Editing Polarization density (section)

==Definition==

An external electric field that is applied to a dielectric material, causes a displacement of bound charged elements.

A '''''bound charge''''' is a charge that is associated with an atom or molecule within a material. It is called "bound" because it is not free to move within the material like '''''free charges'''''. 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.<ref name="Irodov">{{ cite book | author1-link = Igor Irodov | last = Irodov | first = I.E. | year = 1986 | title = Basic Laws of Electromagnetism | publisher = Mir Publishers, CBS Publishers & Distributors | isbn = 81-239-0306-5 }}</ref><ref name="Matveev">{{ cite book | last = Matveev | first = A. N. | year = 1986 | title = Electricity and Magnetism | publisher = Mir Publishers }}</ref>

For a certain volume element <math>\Delta V</math> in the material, which carries a dipole moment <math>\Delta\mathbf p</math>, we define the polarization density {{math|'''P'''}}:
<math display="block">\mathbf P = \frac{\Delta\mathbf p}{\Delta V}</math>

In general, the dipole moment <math>\Delta\mathbf p</math> changes from point to point within the dielectric. Hence, the polarization density {{math|'''P'''}} of a dielectric inside an infinitesimal volume d''V'' with an infinitesimal dipole moment {{math|d'''p'''}} is:
{{NumBlk||<math display="block">\mathbf P = \frac{\mathrm d\mathbf p}{\mathrm d V} </math>|{{EquationRef|1}}}}

The net charge appearing as a result of polarization is called bound charge and denoted <math>Q_b</math>.

This definition of polarization density as a "dipole moment per unit volume" is widely adopted, though in some cases it can lead to ambiguities and paradoxes.<ref name=def_P_M_Maxwell_eqs>{{Cite journal |author = C.A. Gonano |author2 = R.E. Zich | author3 = M. Mussetta |title = Definition for Polarization P and Magnetization M Fully Consistent with Maxwell's Equations |journal = Progress in Electromagnetics Research B |volume = 64 |pages= 83–101 |year = 2015 |doi = 10.2528/PIERB15100606 |url= http://www.jpier.org/PIERB/pierb64/06.15100606.pdf | doi-access = free }}</ref>