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Concept
Electric displacement field
Summary
In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field, combining the two in an auxiliary field. It plays a major role in topics such as the capacitance of a material, as well the response of dielectrics to electric field, and how shapes can change due to electric fields in piezoelectricity or flexoelectricity as well as the creation of voltages and charge transfer due to elastic strains.
In any material, if there is an inversion center then the charge at, for instance, and are the same. This means that there is no dipole. If an electric field is applied to an insulator, then (for instance) the -ve charges can move slightly towards the +ve side of the field, and the +ve charges in the other direction. This leads to an induced dipole which is described as a polarization. There can be slightly different movements of the negative electrons and positive nuclei in molecules, or different displacements of the atoms in an ionic compound. Materials which do not have an inversion center display piezoelectricity and always have a polarization; in others spatially varying strains can break the inversion symmetry and lead to polarization, the flexoelectric effect. Other stimuli such as magnetic fields can lead to polarization in some materials, this being called the magnetoelectric effect.
The electric displacement field "D" is defined aswhere is the vacuum permittivity (also called permittivity of free space), and P is the (macroscopic) density of the permanent and induced electric dipole moments in the material, called the polarization density.
The displacement field satisfies Gauss's law in a dielectric:
In this equation, is the number of free charges per unit volume. These charges are the ones that have made the volume non-neutral, and they are sometimes referred to as the space charge. This equation says, in effect, that the flux lines of D must begin and end on the free charges.
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