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>). | 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> | ||
{{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}} | |||
</ref> | |||
:<math> \gamma_{\rm e} = 2|\mu_{\rm e}|/\hbar = \mathrm{ 1.760\ 859\ 770\ \times \ 10^{11}\ s^{-1} T^{-1} }\ , </math> | |||
where ''μ<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 2π. Similarly, the ''proton'' gyromagnetic ratio is:<ref name=NIST1> | |||
{{cite web |title=electron 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}} | |||
</ref> | |||
:<math> \gamma_{\rm p} = 2\mu_{\rm p}/\hbar = \mathrm{ 2.675\ 222\ 099\ \times \ 10^{11}\ s^{-1} T^{-1} }\ , </math> | |||
where ''μ<sub>p</sub>'' is the [[magnetic moment]] of the proton (1.410 606 662 x 10<sup>-26</sup> J T<sup>-1</sup>). Other ratios can be found on the NIST web site.<ref name=NIST2> | |||
A general search menu for the NIST database is found at {{cite web |title=CODATA recommended values for the fundamental constants |url=http://physics.nist.gov/cuu/Constants/index.html |accessdate 2011-03-28 |publisher= [[National Institute of Standards and Technology]]}} | |||
</ref> | |||
==Notes== | ==Notes== | ||
<references/> | <references/> | ||
Revision as of 14:35, 28 March 2011
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). 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.
- ↑ electron 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.