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3.1 Magnetic Field and Magnetization
of the magnetic moments
the complete magnetization is then given by
∂⃗µ
∂t = γ⃗µ × ⃗ B 0 (3.5)
µ xy = µ xy (0) · e −iγB 0t
(3.6)
µ z = µ z (0),
assuming that B ⃗ 0 points along the z-direction. This magnetization is called bulk magnetization.
Consequently, only the magnetization in z-direction is fixed whereas the magnetization
in xy-direction relates with the angular frequency γB 0 . A common term to
say is that the magnetization precesses with the Larmor-frequency around the magnetic
field-vector B 0 . This precession frequency, also known as the natural resonance
frequency of a spin system, is given by the Larmor equation and illustrated in figure
3.2:
ω 0 = γB 0 (3.7)
f 0 = γB 0 (3.8)
The remaining part to think about is, how much of this directional magnetization
can be used for experiments. The following considerations will lead to a possible bulk
magnetization
∑N s
⃗M = ⃗µ n (3.9)
n=1
of a given huge number of H 1 nuclei, such as contained for example in a small part of
tissue.
Since the magnetic moments can set up both parallel and anti-parallel to B 0 , most
of them will be nullified.
The energy of a spin state is given by
E = −⃗µ · ⃗B 0 = −µ z B 0 = −γm I B 0 (3.10)
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