# What is Larmor precession: Definition and 16 Discussions

In physics, Larmor precession (named after Joseph Larmor) is the precession of the magnetic moment of an object about an external magnetic field. Objects with a magnetic moment also have angular momentum and effective internal electric current proportional to their angular momentum; these include electrons, protons, other fermions, many atomic and nuclear systems, as well as classical macroscopic systems. The external magnetic field exerts a torque on the magnetic moment,

τ

=

μ

×

B

=
γ

J

×

B

,

{\displaystyle {\vec {\tau }}={\vec {\mu }}\times {\vec {B}}=\gamma {\vec {J}}\times {\vec {B}},}
where

τ

{\displaystyle {\vec {\tau }}}
is the torque,

μ

{\displaystyle {\vec {\mu }}}
is the magnetic dipole moment,

J

{\displaystyle {\vec {J}}}
is the angular momentum vector,

B

{\displaystyle {\vec {B}}}
is the external magnetic field,

×

{\displaystyle \times }
symbolizes the cross product, and

γ

{\displaystyle \gamma }
is the gyromagnetic ratio which gives the proportionality constant between the magnetic moment and the angular momentum. The phenomenon is similar to the precession of a tilted classical gyroscope in an external torque-exerting gravitational field.
The angular momentum vector

J

{\displaystyle {\vec {J}}}
precesses about the external field axis with an angular frequency known as the Larmor frequency,

ω
=

γ
B

{\displaystyle \omega =-\gamma B}
where

ω

{\displaystyle \omega }
is the angular frequency, and

B

{\displaystyle B}
is the magnitude of the applied magnetic field.

γ

{\displaystyle \gamma }
is (for a particle of charge

e

{\displaystyle -e}
) the gyromagnetic ratio, equal to

e
g

2
m

{\displaystyle -{\frac {eg}{2m}}}
, where

m

{\displaystyle m}
is the mass of the precessing system, while

g

{\displaystyle g}
is the g-factor of the system. The g-factor is the unit-less proportionality factor relating the system's angular momentum to the intrinsic magnetic moment; in classical physics it is just 1.
In nuclear physics the g-factor of a given system includes the effect of the nucleon spins, their orbital angular momenta, and their couplings. Generally, the g-factors are very difficult to calculate for such many-body systems, but they have been measured to high precision for most nuclei. The Larmor frequency is important in NMR spectroscopy. The gyromagnetic ratios, which give the Larmor frequencies at a given magnetic field strength, have been measured and tabulated here.
Crucially, the Larmor frequency is independent of the polar angle between the applied magnetic field and the magnetic moment direction. This is what makes it a key concept in fields such as nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR), since the precession rate does not depend on the spatial orientation of the spins.

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1. ### I Does Larmor precession change the force exerted on a magnetic dipole?

If we have a spinning spherical charge in a nonuniform magnet field that points in one direction (for simplicity lets say B=<0,0,k*z>). Since the magnetic field is nonuniform, there will be a force exerted on the dipole, F=(mu•∇)B=mu_z*k. So in this case we expect it to be constant. This is...
2. ### A Relationship between Larmor precession and energy eigenstates

Quantum mechanically, a spin 1/2 particle in a uniform magnetic field has two energy eigenstates ##\ket{up}## and ##\ket{down}## and rotational degrees of freedom (distinct from the energy eigenstates) about the axis of the magnetic field. this can be derived from the Pauli matrix commonly...
3. ### I Larmor precession of an electron in a magnetic field?

In QFT where the electromagnetic field is mediated by virtual photons, is it possible to describe the larmor precession of an electron as a series of emission and absorption of virtual photons? how does the spin angular momentum "evolve" over a series of events? This feels like a challenging...
4. ### Larmor Precession and a bar magnet

As stated in the link below, when a magnet bar (or a current loop) is placed in an external magnetic field it (its magnetic moment) becomes aligned with the magnetic field while an orbiting electron would have precession with Larmor frequency. What is the reason for these different behaviors...
5. ### Larmor precession in a 2D B-field

I just tried to find the eigenvalues (for the energy), obtaining E = ±(γħ.√(Bo² + Γo²))/2 and the corresponding eigenvectors for the H matrix. But I don't know what to do to create de state vector χ.
6. ### Quantum version of Larmor precession

Homework Statement Homework Equations I didn't get what this actually means. The Attempt at a Solution I'm not sure whether it is correct. Could you take a look? Regards!
7. ### Deriving Larmor frequency problem

I don't get how they get Eq. 5. Why is the direction of ##\mu## going outwards from the direction of B? And why does the fact that ##\frac{d\mu}{dt}## is perpendicular to both ##\mu## and ##B## mean that ##\mu## goes in circle?
8. ### I Moment and the Larmor precession

Hi, In the Larmor precession, we tend to define the magnetic moment as the current multiplied by the surface (for an electron rotating around a nucleus), sometimes this moment is defined (generally) as the sum of the vectoriel products of half of the position vector and the charge times the...
9. ### I Where Does Larmor Precession Occur?

I have been doing a lot of exercises out of Griffiths lately, and one thing I spent a lot of time thinking about was Larmor precession. It's a fun thing to work out, but where does it actually happen? I'm having a hard time to see where it would apply. The first condition for Larmor precession...
10. ### Larmor precession and magnetic ordering

Homework Statement When we speak about Larmor precession we refer to atomic magnetic moments precessing in a magnetic field. In ordered magnets, such as ferromagnets, I never hear about larmor precession anymore. Are the magnetic moments frozen due to interactions with the surrounding crystal...
11. ### Why does Larmor precession appear to go against the right hand rule?

For some reason, I don't understand the direction of larmor precession. Torque is: \mathbf{\Gamma} = \frac{d \mathbf{L}}{d t} = \mathbf{r} \times \mathbf{F} As an example, I understand with a gyroscope, using the right hand rule and with angular momentum in the direction as shown in this...
12. ### Kinetic Energy in Classical treatment of Larmor Precession

This question pertains to the classical treatment of Larmor precession.I don't know whether to put it in the Classical Physics forum or this so I am putting it here. In the treatment we assume that the potential energy of the dipole-magnetic field system remains constant because there is no...
13. ### Larmor precession pi/2 out of phase

Homework Statement I was going over the solution where it says \s_x, s_y are out of phase by pi/2. They first wrote equation of motion for \s_x, s_y and then did something to the matrix and now the have equation of motion for \s_+, s_- They rewrite \s_x, s_y in terms of \s_+, s_- to see that...
14. ### Spin dynamics and Larmor precession

Homework Statement Consider an electron with spin, which should be in a homogenous magnetic field B=B0ez. This situation is described by the Hamiltonian of the shape \hat{H}=g\frac{\mu_B}{\hbar}\textbf{BS}. Consider now the time dependent state |\psi(t)> of the electron in spin space. The...
15. ### Larmor Precession and Force on a Magnetic Dipole

Homework Statement I have two questions. Both involve derivations from textbooks, not end-of-the-chapter problems. The two textbooks are Quantum Mechanics by Griffiths, and A Modern Approach to Quantum Mechanics by John Townsend. My first question is about the discussion of Larmor...
16. ### Larmor Precession: Understand Charge Orbitting Fixed Charge

i'm familiar with terminology used to denote rates of change in inertial and rotational frames, and the equation that links the two quantities, but working through a derivation/thought experiment to describe charge orbitting around another fixed charge in a weak magnetic field, it results in...