Lorenz field

At microscopic scale, a water molecule is subjected to a local electric field, which is the sum between a macroscopic field generated by sources from outside the medium, and a field generated by the other water molecules surrounding it [26]. For a uniformly polarized medium, the latter corresponds to the field generated in a spherical cavity in a medium, due to the polarization of the whole medium (the Lorenz field ZiLorenz = [26]). Therefore, the local field acting on a water... 

In deriving this equation, the effect of the surroundings of a molecule (internal field) is taken into account by assuming that it resides within a spherical cavity (Lorenz field). This assumption can restrict the applicability of this equation. The macroscopic quantity, P, is related to the microscopic quantity, the molecular polarizability (assumed in this case to be isotropic so that a and P are scalar quantities)... 

Here Id sa /yl, 8 determines the correlation energy, X is extrapolation length of the film in paraelectric phase, E is a mean field in a bulk relaxor, d is the effective dipole moment corrected by Lorenz field, e is dielectric permittivity of a host film. 

Continuum models have a long and honorable tradition in solvation modeling they ultimately have their roots in the classical formulas of Mossotti (1850), Clausius (1879), Lorentz (1880), and Lorenz (1881), based on the polarization fields in condensed media [32, 57], Chemical thermodynamics is based on free energies [58], and the modem theory of free energies in solution is traceable to Bom s derivation (1920) of the electrostatic free energy of insertion of a monatomic ion in a continuum dielectric [59], and Kirkwood and Onsager s... 

In 1935, the Kumpan in der Umwelt des Vogels (The companion in the world of birds) came out. Here, Konrad Lorenz presented the first layout of the field which was later to be termed ethology. ... 

One of the main results obtained by Fajans and Joos was the replacement of the old additivity rule for the molar Lorenz-Lorentz refractivity, R, by the following principle R of a given electronic system of an ion, molecule or solvent decreases in the field of adjacent positively charged particles and increases in that of negative particles, i.e. the electronic system becomes tightened in the first case, loosened in the second case. This priciple found innumerable confirmations in a long series of refracto-metric investigations and led to the conclusion that deviations of Rl, l. 

The electromagnetic field defined above is a solution of Maxwell s equations, provided the new potentials . C are solutions of wave equations and satisfy the Lorenz gauge. 

So now we have the question poased in an interesting form. There are two quite different kinds of antennas, both of which produce electric dipole fields, but different Lorenz potentials, one emphasizing the vector potential and the other, the scalar potential. In a classical electromagnetic sense, one cannot distinguish these two cases by measurements of the fields (the measurable quantities) at distances away from the source region. The gauge invariance of QED implies the same in quantum sense. 

Note that as discussed in previous sections, under static conditions, these two antennas give no fields. In going between two static conditions, one can have the same fields at intermediate times, but a change in the electric impulse, this being related to a change in the Lorenz vector potential or to a nonzero time integral of the gradient of the Lorenz scalar potential. However, with no fields, the vector potential has zero curl, which in a QED sense is not measurable. 

So our choices of the two antennas is not unique for separately emphasizing the Lorenz vector and scalar potentials. All that is required is for the two to have the same exterior fields (say, electric dipole fields, or more general multipole fields) with different potentials (related by the gauge condition). In a classical electromagnetic sense, these antennas cannot be distinguished by exterior measurements. This is a classical nonuniqueness of sources. In a QED sense, the same is the case due to gauge invariance in its currently accepted form. 

Lorentz-Lorenz equation). The A , B ,. .. differ from the Ae, BE,. .. by the absence of the permanent dipole terms. At sufficiently high frequencies, the molecules have not sufficient time to reorient themselves in response to the high-frequency electric field and the contributions of the... 

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