The role of the polarization density P is described below.

First is some discussion of the polarization density P(r).

This is called polarization density of the material.

The field of nonlinear optics studies the changes to material polarization density under extreme electric fields.

This simply means that in this class of materials the polarization density is always parallel to the applied electric field.

At the same time, the electric displacement D is related to the polarization density P by:

The polarizability of individual particles in the medium can be related to the average susceptibility and polarization density by the Clausius-Mossotti relation.

If observation is confined to regions sufficiently remote from a system of charges, a multipole expansion of the exact polarization density can be made.

Assuming the medium is linear, isotropic, and homogeneous (see polarization density), we have the constitutive equation:

Then we have (generally) and , where P and M are polarization density and magnetization vectors.

The polarization density P is defined as the average electric dipole moment d per unit volume V of the dielectric material:

The positive and negative charges in molecules separate under the applied field, causing an increase in the state of polarization, expressed as the polarization density 'P'.

The SI unit of measure is coulombs per square metre, and polarization density is represented by a vector P.

In particular, truncating the expansion at the dipole term, the result is indistinguishable from the polarization density generated by a uniform dipole moment confined to the charge region.

The electric field (E) at an event is the derivative of the action of the electromagnetic field with respect to the electric polarization density at that event.

Electric susceptibility is defined as the constant of proportionality (which may be a tensor) relating an electric field E to the induced dielectric polarization density P such that:

The electric field can be properly determined by using the above relation along with other boundary conditions on the polarization density yielding the bound charges, which will, in turn, yield the electric field.

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.

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.

By convention, the electric constant ε appears in the relationship that defines the electric displacement field D in terms of the electric field E and classical electrical polarization density P of the medium.

In general, χ is seen as a matrix that is applied to E. This class of dielectrics where the polarization density and the electric field are not in the same direction is known as anisotropic materials.

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 equations.