Bloch equations
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- | Bloch equation describes evolution of classical magnetic moment in the magnetic field. The equation is: | + | Bloch equation describes evolution of classical magnetic moment in the magnetic field. The equation in the absence of [[T1]] and [[T2]] relaxation is: |
<math>\frac{dM}{dt} = M(t) \times \gamma B(t)</math> | <math>\frac{dM}{dt} = M(t) \times \gamma B(t)</math> |
Revision as of 01:48, 7 July 2009
Bloch equation describes evolution of classical magnetic moment in the magnetic field. The equation in the absence of T1 and T2 relaxation is:
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.
Wigner-Eckart theorem in quantum mechanics proves that particle's magnetic moment is collinear with it's angular moment so that:
,
where γ is the scalar quantity called gyromagnetic ratio of the particle.
Therefore we have expression (known as Bloch Equation):