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The polarizability of an atom or molecule is defined as the ratio of its induced dipole moment to the local electric field; in a crystalline solid, one considers the dipole moment per unit cell. [1] Note that the local electric field seen by a molecule is generally different from the macroscopic electric field that would be measured externally.
That is, the polarization is a convolution of the electric field at previous times with time-dependent susceptibility given by (). The upper limit of this integral can be extended to infinity as well if one defines χ e ( Δ t ) = 0 {\displaystyle \chi _{\text{e}}(\Delta t)=0} for Δ t < 0 {\displaystyle \Delta t<0} .
The dipole moment density of the array p(r) contains both the location of the array and its dipole moment. When it comes time to calculate the electric field in some region containing the array, Maxwell's equations are solved, and the information about the charge array is contained in the polarization density P(r) of Maxwell's
The total density of induced polarization is the product of the number density of molecules multiplied by the dipole moment of each molecule, i.e.: ...
Electric polarization of a given dielectric material sample is defined as the quotient of electric dipole moment (a vector quantity, expressed as coulombs*meters (C*m) in SI units) to volume (meters cubed). [1] [2] Polarization density is denoted mathematically by P; [2] in SI units, it is expressed in coulombs per square meter (C/m 2).
The electric displacement field "D" is defined as +, where is the vacuum permittivity (also called permittivity of free space), and P is the (macroscopic) density of the permanent and induced electric dipole moments in the material, called the polarization density.
The size of the induced dipole moment is equal to the product of the strength of the external field and the dipole polarizability of ρ. Dipole moment values can be obtained from measurement of the dielectric constant. Some typical gas phase values given with the unit debye are: [7] carbon dioxide: 0; carbon monoxide: 0.112 D; ozone: 0.53 D
The molecule induces polarization in this media which in turn creates a reaction field, sometimes called the Onsager reaction field. Although Onsager 's name is often attached to the technique, because he considered such a geometry in his theory of the dielectric constant, [ 1 ] the method was first introduced by Barker and Watts in 1973.