Dielectrics in static electric fields

When an electric field is applied to an ideal dielectric material there is no long-range transport of charge but only a limited rearrangement such that the dielectric acquires a dipole moment and is said to be polarized. Atomic polarization, which occurs in all materials, is a small displacement of the electrons in an atom relative to the nucleus in ionic materials there is, in addition, ionic polarization involving the relative displacement of cation and anion sublattices. Dipolar materials, such as water, can become polarized because the applied electric field orients the molecules. Finally, space charge polarization involves a limited transport of charge carriers until they are stopped 

In its most elementary form an electric dipole comprises two equal and opposite point charges separated by a distance 5x. The dipole moment p of the dipole, defined as 

A polarized material can be regarded as made up of elementary dipolar prisms, the end faces of which carry surface charge densities of +(7P and —av as shown in Fig. 2.26. The dipole moment per unit volume of material is termed the polarization P and can vary from region to region. From Fig. 2.26 the magnitudes of the vectors are given by 

In general np = n.P where n is the unit vector normal to the surface enclosing the polarized material and directed outwards from the material. 

Important relationships can be developed by considering the effect of filling the space between the plates of a parallel-plate capacitor with a dielectric material, as shown in fig. 2.27. From Gauss s theorem the electric field E between and normal to two parallel plates carrying surface charge density a and separated by a vacuum is 

---