The electric field in dielectrics
Molecules that, in the absence of an external field the centers of gravity of positive and negative charges do not coincide, ie, there is a dipole moment , are called polar. These include H2O, CO, NH, HCl, SO4 etc.
Ionic crystals (NaCl, KBr, KCl) have a crystalline structure. The nodes of the space lattice are interleaved ions of opposite signs. In ionic crystals can not distinguish individual molecules. They need to be seen as a system of two sublattices - positive and negative.
The crystal lattice of salt
where α - polarizability of the molecule (characterizes the "response" of the molecule to the electric field). α - characteristic of an atom or ion.As the quantity characterizing the degree of polarization of the dielectric polarization of the vector - is taken - the dipole moment per unit volume (or the density of the dipole moment)
where - the dipole moment of a single molecule , - the total dipole moment of the volume V.
Three types of dielectric correspond to three types of dielectric polarization
Ionic polarization - the emergence of the dipole moment in ionic crystals induced by the displacement of the sublattices of positive ions along the field, and negative - against the field .
where χ - dielectric susceptibility of the substance, shows how the dielectric response (perceived) to an external electric field.
in weak fields. χ – dimensionless
If between the plates of plate capacitor dielectric layer placed, the resulting polarization of the positive charges in the dielectric will be displaced in the field, and negative - against the field, and on the right side (in the picture) and come into existence the excess of positive there, and on the left side - an excess of negative charges with a surface density + σ 'and -σ'. These charges create inside the dielectric plate a homogeneous field, the intensity of which is equal to the Gauss theorem
where - the surface density of bound charges .
Outside the dielectric . External field and internal directed towards each other, therefore, inside the dielectric
Outside the dielectric .
We define surface density of-related charges . Total dipole moment of the dielectric plate
where S - area of ??the face plate, d - its thickness. On the other hand, the total dipole moment is
where Q'- bound charge of each face, d - arm dipole .
The surface density of bound charges is equal to polarized (polarization) P.
Dimensionless quantity called the dielectric constant. ε shows how many times the dielectric field is weakened, describing the quantitative properties of the dielectric to polarize in an electric field .
§ 3 The electric displacement.
For the description of the electric field, in particular, in the dielectric, introducing the electric displacement vector (the vector of electrostatic induction) , equal
Resulting field is described by a vector in the dielectric intensity . depends on the properties of the dielectric (of ε). Vector describes the electrostatic field generated by the free charges. Bound charges arising in the dielectric, can cause redistribution of free charges up the field. Therefore, the vector describes the electrostatic field generated by the free charges (ie in a vacuum), but with this their distribution in space, which in the presence of a dielectric.
Gauss theorem for the electrostatic field in the dielectric:The flow of the displacement vector of the electrostatic field in the dielectric through any closed surface is equal to the algebraic sum inmates inside this surface free electric charges: