Gyromagnetic ratio: Difference between revisions

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:<math>
:<math>
\mu = \gamma I \ .</math>
\mu = \gamma I \ .</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>). The ''electron'' gyromagnetic ratio is:<ref name=NIST0>
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>).  
 
==Examples==
The ''electron'' gyromagnetic ratio is:<ref name=NIST0>


{{cite web |title=Electron gyromagnetic ratio  |url=http://physics.nist.gov/cgi-bin/cuu/Value?eqgammae|search_for=gyromagnetic+ratio |work=The NIST reference on constants, units, and uncertainty |accessdate=2011-03-28}}
{{cite web |title=Electron gyromagnetic ratio  |url=http://physics.nist.gov/cgi-bin/cuu/Value?eqgammae|search_for=gyromagnetic+ratio |work=The NIST reference on constants, units, and uncertainty |accessdate=2011-03-28}}
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:<math> \gamma_{\rm e} = 2|\mu_{\rm e}|/\hbar  = \mathrm{ 1.760\ 859\ 770\ \times \ 10^{11}\ s^{-1} T^{-1} }\ , </math>
:<math> \gamma_{\rm e} = 2|\mu_{\rm e}|/\hbar  = \mathrm{ 1.760\ 859\ 770\ \times \ 10^{11}\ s^{-1} T^{-1} }\ , </math>


where ''&mu;<sub>e</sub>'' is the [[magnetic moment]] of the electron (-928.476 377 x 10<sup>-26</sup> J T<sup>-1</sup>), and ℏ is [[Planck's constant]] divided by 2&pi;. Similarly, the ''proton'' gyromagnetic ratio is:<ref name=NIST1>
where ''&mu;<sub>e</sub>'' is the [[magnetic moment]] of the electron (-928.476 377 x 10<sup>-26</sup> J T<sup>-1</sup>), and ℏ is [[Planck's constant]] divided by 2&pi;.  
 
Similarly, the ''proton'' gyromagnetic ratio is:<ref name=NIST1>


{{cite web |title=Proton gyromagnetic ratio  |url=http://physics.nist.gov/cgi-bin/cuu/Value?eqgammap|search_for=gyromagnetic+ratio |work=The NIST reference on constants, units, and uncertainty |accessdate=2011-03-28}}
{{cite web |title=Proton gyromagnetic ratio  |url=http://physics.nist.gov/cgi-bin/cuu/Value?eqgammap|search_for=gyromagnetic+ratio |work=The NIST reference on constants, units, and uncertainty |accessdate=2011-03-28}}

Revision as of 14:52, 28 March 2011

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The gyromagnetic ratio (sometimes magnetogyric ratio), , is the constant of proportionality between the magnetic moment () and angular momentum() of a particle:

Its SI units are radian per second per tesla (s−1·T -1) or, equivalently, coulomb per kilogram (C·kg−1).

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

  1. Electron gyromagnetic ratio. The NIST reference on constants, units, and uncertainty. Retrieved on 2011-03-28.
  2. Proton gyromagnetic ratio. The NIST reference on constants, units, and uncertainty. Retrieved on 2011-03-28.
  3. 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.