文档介绍：LECTURE COURSE: NMR SPECTROSCOPY
1. THE PHYSICAL BASIS OF THE NMR EXPERIMENT
Imagine a charge travelling circularily about an axis. This is similar to a current
that flows through a conducting loop:
µ
FIGURE 1.
Such a circular current builds up a ic moment µ whose direction is per-
pendicular to the plane of the conducting loop. The faster the charge travels
the stronger is the induced ic field. In other words, a ic dipole
has been created.
Such dipoles, when placed into a ic field, are expected to align with the
direction of the ic field. In the following we will look at a mechanical
equivalent represented by pass needle that aligns within the gravita-
tional field:
N
φ
FIGURE 2.
When such pass needle is turned away from the north-pole pointing
direction to make an angle φ a force acts on the needle to bring it back. For the
case of a dipole moment that has been created by a rotating charge this force is
proportional to the strength of the field (B) and to the charge (m).
The torque that acts to rotate the needle may be described as
∂J
T ==rF×
∂t
in which J is defined as the angular momentum which is the equivalent for rota-
First Chapter: Physical Basis of the NMR Experiment
LECTURE COURSE: NMR SPECTROSCOPY
tional movements of the linear momentum.
J = r x p
p = m v
FIGURE 3. Left: linear momentum. Right: angular momentum
Excurse: Corresponding parameter for translational and rotational movements
PureTranslation (fixed direction) Pure Rotation (fixed axis)
Position x θ
Velocity v = dx/dt ω=dθ/dt
Acceleration a = dv/dt α= dω/dt
Translational (Rot.) Inertia m I
Force (Torque) F T = r x F
Momentum p = mv J = r x p
Work W = Int F dx W = Int T dθ
ic energy K = 1/2 mv2 K = 1/2 Iω2
Power P = F v P = Τω
Note that the direction of the momentum is tangential to the direction along
which the particle moves. The torque is formed by the vector product between
the radius and the momentum (see additional material) an