Bloch equations

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Bloch equation describes evolution of classical magnetic moment in the magnetic field.

A particle with a magnetic moment M in the magnetic field B will experience change of its mechanical angular moment J, i.e. torque = dJ/dt.

$\frac{dJ}{dt} = M(t) \times B(t)$

Wigner-Eckart theorem proves that particle's magnetic moment is collinear with it's angular moment so that:

$M = γ J$ ,

where γ is the gyromagnetic ratio of the particle.