Dipolar magnetic field

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. 

If quark matter is in the ferromagnetic phase, it may produce the dipolar magnetic field by their magnetic moment. Since the total magnetic dipole moment Mq should be simply given as Mq = fjq (47t/3 rq)nq for the quark sphere with the quark core radius rq and the quark number density nq. Then the dipolar magnetic field at the star surface R takes the maximal strength at the poles,... 

When the nuclear motion is a random proceas, one obtains, for (i), from the theory of random processes (61) the normalized spectral density of the mean square dipolar magnetic field versus frequency (3). The spectral density near a NMR frequency is proportional to the probability of a... 

There is also an intuitive mode to see the effect of an isotropic electron magnetic moment on a nucleus. Fig. 2.7 illustrates that, indeed, the dipolar magnetic field experienced by the nucleus for different orientations of the metal-nucleus vector with the magnetic field changes sign, being positive when the... 

Fig. 2.7. A nucleus N immersed in a dipolar magnetic field of an electron spin, the latter aligned along the external magnetic field, experiences an extra field that adds (6 = 0°) or subtracts (9 = 90°) to the external field.

As the temperature increases, the line width may be reduced by an averaging of the dipolar magnetic field at the nitrogen nuclei when a motion of the neighboring protons takes place 17). 

Any dipolar magnetic field pattern is symmetric with respect to rotations around a particular axis. Hence, it is customary to describe the magnetic dipole moment that creates such a field as a vector with a direction along that axis. The SI units of magnetic moments are thus A m. From Eq. 8.2, the torque experienced by the magnetic moment in the external field is given by the cross product of the magnetic moment and... 

Cyclotrons are also used as heavy-ion sources. In a cyclotron, ions are confined to circular or spiral orbits by a dipolar magnetic field. The ions are accelerated by an alternating electric field projected by a series of plates above and below the orbital plane of the ions. In the simplest case, there are two sets of half-circular plates called "dees , which alternate in polarity to accelerate the ions. 

The effect of k0 is transferred to a higher order where it is negligible. The second contribution involves the internal (dipolar) magnetic field and represents the dipolar hyperfine interaction term... 

For the second possibility, when the internal (dipolar) magnetic field An =, rNe(tLN X Ne)... 

The method can be understood by considering again the magnetic dipolar interaction between the and H nnclei (Figure 2.4). The z component of the dipolar magnetic field prodnced by the H nucleus on the C site is given (in SI units) by [2]... 

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