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
socalled
ClausiusMosotti
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
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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
0
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)
(23)
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
viceversa (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
0
(el)
=
X
e
0
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=
(e1)
is
called
the
susceptability
of
the
medium.
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 Spring '10
 DR
 Permittivity, Fundamental physics concepts, Dielectric, dipole moment, Marcel Dekker

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