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In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the volumetric density of permanent or induced electric dipole moments in a dielectric material.
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 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.
A dipole is characterised by its dipole moment, a vector quantity shown in the figure as the blue arrow labeled M. It is the relationship between the electric field and the dipole moment that gives rise to the behaviour of the dielectric. (Note that the dipole moment points in the same direction as the electric field in the figure.
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
A similar parameter exists to relate the magnitude of the induced dipole moment p of an individual molecule to the local electric field E that induced the dipole. This parameter is the molecular polarizability (α), and the dipole moment resulting from the local electric field E local is given by: =
This means that there is no dipole. If an electric field is applied to an insulator, then (for instance) the negative charges can move slightly towards the positive side of the field, and the positive charges in the other direction. This leads to an induced dipole which is described as a polarization.
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.: ...