Gyromagnetic ratio

The gyromagnetic ratio (sometimes magnetogyric ratio), $\gamma$, is the constant of proportionality between the magnetic moment (μ) and the angular momentum(J) of an object:

${\boldsymbol {\mu }}=\gamma \mathbf {J} \ .$

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:

$\gamma _{\rm {e}}=2|\mu _{\rm {e}}|/\hbar =\mathrm {1.760\ 859\ 770\ \times \ 10^{11}\ s^{-1}T^{-1}} \ ,$

where μ_e 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:

$\gamma _{\rm {p}}=2\mu _{\rm {p}}/\hbar =\mathrm {2.675\ 222\ 099\ \times \ 10^{11}\ s^{-1}T^{-1}} \ ,$

where μ_p 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.