Page 244 - Electrical Properties of Materials

226 Dielectric materials

V reason is the appearance of charges on the surface of the dielectric (Fig. 10.1)
necessitating the arrival of fresh charges from the battery to keep the voltage
Dielectric
constant.
In vacuum the surface charge density on the condenser plates is
V
Q = 0 , (10.2)
d
Capacitor plates where d is the distance between the plates. In the presence of the dielectric the
surface charge density increases to
Fig. 10.1
Inserting a dielectric between the V
. (10.3)
plates of a capacitor increases the Q = 0 r d
surface charge.
Remember now from electromagnetic theory that the dielectric displacement,
D, is equal to the surface charge on a metal plate. Denoting the increase in
surface charge density by P, and defining the ‘dielectric susceptibility’ by

χ = r – 1, (10.4)
we may get from eqns (10.2) and (10.3) the relationships

P = D – 0 E and P = 0 χE . (10.5)

10.3 Microscopic approach
We shall now try to explain the effect in terms of atomic behaviour, seeing how
individual atoms react to an electric field, or even before that recalling what an
atom looks like. It has a positively charged nucleus surrounded by an electron
cloud. In the absence of an electric field the statistical centres of positive and
negative charges coincide. (This is actually true for a class of molecules as
well.) When an electric field is applied, there is a shift in the charge centres,
particularly of the electrons. If this separation is δ, and the total charge is q,the
molecule has an induced dipole moment,
μ = qδ. (10.6)

Let us now switch back to the macroscopic description and calculate the
amount of charge appearing on the surface of the dielectric. If the centre of
electron charge moves by an amount δ, then the total volume occupied by these
electrons is Aδ, where A is the area. Denoting the number of molecules per unit
volume by N m and taking account of the fact that each molecule has a charge q,
the total charge appearing in the volume Aδ is AδN m q,orsimply N m qδ per unit
area—this is what we mean by surface charge density.
It is interesting to notice that this polarized surface charge density (denoted
previously by P, known also as induced polarization or simply polarization) is
exactly equal to the amount of dipole moment per unit volume, which from
eqn (10.6) is also N m qδ, so we have obtained our first relationship between the
microscopic and macroscopic quantities,
P = N m μ. (10.7)