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Unformatted text preview: Seek simplicity, and distrust it.-Alfred North Whitehead POLARIZATION and STATIC DIELECTRIC CONSTANT T he purposes of this chapter are (i) to develop equations relating the macroscopic properties (dielectric constant, density, etc.) with microscopic quantities such as the atomic radius and the dipole moment, (ii) to discuss the various mechanisms by which a dielectric is polarized when under the influence of a static electric field and (iii) to discuss the relation of the dielectric constant with the refractive index. The earliest equation relating the macroscopic and microscopic quantities leads to the so-called Clausius-Mosotti equation and it may be derived by the approach adopted in the previous chapter, i.e., finding an analytical solution of the electric field. This leads to the concept of the internal field which is higher than the applied field for all dielectrics except vacuum. The study of the various mechanisms responsible for polarizations lead to the Debye equation and Onsager theory. There are important modifications like Kirkwood theory which will be explained with sufficient details for practical applications. Methods of Applications of the formulas have been demonstrated by choosing relatively simple molecules without the necessity of advanced knowledge of chemistry. A comprehensive list of formulas for the calculation of the dielectric constants is given and the special cases of heterogeneous media of several components and liquid mixtures are also presented. 2.1 POLARIZATION AND DIELECTRIC CONSTANT Consider a vacuum capacitor consisting of a pair of parallel electrodes having an area of cross section A m 2 and spaced d m apart. When a potential difference V is applied between the two electrodes, the electric field intensity at any point between the electrodes, perpendicular to the plates, neglecting the edge effects, is E=V/d. The capacitance of the vacuum capacitor is Co = So A/d and the charge stored in the capacitor is Qo=A£oE (2.1) in which e is the permittivity of free space. If a homogeneous dielectric is introduced between the plates keeping the potential constant the charge stored is given by Q = s Q sAE (2.2) where s is the dielectric constant of the material. Since s is always greater than unity Qi > Q and there is an increase in the stored charge given by * -l) (2-3) This increase may be attributed to the appearance of charges on the dielectric surfaces. Negative charges appear on the surface opposite to the positive plate and vice-versa (Fig. 2. 1) 1 . This system of charges is apparently neutral and possesses a dipole moment (2.4) Since the volume of the dielectric is v =Ad the dipole moment per unit volume is P = - ^ = Ee (e-l) = X e E (2.5) Ad The quantity P, is the polarization of the dielectric and denotes the dipole moment per fj _ unit volume. It is expressed in C/m . The constant yj= (e-1) is called the susceptability of the medium....
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This note was uploaded on 03/03/2010 for the course POWER 332 taught by Professor Dr during the Spring '10 term at Ain Shams University.
- Spring '10