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The electric field in dielectrics
§ 1 The conductors and insulators. Polar and non-polar molecules. Ionic crystals. Free and bound charges. Types of polarization.


  • I. Conductors and insulators, see Lecture 1 on electrostatics.
    II. Types of insulators.
    Dielectric molecule as a molecule of any other substance are electrically neutral. This means that the net negative charge of the electrons is the sum of the positive charge of the nuclei.

If the molecules in the absence of an external electric field the centers of gravity of the positive and negative charges are the same, that is, the dipole moment of the molecule , these molecules are called non-polar. These include molecules H2, O2, N2.

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




  • III. Types of polarization.
    Dielectric polarization is the process of dipole orientation or appearance under the influence of an electric field oriented along the field dipoles.
    (The appearance of the dipole moment in the dielectric is called polarization)
    As a result of the polarization of the molecule acquires a dipole moment
    ,which is proportional to the field

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

  • Electronic polarization - the emergence of the dipole moment in the non-polar molecules. Electronic polarization due to the displacement of the electron orbit of the atom relative to the nucleus in an external field .


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



  • Orientational (dipole) polarization - the emergence of the dipole moment in the dielectric with polar molecules due to the orientation of the dipole moments of the molecules in the direction of the field .







    IV. Free and connected charges

    Charges that when an external electric field can move freely through a conductor, and are not associated with the ions of the crystal lattice are called free.

    The charges are part of the molecule, which under the action of the external field is only slightly displaced from their equilibrium positions, and leave the molecules can not, said to be linked.

    § 2 Field intensity in the dielectric.

    In isotropic dielectric polarization vector is linearly dependent on the field


where χ - dielectric susceptibility of the substance, shows how the dielectric response (perceived) to an external electric field.
α - characteristic of a single molecule (or ion), χ - characteristic of the dielectric, ie characteristic matter altogether. χ is independent of    and  

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.
Then the field inside the dielectric



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.
Gauss theorem
 for the electrostatic field in the dielectric.

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.
The lines of force vectors
 can begin and end as in free, and the bound charges. The lines of force vectors  - only free. Through the area of the field where the bound charges, the field lines are vector without interruption.

Vector flux  through any closed surface



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:



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