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The Lorentz–Lorenz equation is similar to the Clausius–Mossotti relation, except that it relates the refractive index (rather than the dielectric constant) of a substance to its polarizability. The Lorentz–Lorenz equation is named after the Danish mathematician and scientist Ludvig Lorenz , who published it in 1869, and the Dutch ...
By using elementary electrostatics, we get for a spherical inclusion with dielectric constant and a radius a polarisability : = (+) If we combine with the Clausius Mosotti equation, we get: (+) = (+) Where is the effective dielectric constant of the medium, of the inclusions; is the volume fraction of the inclusions.
Ericson-Ericson Lorentz-Lorenz correction, also called the Ericson-Ericson Lorentz-Lorenz effect (EELL), refers to an analogy in the interface between nuclear, atomic and particle physics, which in its simplest form corresponds to the well known Lorentz-Lorenz equation (also referred to as the Clausius-Mossotti relation) for electromagnetic waves and light in a refractive medium.
The factor in curly brackets is known as the complex Clausius-Mossotti function [2] [4] [5] and contains all the frequency dependence of the DEP force. Where the particle consists of nested spheres – the most common example of which is the approximation of a spherical cell composed of an inner part (the cytoplasm) surrounded by an outer layer ...
The factor (κ − 1)/(κ + 2) is called the Clausius–Mossotti factor and shows that the induced polarization flips sign if κ < 1. Of course, this cannot happen in this example, but in an example with two different dielectrics κ is replaced by the ratio of the inner to outer region dielectric constants, which can be greater or smaller than one.
This discrepancy is taken into account by the Clausius–Mossotti relation (below) which connects the bulk behaviour (polarization density due to an external electric field according to the electric susceptibility =) with the molecular polarizability due to the local field.
This has a similar form to the Clausius–Mossotti relation: [7] = () () = () This frequency dependence of the susceptibility leads to frequency dependence of the permittivity. The shape of the susceptibility with respect to frequency characterizes the dispersion properties of the material.
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