Bloch equations

Bloch equation describes evolution of classical magnetic moment in the magnetic field. The equation in the absence of T1 and T2 relaxation is:

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

Summary explanation

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 in quantum mechanics proves that particle's magnetic moment is collinear with it's angular moment so that:

$\displaystyle M = \gamma J$ ,

where γ is the scalar quantity called gyromagnetic ratio of the particle.

Therefore we have expression (known as Bloch Equation):

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