google, the magnetic moment in 3.87 ##Fe## is in +1 oxidation state. So configuration is $$[Ar]3d^64s^1$$ There are 5 unpaired electrons. How does magnetic...