For a strong and rectangular RF-pulse of constant amplitude (B1) and duration (tp), the resultant flip angle (α) is approximately proportional to the frequency (f1) of the B1 field:
Here is a solved problem that may help show how these equations may be used:
Question: Suppose we are performing conventional ¹H MRI in a scanner where the B1 field has magnitude of 1μT. How long should this RF field be applied to flip M by 180°?
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The above equation for excitation flip angle is valid only in for relatively small angles (α<30°) and for spins close to the central resonance frequency of the RF-pulse. The equation falls apart for angles much greater than 90° where the Bloch equations behave non-linearly.
Wang J, Mao W, Qiu M et al. Factors influencing flip angle mapping in MRI: RF-pulse shape, slice-select gradients, off-resonance excitation, and Bo inhomogeneities. Magn Reson Med 2006; 56(2):463-468.
How does B1 tip the net magnetization (M)?