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 polarization density ： ウィキペディア英語版
polarization density

In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is said to be polarized. The electric dipole moment induced per unit volume of the dielectric material is called the electric polarization of the dielectric.〔''Introduction to Electrodynamics'' (3rd Edition), D.J. Griffiths, Pearson Education, Dorling Kindersley, 2007, ISBN 81-7758-293-3〕〔''McGraw Hill Encyclopaedia of Physics'' (2nd Edition), C.B. Parker, 1994, ISBN 0-07-051400-3〕
Polarization density also describes how a material responds to an applied electric field as well as the way the material changes the electric field, and can be used to calculate the forces that result from those interactions. It can be compared to magnetization, which is the measure of the corresponding response of a material to a magnetic field in magnetism. The SI unit of measure is coulombs per square meter, and polarization density is represented by a vector P.〔
==Definition==

An external electric field that is applied to a dielectric material, causes a displacement of bound charged elements. These are elements which are bound to molecules and are not free to move around the material. Positive charged elements are displaced in the direction of the field, and negative charged elements are displaced opposite to the direction of the field. The molecules may remain neutral in charge, yet an electric dipole moment forms.〔Irodov, I.E. (1986). ''Basic Laws of Electromagnetism''. Mir Publishers, CBS Publishers & Distributors. ISBN 81-239-0306-5〕〔Matveev. A. N. (1986). ''Electricity and Magnetism''. Mir Publishers.〕
For a certain volume element in the material $\Delta V$, which carries a dipole moment $\Delta\mathbf p$, we define the polarization vector P:
:$\mathbf P = \frac$
In general, the dipole moment $\Delta\mathbf p$ changes from point to point within the dielectric. Hence, the polarization density P of an infinitesimal change dp in the dipole moment for a given change d''V'' in the volume is:
:$\mathbf P= \qquad \left(1\right)$
The net charge appearing as a result of polarization is called bound charge and denoted $Q_b$.

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