Field magnetization 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... 

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. 

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.

The transverse magnetization and the applied radiofrequency field will therefore periodically come in phase with one another, and then go out of phase. This causes a continuous variation of the magnetic field, which induces an alternating current in the receiver. Furthermore, the intensity of the signals does not remain constant but diminishes due to T and T2 relaxation effects. The detector therefore records both the exponential decay of the signal with time and the interference effects as the magnetization vectors and the applied radiofrequency alternately dephase and re-... 

Magnetization vector (M) The resultant of individual magnetic moment vectors for an ensemble of nuclei in a magnetic field. 

The integral is taken along a trajectory I parallel to the optical axis, passing inside and outside the specimen, and which must include stray fields V(f, z) and Az(r, z) are the electrostatic potential and the z component of the magnetic vector potential A(f,z), respectively E a factor that becomes the accelerating voltage in the non-relativistic... 

The time dependence of the magnetization vector, M(t), is thus related to the cross-product of M and B. Keep in mind also that the magnetic field can be time-dependent. We have replaced B0 by B to indicate that the magnetic field can consist... 

Fig. 1.2 Behavior of the magnetization in a simple echo experiment. Top a free induction decay (FID) follows the first 90° pulse x denotes the phase of the pulse, i.e., the axis about which the magnetization is effectively rotated. The 180° pulse is applied with the same phase the echo appears at twice the separation between the two pulses and its phase is inverted to that of the initial FID. Bottom the magnetization vector at five stages of the sequence drawn in a coordinate frame rotating at Wo about the z axis. Before the 90° pulse, the magnetization is in equilibrium, i.e., parallel to the magnetic field (z) immediately aftertbe 90° pulse, it has been rotated (by90° ) into the transverse (x,y) plane as it is com-...

Magnetization vector M(B) for specified directions of external magnetic field B... 

If the foregoing created the impression that the electric and magnetic vectors of a propagating electromagnetic field are confined to vibrate in fixed planes, that was unintentional. A field like that would be plane polarized and to create that requires a special device known as a polarizer. Ordinary unpolarized light consists of an array of plane waves that are randomly oriented with respect to a plane perpendicular to the directions of propagation. 

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