Magnetic field vectors

TRIFOU is a combined Finite Elements/Boundary Integral formulation code. The BIM formulation in vacuum is suitable for NDT simulation where the probe moves in the air around the test block. The FEM formulation needs more calculation time, but tetrahedral elements enable a large variety of specimens and defect geometries to be modelled. TRIFOU uses a formulation of Maxwell Equations using magnetic field vector h, where h is decomposed as h = hs + hr (hj source field, and hr reaction field). 

Show that we can check the magnitude of the magnetic field vector and correct for an axial field due to the drill collars. 

Compute the dip angle of the magnetic field vector after correction for the drill collar field, it should check with the local magnetic field data. What do you conclude if it does not ... 

The accuracy of MWD directional measurements is generally much better than the single- or multishot-type measurements since the sensors are more advanced and the measurements more numerous. The azimuth measurement is made with the three components of the earth magnetic field vector and only with the horizontal component in the case of the single shot or multishot. The accelerometer measurements of the inclination are also more accurate whatever the value of the inclination. The average error in the horizontal position varies from... 

Bi Oscillating magnetic field vector of the f, fg, fmol Femto (10 15) femtogram, femtomole... 

The magnetic field vector in that coordinate system is ... 

Here, 0 is the angle between the magnetic field vector and the unique symmetry axis. Any anisotropy in the g value is assumed to be small compared to the zero field splitting effects. For Cr3+, which is characterized by S = , and mB = f, , — J, — the polycrystalline spectrum has the shape indicated in Fig. 18 (39). An example of the polycrystalline spectrum for the S = 1 case in which both D and E are nonzero is shown in Fig. 19 (40). A numerical evaluation of D and E may be made from the structure indicated in the spectrum. 

The significance of the terms in the g tensor can best be illustrated by means of a simple example. Let us redefine our coordinates such that the spin is quantized along the z axis. The magnetic field vector is now at some different position in space as shown in Fig. 11. Expanding the Hamiltonian in Eq. (1C) gives,... 

Figure 6.4 shows the magnetic field vector B in the molecular Cartesian axes system xyz whose orientation is defined by the polar angles 0 (between B and z) and < ) (between the projection of B on the x-y plane and x). The third dimension of the... 

FIGURE 6.4 Vectors to describe a walk on the unit sphere. The orientation of a vector b of unit length along the dipolar magnetic field vector B in a Cartesian molecular axes system xyz is defined by the two polar angles 9 between b and the z-axis, and cp between the projection of b on the x-y plane and the x-axis. 

Figure 1, Representation of the geometric arrangement for a sample spinning at the magic angle to the magnetic field vector H0. (Reproduced with permission from Ref, 40, Copyright 1982, Royal Society of London,)...

The electromagnetic field in free space is described by the electric field vector E and the magnetic field vector H, which in the absence of charges satisfy Maxwell s equations... 

The nonvanishing components of the tensors y a >--eem and ya >-mee can be determined by applying the symmetry elements of the medium to the respective tensors. However, in order to do so, one must take into account that there is a fundamental difference between the electric field vector and the magnetic field vector. The first is a polar vector whereas the latter is an axial vector. A polar vector transforms as the position vector for all spatial transformations. On the other hand, an axial vector transforms as the position vector for rotations, but transforms opposite to the position vector for reflections and inversions.9 Hence, electric quantities and magnetic quantities transform similarly under rotations, but differently under reflections and inversions. As a consequence, the nonvanishing tensor components of x(2),eem and can be different... 

Electromagnetic radiation consists of an electric vector E directed atong the displacement direction of the wave. The associated magnetic field vector H, lies perpendicular to the electric vector and perpendicular to the direction of propagation. The oscillations of the two fields are given by... 

An ion with charge ze and velocity v traveling perpendicular to a magnetic field B experiences a force z.exB that is perpendicular to both the velocity vector and the magnetic field vector. This force deflects the ion through a circular path of radius r. The centripetal force (mx2/r) required to deflect the particle is provided by the magnetic field. 

Besides its appearance in the FFMF equation in plasma physics, as well as associated with time-harmonic fields in chiral media, the chiral Beltrami vector field reveals itself in theoretical models for classical transverse electromagnetic (TEM) waves. Specifically, the existence of a general class of TEM waves has been advanced in which the electric and magnetic field vectors are parallel [59]. Interestingly, it was found that for one representation of this wave type, the magnetic vector potential (A) satisfies a Beltrami equation ... 

In terms of these vectors the electric and magnetic field vectors are expressed as... 

The absolute value of the transverse magnetization component at any angle ip (0 < < 10°) is of such a value, that the total-magnetization vector coincides with the magnetic field vector H. Hence, there are no magnetization components normal to H at any values of the intensity H and the angle ip. 

On the other hand, when rotational motion is slow, or when the symmetry of the complex is less than cubic, as in Mn2+ complexes with macromolecules, Au)Xr is often greater than one, the anisotropic interactions are incompletely averaged and EPR spectra similar to those for randomly oriented solid samples are observed. In these cases the spectra depend upon the angular relationships between the magnetic field vector and the crystal field axis of the ion. Moreover, when the symmetry of the manganese ion complexes deviate greatly from cubic, the EPR spectra depend upon the sharing of spectral intensity between the normal and forbidden (AMS = + 1, Amp = + 1) transitions. 

The electric and magnetic field vectors in vacuo are, respectively,... 

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