Polarization density

Polarization density is the electric dipole moment per unit volume in a material. It is a vector field whose magnitude and direction describe the material’s local polarization.

Electric dipole moment: A measure of the separation and strength of positive and negative electric charge. Polarization density is the local dipole moment divided by volume.
Dipole: A system with separated positive and negative charges, characterized by a dipole moment. Microscopic dipoles are the building blocks whose moments contribute to polarization density.
Dielectric: An electrical insulator that polarizes in an electric field and alters the field within it. Its response is described macroscopically by polarization density.
Free charge: Electric charge that can move independently through a material or be supplied externally. Free charge is distinct from bound charge arising from polarization.
Bound charge: Electric charge associated with the polarization of matter rather than freely mobile charge. Spatial changes in polarization density produce bound volume charge.
Vector field: A function that assigns a vector to every point in a region of space. Polarization density assigns a direction and magnitude throughout a material.
Capacitance: A measure of a system’s ability to store electric charge per applied potential difference. Polarization within a capacitor dielectric changes the charge and voltage relation.
Magnetization: The magnetic dipole moment per unit volume in a material. Magnetization is the magnetic analogue of electric polarization density.
Electric displacement field: A macroscopic vector field that combines the electric field with the material’s polarization. It separates free charge from polarization’s bound-charge contribution in Maxwell’s equations.
Volume density: A quantity measured per unit volume, describing its spatial distribution in three dimensions. The defining normalization divides dipole moment by material volume.

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