 Lecture 3 

 Dielectric Materials  Dielectric materials are also called as insulators.  In dielectric materials, all the electrons are tightly bound to their parent molecules and there are no free charges. In addition, the forbidden energy band gap (e.g.) for dielectric materials is more than 3eV.  Not possible for the electrons in the valence band to excite to the conduction band, by crossing the energy gap, even with normal voltage or thermal energy.  Dielectrics are non-metallic materials of high specific resistance and negative temperature coefficient of resistance

 Active and Passive Dielectrics  The dielectric materials can be classified into active and passive dielectric materials.  i.Active dielectrics  When a dielectric material is kept in an external electric field, if it actively accepts the electricity, then it is known as active dielectric material. Thus, active dielectrics are the dielectrics, which can easily adapt themselves to store the electrical energy in it.  ii.Passive dielectrics  Passive dielectrics are the dielectrics, which restrict the flow of electrical energy in them. So, these dielectrics act as insulators.  Examples: All insulating materials such as glass, mica, rubber etc., 

 Basic Definitions in Dielectrics Electric Field The region around the charge within which its effect is felt or experienced is known as electric field. The electric field is assumed to consist of imaginary electric lines of force. These lines of force originate from the positive charges and terminate to the negative charges. Electric field strength or electric field intensity (E) Electric field strength at any point is defined as the force experienced by an unit positive charge placed at the point. It is denoted by ‘E’. ‘q’ - magnitude of the charge in coulombs ‘f’ - force experienced by that charge in Newton, electric field strength (E). Its unit is Newton / Coulomb (or) volt / metre.

Electric flux It is defined as the total number of electric lines of force passing through a given area in the electric field. (Emanated from the positive charge). Unit: Coulomb Electric flux density or electric displacement vector (D) It is defined as the number of electric lines of force passing normally through an unit area of cross section in the field. Its unit is Coulomb / m 2

Permittivity Permittivity is defined as the ratio of electric displacement vector (D) in a dielectric medium to the applied electric field strength (E). Mathematically the permittivity is,.Its unit is Farad /metre The permittivity indicates the degree to which the medium can resist the flow of electric charge and is always greater than unity. Dielectric Constant The dielectric constant or relative permittivity of a material determines its dielectric characteristics. It is the ratio of the permittivity of the medium and the permittivity of free space

 Electric Polarization  Consider an atom. We know that it is electrically neutral. Furthermore, the centre of the negative charge of the electrons coincides with the positive nuclear charge, which means that the atom has no net dipole moment.  However, when this atom is placed in an external electric field, the centre of the positive charge is displaced along the field direction while the centre of the negative charge is displaced in the opposite direction.  When a dielectric material is placed inside an electric field, such dipoles are created in all the atoms inside.

Polarizability (  ) When the electric field strength ‘E’ is increased, the strength of the induced dipole is also increased. Thus, the induced dipole moment is proportional to the intensity of the electric field. Polarization vector The dipole moment per unit volume of the dielectric material is called polarization vector. ‘  ’ - average dipole moment per molecule and ‘N’ - number of molecules per unit volume polarization vector is given by, Unit: Coulomb / m2

Relation between P,  0,  r and E The polarization ‘P’ is related to the electric flux density D as, D =  0 E + P Since D =  0  r E, the above relation becomes,  0  r E=  0 E + P (or) P =  0  r E   0 E i.e. P =  0 (  r  1 )E Electric susceptibility The polarization P is proportional to the applied electric field intensity E and it is in the same direction of ‘E’ It can be written as,

P  E (or) P =  0  e E Various Polarization mechanisms in Dielectrics Dielectric polarization is the displacement of charged particles under the action of the external electric field. Several microscopic mechanisms are responsible for electric polarization.  Four types of microscopic polarization mechanisms.  Electronic polarization  Ionic polarization  Orientation polarization and  Space-charge polarization.

 i.Electronic Polarization  Electronic Polarization occurs due to the displacement of positively charged nucleus and negatively charged electrons in opposite directions, when an external electric field is applied, and thereby a dipole moment is created in the dielectric.   The induced dipole moment µ =  eE  where  e = electronic polarizability.  Monoatomic gases exhibit this kind of polarization, Electronic polarizability is proportional to the volume of the atoms and is independent of temperature.  The electronic polarizability =  e = 4  e0R3 ( Farad.m2) where R is the radius of the atom.

Nucleus Sphere of electronic charge +Ze  Ze Original Position Field direction Displaced Equilibrium position x Fig. (a) Position of +ve and –ve charges in an atom without field (b) Position of +ve and –ve charges in an atom with field

ii. Ionic Polarization Ionic polarization arises due to the displacement of -ve ions and + ve ions in opposite directions and it occurs in ionic solids, in the presence of electric field. The displacement is independent of temperature. Example : NaCl crystal -+ ClNa - + x 2 x 1 Fig. (a) Without field (b) With field

iii.Orientation Polarization The orientation polarization arises due to the presence of polar molecule in the dielectric medium. Fig. (a) Without field (b) With field

 Explanation:  In the case of a CH 3 Cl molecule, the positive and negative charges do not coincide. The Cl - has more electro negativity than hydrogen. Therefore, the chlorine atoms pull the bonded electrons towards them more strongly than hydrogen atoms. Therefore, even in the absence of field, there exists a net dipole moment.  Now, when the field is applied, positive portion align along the direction of field and negative portion align in the opposite direction of the field. This kind of polarization is called as orientation polarization.  This depends on temperature; when temperature is increased, the thermal energy tends to randomize the alignment

Space-Charge Polarization The space-charge polarization occurs due to the diffusion of ions, along the field direction, thereby giving rise to redistribution of charges in the dielectrics Fig. (a) Without field (b) With field

 Explanation  Without the application of external field, the ions are orderly arranged as shown in the Fig.  Now, when the field is applied, the ions diffuse with respect to the direction of applied field. Thus the polarization occurs, known as space charge polarization.  Normally, this type of polarization occurs in ferrites and semiconductors and will be very small.

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