Assume that:
*at t = 0 the transverse nuclear magnetization M(0) experiences a constant magnetic field B(t) = (0, 0, B);
*B is positive;
*there are no longitudinal and transverse relaxations (that is T and T → ∞).
Then the Bloch equations are simplified to:
These are two (not coupled) linear differential equations. Their solution is:
Thus the transverse magnetization, M, rotates around the z axis with angular frequency ω = γB in clockwise direction (this is due to the negative sign in the exponent).
The longitudinal magnetization, M remains constant in time. This is also how the transverse magnetization appears to an observer in the laboratory frame of reference (that is to a stationary observer).
M(t) is translated in the following way into observable quantities of M(t) and M(t): Since
then
where Re(z) and Im(z) are functions that return the real and imaginary part of complex number z. In this calculation it was assumed that M(0) is a real number.