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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
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.  
For a certain volume element in the material, which carries a dipole moment , we define the polarization density P:
In general, the dipole moment changes from point to point within the dielectric. Hence, the polarization density P of a dielectric inside an infinitesimal volume dV with an infinitesimal dipole moment dp is:
The net charge appearing as a result of polarization is called bound charge and denoted .
This definition of polarization as a "dipole moment per unit volume" is widely adopted, though in some cases it can lead to ambiguities and paradoxes.