Electric Susceptibility

5 Key excerpts on "Electric Susceptibility"

• 

  eBook - PDF

  Electronic, Magnetic, and Optical Materials

  • Pradeep Fulay, Jung-Kun Lee(Authors)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  We also use another parameter called the diElectric Susceptibility ( χ e ) to describe the relationship between polarization (the effect) and the electric field (the cause): P = χ e ε 0 E (7.31) The subscript e in χ e distinguishes the diElectric Susceptibility from the magnetic susceptibility ( χ m ), which is defined in Chapter 9. The diElectric Susceptibility ( χ e ) describes how susceptible or polarizable a material is—that is, how easily the atoms or molecules in the material are polarized by the presence of an electric field. Comparing Equations 7.23 and 7.31, χ e = ( k − 1) = ( ε r −1) (7.32) Also, from Equations 7.31 and 7.32, P = ( ε r − l) ε 0 E (7.33) Another way to express the diElectric Susceptibility is as follows: 1 Bound surface charge density Free surface charge density e r 0 P D ) ( χ = ε -= = (7.34) The diElectric Susceptibility ( χ e ), which is another way to express the dielectric constant ( k ), depends on the composition of the material. We can show from Equations 7.29 and 7.31 that χ = α ε e 0 N (7.35) From Equation 7.35, we can see that the diElectric Susceptibility ( χ e ) of the vacuum is zero or the dielectric constant ( k ) is 1. This is expected because there are no atoms or molecules in a vacuum, so N = 0. The more polarizable the atoms, ions, or molecules in the material are, the higher the bound charge density is, and the higher the diElectric Susceptibility ( χ e ) or dielectric constant ( k ) is. In Section 7.5, we will see that several different polarization mechanisms exist for a material (Figure 7.8). 254 Electronic, Magnetic, and Optical Materials The diElectric Susceptibility values ( χ e ) of silicon, Al 2 O 3 , and polyethylene are approximately 10, 8.9, and 1.2, respectively, because the dielectric constants are approximately 11, 9.9, and 2.2, respectively (Table 7.1).

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Electric Field

  • Mohsen Sheikholeslami Kandelousi(Author)
  • 2018(Publication Date)
  • IntechOpen

    (Publisher)

  Dielectrics under Electric Field http://dx.doi.org/10.5772/intechopen.72231 75 In general, the relation between polarization P and electric field E follows [12]: P ¼ εχ E þ higher terms in E (5) where ε 0 is the permittivity of free space, and χ is the susceptibility. The equation does not include spontaneous polarization of ferroelectrics. For most dielectrics, the first term is domi-nant. Higher terms are commonly omitted except for nonlinear dielectrics. From Eq. (5), we can see that χ represents the polarizability. But the most widely used parameter is dielectric permittivity ε : ε ¼ D E (6) Here D is electric displacement. And in engineering, the relative dielectric permittivity ε r = ε / ε 0 , or more generally called dielectric constant, is used because ε is too small in SI unit. For a capacitor, electric displacement equals to the surface charge density. Assume a planar capacitor consisting of two parallel electrodes with surface S and distance d . When a voltage V is applied and there is no dielectric material between electrodes, the surface charge density Q 0 = ε 0 V /t appears according to Gauss ’ law. If a dielectric material with susceptibility χ is filled in between two electrodes, it contributes surface charge density Q d = P = ε 0 χ V /t . As a result, the total surface charge equals the sum of two: Q = ε 0 (1+ χ ) V /t. As a result, combining Eqs. (5) and (6), we can get the relation between relative dielectric permittivity ε r and susceptibility χ : ε r ¼ 1 þ χ ð Þ (7) Both ε r and χ are parameters describing the polarizable property of dielectrics under electric field. 2.3. Dielectric dissipation Under AC electric field, there are two types of current flowing through a capacitor, the so-called polarization current I P and conduction current I R .

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Understanding Physics

  • Michael M. Mansfield, Colm O'Sullivan(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  Experimentally, for most dielectric materials, it is found that | E pol | is directly proportional to | E | over a reasonably wide range of field strength values, that is The constant of proportionality χ e is called the Electric Susceptibility and is characteristic of the material involved. Note that, since P = − ε 0 E pol, the electric polarization is Thus, using Equation (17.3), the electric field strength at a point within a dielectric material is given by Hence and we can now interpret the permittivity of the medium to be Values of permittivity are often given in terms of relative permittivity, the value of the permittivity relative to that of vacuum, that is For most dielectric materials in typical electric fields, therefore, a plot of D versus E (or P versus E) yields a straight line (Figure 17.7). Such substances are described as linear materials. Figure 17.7 Plot of polarization versus electric field strength for a linear material. The slope of the straight line is ε 0 χ e. In the discussion above it has been assumed that substances under discussion were linear, isotropic and homogeneous (that is, l.i.h. materials). Examples of materials with non‐linear electrical properties will be discussed in Section 17.5. 17.4 Boundaries between dielectric media In the discussion presented in earlier sections of this chapter it has been assumed that all sources of electric field have either been in vacuum or embedded in an effectively infinite non‐conducting medium. In the case of situations involving two or more media of different electric permittivities, however, care must be exercised in applying the results obtained. Issues do not generally arise when the electric field is applied at right angles to the surfaces of the specimen

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  One- and Two-Dimensional Fluids

  Properties of Smectic, Lamellar and Columnar Liquid Crystals

  • Antal Jakli, A. Saupe(Authors)
  • 2006(Publication Date)
  • CRC Press

    (Publisher)

  221 8 Electrical Properties 8.1 Dielectrics Dielectric fluids such as liquid crystals are leaky insulators, i.e., they have low electrical conductivity and polarize in the presence of an electric field . This means that the electric field induces internal charge reorgani-zation, or distortion such as a net electric dipole moment per unit volume P appears. This is the polarization with units C/m 2 . The sign of the polar-ization is defined as P > 0 if the direction is pointing from negative to positive charges. The polarization per unit electric field of an anisotropic material is described by the Electric Susceptibility tensor as: (8.1) where and ε o = 8.85 × 10 –12 C 2 /Nm 2 (or C/Vm) is the vacuum permittivity. It is usual to define the dielectric tensor as: (8.2) The reason for introducing is that it gives the electric displacement (its magnitude is the free surface charge per unit area). (8.3) The dielectric permittivity is a macroscopic quantity; it relates the external electric field to the macroscopic polarization. In the special case of isotropic materials, the tensor becomes a scalar, i.e., E ˆ χ e P E o e α α β β ε χ = α β , , , , = x y z ˆ ε ˆ ˆ ˆ ε χ = + I o e ˆ ε D D P E E E o o = + = + = ε χ ε ε ( ) ˆ 1 E ˆ ˆ . ε ε − → − I 1 222 One- and Two-Dimensional Fluids For uniaxial materials, like ordinary calamitic (rod-shape) nematics, SmA, SmB, the dielectric tensor is symmetric and has a traceless form in a coor-dinate system fixed to the director: (8.4) where are the components normal and along the director. The eigen-values of the dielectric tensor are related to the order parameter as: (8.5) and (8.6) where is the dielectric anisotropy, and is the isotro-pic part of the dielectric constant, thus independent of the orientational order. Apart from density changes, is typically continuous through all uniaxial liquid crystal phase transitions. A uniaxial material is said to be positive when ε a > 0 and said to be negative when ε a < 0 .

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Electromagnetism

  • I. S. Grant, W. R. Phillips(Authors)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  Figure 2.11 . The field in a spherical cavity in a uniformly polarized liquid.

  The minus sign arises because the outward normal to the dielectric is the inward normal to the cavity. By symmetry the net field generated at the centre of the cavity by the polarization charges is directed along the z -axis. At the centre the z -component of the field due to the charge σ p (θ ) dS is

  The area of the band on the surface of the cavity lying between θ and (θ + dθ ) is 2πR 2 sin θ dθ , and hence the field due to the band is

  The field at the centre of the cavity generated by all the polarization charge is thus in the same direction as the macroscopic field E and is of magnitude

  The field in the cavity is uniform (this is proved in section 3.3.2 of the next chapter), and so our estimate of the local field is

  Substituting this value for Elocal in Equation (2.15) we find

  Comparing this equation with the definition of susceptibility given in Equation (2.6) , we see that

  (2.16)

  This approximation, which is known as the Clausius–Mossotti formula, cannot be expected to be very accurate since it is based on such a crude representation of the neighbouring molecules. However, the Clausius–Mossotti formula does demonstrate that polarization in the liquid dielectric causes the local field to be larger than the macroscopic field, and makes a reasonable estimate of the susceptibility in terms of molecular polarizability.

  The molecular polarizability can be derived from the susceptibility of a gas (Equation (2.10) ):

  Table 2.3 . Electric susceptibilities of gases and liquids.

  ρ is the density in g/cm3 . The data for gases are at atmospheric pressure.

  Comparison of the susceptibility of liquids and gases therefore gives a measure of the local field in the liquid, since

  where ρ is the density. Some experimental values are listed in Table 2.3 , which compares the value of E local /E derived from this expression with the Clausius–Mossotti prediction

  Sign up to read

  Learn more about book