Magnetic Property Field

To define the thennodynamic state of a system one must specify fhe values of a minimum number of variables, enough to reproduce the system with all its macroscopic properties. If special forces (surface effecls, external fields—electric, magnetic, gravitational, etc) are absent, or if the bulk properties are insensitive to these forces, e.g. the weak terrestrial magnetic field, it ordinarily suffices—for a one-component system—to specify fliree variables, e.g. fhe femperature T, the pressure p and the number of moles n, or an equivalent set. For example, if the volume of a surface layer is negligible in comparison with the total volume, surface effects usually contribute negligibly to bulk thennodynamic properties. 

Not only can electronic wavefiinctions tell us about the average values of all the physical properties for any particular state (i.e. above), but they also allow us to tell us how a specific perturbation (e.g. an electric field in the Stark effect, a magnetic field in the Zeeman effect and light s electromagnetic fields in spectroscopy) can alter the specific state of interest. For example, the perturbation arising from the electric field of a photon interacting with the electrons in a molecule is given within die so-called electric dipole approximation [12] by ... 

By using the property that ions are deflected in a magnetic field in proportion to both the square root of their m/z values and the potential through which they have been accelerated, it is possible to measure the m/z values very accurately. 

The electric fields in such instruments are used to focus the fast-moving ion beam according to the kinetic energies of the ions contained in it. This property allows ions of individual m/z values to be focused sharply before or after deflection in the magnetic field. 

Another important property of electric and magnetic fields is their ability to separate ions according to their individual masses (m, mj,. .., m ) or, more strictly, their mass-to-charge ratio (mj/z, raji,. mjz). 

In the absence of an electric or magnetic field all the functions with f 0 are (2f + l)-fold degenerate, which means that there are (2f + 1) functions, each having one of the (2f + 1) possible values of m, with the same energy. It is a property of degenerate functions that linear combinations of them are also solutions of the Schrddinger equation. For example, just as IJ2p,i solutions, so are... 

Molecules of nematic Hquid crystals also are aligned in flow fields which results in a viscosity that is lower than that of the isotropic Hquid the rod-shaped molecules easily stream past one another when oriented. Flow may be impeded if an electric or magnetic field is appHed to counter the flow orientation the viscosity then becomes an anisotropic property. 

In order to calculate the distribution function must be obtained in terms of local gas properties, electric and magnetic fields, etc, by direct solution of the Boltzmann equation. One such Boltzmann equation exists for each species in the gas, resulting in the need to solve many Boltzmann equations with as many unknowns. This is not possible in practice. Instead, a number of expressions are derived, using different simplifying assumptions and with varying degrees of vaUdity. A more complete discussion can be found in Reference 34. 

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