Induced magnetic fields

The intensity of the magnetic field produced by eddy current is depended on electrical conductivity and magnetic permeability of the studied area. In case of a uniform structure, when the conductivity of the material is high, the intensity of the induced magnetic field is big and signal received by probe Hp is small. 

Structure defects decrease conductivity of the studied material, and then the intensity of the induced magnetic field is small and the signal received by the probe Hp is big (Fig.2). Low conductivity of austenite is a defects of the structure in case of residual austenite in the martensite structure, which with regard to the magnesite structure is as 1 5. Eddy currents produced in the studied area are subject to excitation in effect of small conductivity of austenite grains in the structure of the studied material. 

The first equation (1) is the equation of state and the second equation (2) is derived from the measurement process. Finally, G5 (r,r ) is a row-vector that takes the three components of the anomalous ciurent density vector Je (r) = normal component of the induced magnetic field. This system is non hnear (bilinear) because the product of the two unknowns /(r) and E(r) is present. 

FIGURE 13 6 The induced magnetic field of the elec trons in the carbon-hydrogen bond opposes the external magnetic field The resulting magnetic field ex perienced by the proton and the carbon is slightly less than Xr,... 

Acetylenic hydrogens are unusual in that they are more shielded than we would expect for protons bonded to sp hybridized carbon This is because the rr electrons circulate around the triple bond not along it (Figure 13 9a) Therefore the induced magnetic field is parallel to the long axis of the triple bond and shields the acetylenic proton (Figure 13 9b) Acetylenic protons typically have chemical shifts near 8 2 5... 

FIGURE 13 8 The induced magnetic field of the tt elec trons of (a) an alkene and (b) an arene reinforces the applied field in the regions where vinyl and aryl protons are located... 

FIGURE 13 9 (a) The TT elec trons of acetylene circulate in a region surrounding the long axis of the molecule (b) The induced magnetic field associated with the tt electrons opposes the applied field and shields the protons... 

FIGURE 13 10 More shielded (red) and less shielded (blue) protons in (a) [18]annulene and (b) [16]annulene The induced magnetic field associated with the aromatic ring current in [18]annulene shields the inside protons and deshields the out side protons The opposite occurs in [16]annulene which is antiaromatic... 

G) The induced magnetic field associated with the tt electrons opposes the applied field and shields the protons. 

Figure 15.14 The origin of aromatic ring-current. Aromatic protons are deshielded by the induced magnetic field caused by delocalized tt electrons circulating in the molecular orbitals of the aromatic ring.

Induced magnetic field because of ring current... 

Focussing on terms linear in the applied field B, the induced magnetic field at the field point R obtains as the expectation value of B "(R, Ro,B) with respect to the first order wave function corresponding to eq.(6), yielding... 

Diamagnetism Substances that have no unpaired electrons are diamagnetic. When placed in an applied magnetic field, their induced magnetic fields oppose the applied magnetic field. 

Parami netism Magnetic behavior of nuclei that contain unpaired electrons. When such substances are placed in a magnetic field, the induced magnetic field is parallel to the applied magnetic field. 

The goal of the calculation is, therefore, to compute the strength of the induced magnetic field in space, relative to the strength of the external one. Because one of the main assumptions is that all fields are small on the typical energy scale of atoms or molecules, this calculation can be performed in the framework of perturbation theory. 

When the electronic current density j(r) has been calculated, the Biot-Savart law for the induced magnetic field reads ... 

We have not considered the electromagnetic interaction between quarks and the induced magnetic field. It would be interesting to see how the situation... 

FIGURE 7.4 Microcoil CE-NMR spectra of triethylamine methyl peak in 1 M borate buffer with increasing applied voltage 0.0-9.0 kV by increments of 1.0 kV. Inset is a schematic of electrophoretic current-induced magnetic field. (Reproduced from Jayawickrama, D. A., Sweedler, J. V. J. Chromatogr. A 2003, 1000, 819-840, with permission from Elsevier.)... 

When k E O and x E = 0, there is a purely longitudinal S wave without a magnetic field. Thus x E = 0 and x C = 0 due to Eq. (48). The dispersion relation and the phase and group velocities are the same as (51) for the EM wave. The field vectors E and C are parallel with the wave normal. Possibly this mode may form a basis for telecommunication without induced magnetic fields. 

Let us consider a group of identical nuclei with a spin number I = 1/2. In the absence of an external field, the vector orientation of individual spins will be random and will vary constantly. These nuclei form a population that is considered a degenerate state (Fig. 9.2). When these nuclei are placed in a strong, induced magnetic field B0 (Oz orientation), an interaction between each vector and the magnetic field will be generated (cf. 9.2). 

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