The effect of magnetic fields

The nonnal threads are called vortices or fluxoids. The currents act so as to repel each other, so that the flux lines form an ordered structure called a fluxon lattice, flux lattice or vortex lattice. At the core of each flux vortex the material is effectively normal, but is surrounded by a region of superconductor. 

The magnetic flux enclosed by a loop of superconductor must be quantised in multiples of hj2e, where h is the Planck constant, and e is the electronic charge. The unit of flux is called the flux quantum, or fluxon, with a value of 2.07 x 10 Wb (T m ). The flux enclosed in any circuit must then be nhjle, with n taking integral values. 

As the magnetic field increases, the amount of normal phase also increases relative to the superconducting part. Ultimately, the flux lines are so close together that no superconducting material exists between them, and the solid becomes normal. The field that finally destroys the superconductivity is the upper critical field, Hd- 

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Fahidy, T.Z. The Effect of Magnetic Fields on Electrochemical Processes 32... 

Figure 2.2 Effect of 180 pulse on phase imperfections resulting from magnetic field inhomogeneities. Spin-echo generated by 180 refocusing pulse removes the effects of magnetic field inhomogeneities.

The Effect of Magnetic Field on Liquid-Crystalline Polymers.238... 

Snider is best known for his paper reporting what is now referred to as the Waldmann-Snider equation.34 (L. Waldmann independently derived the same result via an alternative method.) The novelty of this equation is that it takes into account the consequences of the superposition of quantum wavefunctions. For example, while the usual Boltzmann equation describes the collisionally induced decay of the rotational state probability distribution of a spin system to equilibrium, the modifications allow the effects of magnetic field precession to be simultaneously taken into account. Snider has used this equation to explain a variety of effects including the Senftleben-Beenakker effect (i.e., is, the magnetic and electric field dependence of gas transport coefficients), gas phase NMR relaxation, and gas phase muon spin relaxation.35... 

Bishop has recently been studying the magnetic properties of small systems (including the Cotton-Mouton effect and the Faraday effect), once again providing accurate values with which the experiments can be judged. As well, his concerns with the effects of magnetic fields on vibrations have received widespread attention. 

The effect of magnetic field on a spin - dependent reactions in solids is valid, provided that [7] the time Tpair of particles staying in the paired state must be longer than the time needed for mixing the spin states tev, but shorter than the relaxation time rrei with the value typical for molecular crystals 10 6... 

The application of the reference deconvolution technique to overcome the effect of magnetic field inhomogeneity in high-resolution NMR has recently been reviewed by Metz et al.21 In this technique, the observed resonance lineshape from a single resonance line is used to deconvolve the observed lineshapes to produce the Lorentzian lineshapes associated with liquid samples. 

Although it is not the purpose of this Report to consider magnetic properties in detail, the effect of magnetic fields on the -doubling will be briefly considered because further insight is given into the phenomenon of pure precession. Detailed formulae have been given by Radford.135 138 It is found that gas-phase e.p.r. spectra will yield information about differences in lg values, quantities which depend essentially upon p and q, as well as on two similar constants,... 

Figure 5. Temperature variation of the electrical reislstivity of (a) Pro.e4Cao36Mn03 and (b) Pr036Cao.64Mn03. The effect of magnetic fields is shown.

Figure 9. Effect of 3% Cr3+ doping on (a) the magnetization and (b) the resistivity of Lao,33Cao.33Sro.34Mn03. The effect of magnetic fields on the resistivity is also shown. Insets in a and b show the effect of 3% Ru doping.

It is necessary to caution that the foregoing analysis is a highly idealized one, which has been used primarily to illustrate the effects of magnetic fields on heat transfer. A more realistic analysis would consider the variation of electrical conductivity of the fluid and take into account the exact velocity profile rather than the slug-flow model. A survey of more exact relations for heat transfer in MFD systems is given in Refs. 1 and 2. 

Refs. [i] Fahidy TZ (1999) The effect of magnetic fields on electrochemical processes. In Conway BE, Bockris JO M, White RE (eds) Modern aspects of electrochemistry, vol 32. Kluwer/Plenum, New York, pp 333-354 [ii] Fahidy TZ (2001) Progr Surf Sci 68 155 [Hi] Special issue on magnetic effects in electrochemistry (2007) Solid State Electrochem 11 677-756... 

The rephasing effect of a 180° pulse not only removes the effects of magnetic field inhomogeneities, it also rephases signals from nuclei that differ in precession frequency because of differing chemical shifts, as illustrated in Fig. 9.1. However, if the two magnetizations differ in frequency because of scalar coupling between them, the situation is more complex. 

Consider the formation of a spin echo following a 180° pulse applied to a spin system consisting of two protons, (a) Assume that the protons have the same chemical shift (as in H20, for example). Explain why the echo forms and eliminates the effect of magnetic field inhomogeneity, (b) Assume that the two protons differ in chemical shift but are not spin... 

As a second example, we look at echoes. We saw in Chapter 9 that a 180° pulse refocuses not only chemical shifts and the effects of magnetic field inhomogeneity but also spin coupling provided that the pulse does not also disturb the spin state of the coupled nucleus (see Fig. 9.2) However, in a homonuclear spin system a nonselective pulse does effect spin states. We found in Chapter 7 that dipolar interactions have the same mathematical from as indirect spin coupling, and it is known that a 180° pulse does not produce an echo in a solid because spin states are disturbed. However, it is possible to obtain a solid echo or dipolar echo by applying the pulse sequence 90, T, 90r It is very difficult to rationalize an echo from... 

FIGURE 8.6 The effect of magnetic field strength on the yield of geminate product and radicals escaping the geminate cage for a triplet-horn RP. 

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