Gyromagnetic ratio: Difference between revisions
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The '''gyromagnetic ratio''' (sometimes ''magnetogyric ratio''), <math>\gamma</math>, is the constant of proportionality between the [[magnetic moment]] ( | The '''gyromagnetic ratio''' (sometimes ''magnetogyric ratio''), <math>\gamma</math>, is the constant of proportionality between the [[magnetic moment]] ('''''μ''''') and the [[angular momentum]]('''''J''''') of an object: | ||
:<math> | :<math> | ||
\mu = \gamma | \mathbf {\mu} = \gamma \mathbf{J} \ .</math> | ||
Its [[SI]] units are '''[[radian]] per [[second]] per [[tesla (unit)|tesla]]''' (s<sup>−1</sup>·T<sup> -1</sup>) or, equivalently, '''[[coulomb]] per [[kilogram]]''' (C·kg<sup>−1</sup>). | Its [[SI]] units are '''[[radian]] per [[second]] per [[tesla (unit)|tesla]]''' (s<sup>−1</sup>·T<sup> -1</sup>) or, equivalently, '''[[coulomb]] per [[kilogram]]''' (C·kg<sup>−1</sup>). When the object is placed in a [[magnetic flux density]] '''''B''''', because of its magnetic moment, it experiences a [[torque]] and precesses about the field. | ||
==Examples== | ==Examples== | ||
Revision as of 14:00, 28 March 2011
The gyromagnetic ratio (sometimes magnetogyric ratio), , is the constant of proportionality between the magnetic moment (μ) and the angular momentum(J) of an object:
Its SI units are radian per second per tesla (s−1·T -1) or, equivalently, coulomb per kilogram (C·kg−1). When the object is placed in a magnetic flux density B, because of its magnetic moment, it experiences a torque and precesses about the field.
Examples
The electron gyromagnetic ratio is:[1]
where μe is the magnetic moment of the electron (-928.476 377 x 10-26 J T-1), and ℏ is Planck's constant divided by 2π.
Similarly, the proton gyromagnetic ratio is:[2]
where μp is the magnetic moment of the proton (1.410 606 662 x 10-26 J T-1). Other ratios can be found on the NIST web site.[3]
Notes
- ↑ Electron gyromagnetic ratio. The NIST reference on constants, units, and uncertainty. Retrieved on 2011-03-28.
- ↑ Proton gyromagnetic ratio. The NIST reference on constants, units, and uncertainty. Retrieved on 2011-03-28.
- ↑ A general search menu for the NIST database is found at CODATA recommended values for the fundamental constants. National Institute of Standards and Technology. Retrieved on 2011-03-28.