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54 Chapter 2

in dielectric dipoles have been aligned at some field and its further increase cannot enlarge their
number. Besides, we exclude also the cases when the dielectric crystal lattice blocks or restricts
free rotation of dipoles that leads to anisotropy. Putting in other words, we indicate that the
dielectric must be linear and isotropic while the polarization vector P is directly proportional
to the internal field
= (2.11)
⁄
0

Here is the dimensionless and in most cases positive parameter called the electric
5

susceptibility shows how easy a given material can response to an applied electric field.
Substituting (2.11) into (2.10) we obtain
= ⁄ (1 + ) = / (2.12)
0

0

The dimensionless factor = 1 + by which the internal field is decreased by the

polarization effect is called the relative dielectric constant of the dielectric. Now, let us look at
the displacement vector D. Since the polarization just rotates an equal number of already
existing in material positive and negative charges, the net charge of material is constant. If so,
in accordance with the charge conservation law (1.26) the flux of displacement field vector D
and the displacement field vector itself is defined by only the sources inducing external electric
field and does not depends on polarization vector P. Thus, according to (1.27)
0
= (2.13)
0 0
and the internal electrical field and displacement field are related as
= (1 + ) = (2.14)

0
0
or alternatively in the form
= + (2.15)
0
It is important to note that in (2.15) any change in polarization vector is totally compensated
by the corresponding variation in the internal electrical field E just as the vector D holds
constant. Besides, from the above discussion surrounding the equation (2.14), we know that
increase or decrease in dielectric constant leads to an inverse variation of the internal electrical
fields. The displacement fields holds unchanged and independent of material dielectric
constant.
2.2.3 Dielectric Constant of Composite Materials

A large variety of dielectric materials is used for applications. Part of them like wood, cotton,
silk, oil, rubber, natural quartz, resin, diamonds, sapphires, metal oxides is natural. The others
are human-made/artificial material as plastics, glasses, polymers, nanocomposites, ceramics,
epoxies, silicon, fused quartz, you name them. The most advanced artificial materials are
composites or a mixture of two or more different dielectric materials mainly in the form of tiny
spheres (see Figure 2.2.5a ) or fiber compressed into plates as shown in Figure 2.2.5b . The
6
7
relative dielectric constant of the composite is something intermediate between the
relative permittivity of the components in it and can be calculated for the mixtures as [15]

5 Can be negative in some artificial material such as metamaterial discussed later.
6 Public Domain Image, source: http://www.mpdigest.com/
7 Public Domain Image, source: http://www.toray.com/