Magnetic vector

Maxwell s equation are the basis for the calculation of electromagnetic fields. An exact solution of these equations can be given only in special cases, so that numerical approximations are used. If the problem is two-dimensional, a considerable reduction of the computation expenditure can be obtained by the introduction of the magnetic vector potential A =VxB. With the assumption that all field variables are sinusoidal, the time dependence... 

The concept of relaxation time was introduced to the vocabulary of NMR in 1946 by Bloch in his famous equations of motion for nuclear magnetization vector M [1] ... 

Magnetic vector potential A Mole fraction, condensed X... 

At equilibrium, the transverse magnetization equals zero. A net magnetization vector rotated off the -axis creates transverse magnetization. 

Figure 3 describes for nine magnetization vectors the effect of the appHcation of a phase-encoding gradient, G, and a frequency-encoding gradient, G. ... 

Equation (4-53) describes the precession of the magnetization vector about the field vector with angular frequency yHo, in the absence of the rotating field W, (see Fig. 4-4A). 

The quantitative formulation of chemical exchange involves modification of the Bloch equations making use of Eq. (4-67). We will merely develop a qualitative view of the result." We adopt a coordinate system that is rotating about the applied field Hq in the same direction as the precessing magnetization vector. Let and Vb be the Larmor precessional frequencies of the nucleus in sites A and B. Eor simplicity we set ta = tb- As the frequency Vq of the rotating frame of reference we choose the average of Va and Vb, thus. 

As a consequence, from the point of view of this rotating frame, a nucleus at site A precesses at frequency (vq i a). whereas a nucleus at site B precesses at frequency (vb — vo) that is, the two nuclei (actually their magnetization vectors) precess in opposite directions. We imagine several possible cases. 

In the presence of Hq but the absence of H, a steady state is established, the magnetization vector having component Mq along the z axis, but because of symmetry owing to randomization there is no net magnetization in the x y plane. This situation is shown in Fig. 4-9A. 

Figure 4-9. (Ai Precessing moment vectors in field tfo creating steady-state magnetization vector Afo. with//i = 0. (B) Immediately following application of a 90° pulse along the x axis in the rotating frame. (C) Free induction decay of the induced magnetization showing relaxation back to the configuration in A.

I mentioned above the magnetic vector potential A. This is given in the static case by... 

Figure 1.13 (a) Bulk magnetization vector, M°, at thermal equilibrium, (b) Magnetization vector after the application of a radiofrequency pulse. 

Figure 1.14 Effect of radiofrequency pulses of different durations on the position of the magnetization vector.

Figure 1.18 Effect of applying a 90° pulse on the equilibrium magnetization Continuous application of a pulse along the x -axis will cause the magnetization vector (Ml) to rotate in the y z-plane. If the thumb of the right hand points in the direction of the applied pulse, then the partly bent fingers of the right hand point in the direction in which the magnetization vector will be bent.

Figure 1.19 Applying a 90°, pulse will bend the magnetization vector lying along the —y -axis to the —z-axis, while continued application of the pulse along the x -axis will cause the magnetization to rotate in y zrplane.

Based on the right-hand thumb rule described in the text, and assuming that only an equilibrium magnetization directed along the z-axis exists, draw the positions of the magnetization vectors after the application of ... 

After the 90° pulse is applied, all the magnetization vectors for the different types of protons in a molecule will initially come to lie together along the y -axis. But during the subsequent time interval, the vectors will separate and move away from the y -axis according to their respective precessional frequencies. This movement now appears much slower than that apparent in the laboratory frame since only the difference between the... 

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