In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic dipole moment to its angular momentum, and it is often denoted by the symbol γ, gamma. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. A ratio is an expression which compares quantities relative to each other In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position Gamma (uppercase &Gamma, lowercase γ Γάμμα is the third letter of the Greek alphabet. Its SI units are radian per second per tesla (s-1T -1) or, equivalently, coulomb per kilogram (C/kg). The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units The tesla (symbol T) is the SI derived unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb.

## Gyromagnetic ratio and Larmor precession

Main article: Larmor precession

Any free system with a constant gyromagnetic ratio, such as a rigid system of charges, a nucleus, or an electron, when placed in an external magnetic field B (measured in teslas) that is not aligned with its magnetic moment, will precess at a frequency f (measured in hertz), that is proportional to the external field:

$f=\frac{\gamma}{2\pi}B$ . In Physics, Larmor precession (named after Joseph Larmor) refers to the Precession of the Magnetic moments of Electrons atomic The nucleus of an Atom is the very dense region consisting of Nucleons ( Protons and Neutrons, at the center of an atom The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current Precession refers to a change in the direction of the axis of a rotating object Frequency is a measure of the number of occurrences of a repeating event per unit Time. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second.

For this reason, values of γ/(2π), in units of hertz per tesla (Hz/T), are often quoted instead of γ. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second. The tesla (symbol T) is the SI derived unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic

This relationship also explains an apparent contradiction between the two equivalent terms, gyromagnetic ratio versus magnetogyric ratio: whereas it is a ratio of a magnetic property (i. e. dipole moment) to a gyric (rotational, from Greek: γύρος, "turn") property (i. In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly e. angular momentum), it is also, at the same time, a ratio between the angular precession frequency (another gyric property) ω = 2πf and the magnetic field. In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position Do not confuse with Angular velocity In Physics (specifically Mechanics and Electrical engineering) angular frequency In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges

## Gyromagnetic ratio for a classical rotating body

Consider a charged body rotating about an axis of symmetry. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. According to the laws of classical physics, it has both a magnetic dipole moment and an angular momentum on account of its rotation. It can be shown that as long as its charge and mass are distributed identically (e. g. , both distributed uniformly), its gyromagnetic ratio is

$\gamma = \frac{q}{2m}$

where q is its charge and m is its mass. The derivation of this relation is as follows:

It suffices to demonstrate this for an infinitesimally narrow circular ring within the body, as the general result follows from an integration. The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space Suppose the ring has radius r, area A = πr2, mass m, charge q, and angular momentum L=mvr. Then the magnitude of the magnetic dipole moment is

$\mu = IA = \frac{qv}{2\pi r}*\pi r^2 = \frac{q}{2m}*mvr = \frac {q}{2m} L$

as desired.

## Gyromagnetic ratio for an isolated electron

An isolated electron has an angular momentum and a magnetic moment resulting from its spin. In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin While an electron's spin is sometimes visualized as a literal rotation about an axis, it is in fact a fundamentally different, quantum-mechanical phenomenon[1] with no true analogue in classical physics. Consequently, there is no reason to expect the above classical relation to hold. In fact it does not, giving the wrong result by a dimensionless factor called the electron g-factor, denoted ge (or just g when there is no risk of confusion):

$\gamma_\mathrm{e} = \frac{-e}{2m_\mathrm{e}}g_\mathrm{e} = -g_\mathrm{e} \mu_\mathrm{B}/\hbar,$

where μB is the Bohr magneton. For the acceleration-related quantity in mechanics see ''g''-force. In Atomic physics, the Bohr magneton (symbol \mu_\mathrm{B} is named after the Physicist Niels Bohr. The electron g-factor ge is a bit more than two, and has been measured to twelve decimal places:[2]

ge = 2. 0023193043617(15)

The electron gyromagnetic ratio is given by NIST[3] as

$\gamma_\mathrm{e} = 1.760\,859\,770(44) \times 10^{11}\,rad\ s^{-1}T^{-1}.$

## Gyromagnetic ratio for a nucleus

Protons, neutrons, and many nuclei carry nuclear spin, which gives rise to a gyromagnetic ratio as above. In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin The ratio is conventionally written in terms of the proton mass and charge, even for neutrons and for other nuclei, for the sake of simplicity and consistency. The formula is:

$\gamma = \frac{e}{2m_p}g = g \mu_\mathrm{N}/\hbar,$

where μN is the nuclear magneton, and g is the g-factor of the nucleon or nucleus in question. The nuclear magneton (symbol \mu_\mathrm{N}\! is a Physical constant of Magnetic moment, defined by \mu_\mathrm{N} = For the acceleration-related quantity in mechanics see ''g''-force.

The gyromagnetic ratio of a nucleus is particularly important because of the role it plays in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). These procedures rely on the fact that nuclear spins precess in a magnetic field at a rate called the Larmor frequency, which is simply the product of the gyromagnetic ratio with the magnetic field strength. Precession refers to a change in the direction of the axis of a rotating object In Physics, Larmor precession (named after Joseph Larmor) refers to the Precession of the Magnetic moments of Electrons atomic

Approximate values for some common nuclei are given in the Table below. [4]

Nucleusγ / 2π (MHz/T)
1H42. 576
3He-32. 434
7Li16. 546
13C10. 705
14N3. 0766
15N-4. 3156
17O-5. 7716
23Na11. 262
31P17. 235
129Xe-11. 777

## References

• Note 1: Marc Knecht, The Anomalous Magnetic Moments of the Electron and the Muon, Poincaré Seminar (Paris, Oct. In Physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides In Physics, the Landé g-factor is a particular example of a G-factor, namely for an Electron with both spin and Orbital angular In Nuclear magnetic resonance (NMR the chemical shift describes the dependence of nuclear magnetic energy levels on the electronic environment in a Molecule. In Physics, Larmor precession (named after Joseph Larmor) refers to the Precession of the Magnetic moments of Electrons atomic 12, 2002), published in : Duplantier, Bertrand; Rivasseau, Vincent (Eds. ) ; Poincaré Seminar 2002, Progress in Mathematical Physics 30, Birkhäuser (2003), ISBN 3-7643-0579-7.
1. ^ S J Brodsky, V A Franke, J R Hiller, G McCartor, S A Paston and E V Prokhvatilov (2004). "A nonperturbative calculation of the electron's magnetic moment". Nuclear Physics B 703 (1-2): 333-362. doi:10.1016/j.nuclphysb.2004.10.027. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
2. ^ B Odom, D Hanneke, B D'Urso and G Gabrielse (2006). "New measurement of the electron magnetic moment using a one-electron quantum cyclotron". Physical Review Letters 97 (3): 030801. doi:10.1103/PhysRevLett.97.030801. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
3. ^ NIST
4. ^ M A Bernstein, K F King and X J Zhou (2004). Handbook of MRI Pulse Sequences. Elsevier Academic Press, 960. ISBN 0-1209-2861-2.

## gyromagnetic ratio

### -noun

1. (physics) the ratio of the angular momentum to the magnetic moment in an atom etc
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