Polarization in Dielectrics | Applied Physics - II | Dielectrics

Polar and Non Polar Molecules
Dielectric Polarization
Gauss Law for Dielectric Materials
Types of Polarization

1. Dielectrics
POLARIZATION IN DIELECTRICS

(An assignment in Applied Physics - II)
Submitted by:
Ayush Agarwal
A2305216324
2CSE-5X
Submitted to:
Ms. Monika Bahl

2. A dielectric is an insulator or non-conductor of electricity. Its effects are defined
in terms of the ratio of the capacitance of a capacitor with a dielectric between
the plates to the capacitance of a capacitor without a dielectric between the
plates.
Polar and Non Polar Molecules
Molecules can be grouped as polar and non-polar molecules. The arrangement or
geometry of the atoms in some molecules is such that one end of the molecule has a
positive electrical charge and the other side has a negative charge. If this is the case,
the molecule is called a polar molecule, meaning that it has electrical poles.
Otherwise, it is called a non-polar molecule.
Polar Molecules
Polar means having electrical poles. The molecules in which the arrangement
or geometry of the atoms is such that one end of the molecule has a positive
electrical charge and the other side has a negative charge are called as polar
molecules. Examples of polar molecules are Water (H2O) (Fig. 2.1a), Ammonia
(NH3), etc.

Nonpolar molecules
A non-polar molecule is that in which the electrons are distributed more
symmetrically and thus does not have an excess of charges at the opposite
sides i.e. electric poles are absent. The charges all cancel out each other.
e.g. CO2, H2, N2, O2, etc.

3. Dielectric Polarization
When insulators are placed in an electric field, no current flows in them, unlike in
metals. Instead in some insulators, electric polarization occurs. A dielectric is an
insulator that undergoes electric polarization on the application of electric field. The
charges in dielectric material does not move but only shifts slightly from the
equilibrium position resulting in the dielectric polarization.
Both polar and nonpolar molecule experience polarization on exposure to electric
field but the difference between a nonpolar and a polar molecule is that, nonpolar
molecules are induced with a dipole by current whereas polar molecules have
permanent dipoles. Due to the induced nature of polarity, on the removal of the
electric field, a nonpolar material loses its polarity are returns to its original state.
Dielectric Polarization in Non Polar Dielectric
In spite of the lack of a dipole, a dielectric nonpolar material introduced in an electric
field will be affected. In an electric field, the positive and the negative charges in a
nonpolar molecule experience forces in opposite directions as a result of their
opposite polarities. This force causes the electron cloud of a nonpolar molecule to be
displaced in the direction of the attraction. This displacement goes on till the
attraction by the electric field is balanced by the internal forces of the molecule.
Thus, in the presence on an electric field, even a nonpolar molecule experiences
induced dipole moment.


Dielectric Polarization in Polar Dielectrics
Polar molecules undergo Dipolar Polarization or Orientation Polarization. Due to
thermal agitation, the dipoles in a polar material are oriented randomly. Therefore
the dipole moment of the molecules in the material cancels out resulting in a net
dipole moment of zero.
When an electric field is applied, the individual dipole moments align themselves in
the direction of the electric field. This alignment when summed up over all the
molecules leads to a net dipole moment in the direction of the electric field. The

4. extent to which the polar molecules get polarizes and align themselves is related to
two factors, the strength of the external field and the thermal energy that breaks this
alignment.


Dielectric Polarizability
Thus, irrespective of whether a material is polar or nonpolar, the application of an
electric field results in the creation of a net dipole moment across the material. The
dipole moment per net unit volume is called Polarisation. The property of dielectric
to get polarised in the presence of external electric field is known as Dielectric
Polarizability.
For an ideal dielectric material,
P = αχ
e
E
where,
α = Polarizability of dielectric
χ
e
= Electric Susceptibility of the dielectric medium
P = Polarization due to the applied electric field ‘E’

5. Relation between Polarization Vector (P), Displacement Vector (D) and Electric
Field (E)
Let E0 be the external electric field and Ep be the electric field due to polarization
Therefore, Net Electric Field,
E = Eo – Ep (1)
Polarization vector, P is equal to the bound charge per unit area or equal to the
surface density of bound charges (because surface charge density is charge per unit
area), thus
P = qb/A = σp (2)
where,
qb is the bound charge,
σp is surface density of bound charges.
P is also defined as the electric dipole moment of material per unit volume.
P = np
where, n is number of molecules per unit volume.
Displacement vector, D is equal to the free charge per unit area or equal to the
surface density of free charges, thus
D = q/A = σ (3)
where,
q is the free charge
σ is surface density of free charges.

As for parallel plate capacitor,
E = σ /ε0 (4)
Ep = σp /ε0 (5)
By substituting equations 4 and 5 in equation 1, we get
E = σ /ε0 – σp /ε0
Or ε0E = σ – σ0
By putting equations 2 and 3 in above equation, we get
ε0E = D – P
Or D = ε0E + P

6. Gauss Law for Dielectric Materials
Electrostatic field in the dielectric material is modified due to polarization and is not
the same as in vacuum. Hence the Gauss law which is applicable in vacuum
is reconsidered for dielectric media. It can be expressed in two forms:
A) Integral Form of Gauss Law
Consider two parallel-plate conductors having plane area S, separation d and vacuum
between plates. Let charge +q and –q be the charges on the plates. Due to the
charges, E0 is the uniform electric field directed from positive to negative plate
Consider the Gaussian surface around the upper conducting plate of positive
charges. Applying Gauss’s law the electric flux passing through the closed surface is
given by
Or
….(1)
The field is normal to the plate surfaces.
Consider that a dielectric material of permittivity ε is filled completely between the
plates. Charges –q’ and +q’ are induced on the surfaces of the dielectric that are in
the proximity of the plates having charges q and -q respectively. The induced charges
set up an electric field E in the dielectric. The dielectric is polarized. It remains as a
whole electrically neutral as the positive induced surface charge must be equal to the
negative induced surface charge.
If the dielectric is present, the surface encloses two types of charge:
Free charge on the upper conducting plate is q and
Induced charge on the top face of dielectric due to polarization is -q’
The net charge enclosed by the Gaussian surface around the (same upper
conducting) plate (of positive charges +q) is q-q’.
According to Gauss’s law
............(2)

7. ............. (3)
Field E in the dielectric is in the opposite direction to that of the applied electric
field E0. The effect of the dielectric is to weaken the original field by the factor k= ε/
ε0.

Or ... (4)
...(5)

...(6)
The magnitude of the net induced charge q` is always less than magnitude of the free
charge q applied to the plates and is equal to zero if dielectric is absent.

Or
Or
i.e.
Where D = ε E = ε0 k E (k= ε/ ε0).
D is called as the displacement vector. The induced surface charge is purposely
ignored on the right side of this equation, since it is taken into account fully by
introducing the dielectric constant k on the left side.
The equation states that “the surface integral of displacement vector ‘D’ over a
closed surface is equal to the free charge enclosed within the surface” or “The
outward flux of D over any closed surface S equals the algebraic sum of the free
charges enclosed by S”. It is the most general form of Gauss’ law. The charge q
enclosed by the Gaussian surface is the free charge only, which can be controlled and
measured. Hence this form of Gauss law is very useful.

8. (B) Differential Form of Gauss Law
Consider a dielectric material kept in an electric field is polarized. It has bound or
polarization charge density ρb due to accumulation of bound charges
The applied electric field itself is created by transferring electric charges.They are
called as free charges (charges brought from outside e.g. conduction electrons in
metals).They give rise to ρf the charge density due to free charges i.e. which is not
due to polarization. The total charge density ρ consists of two parts as follows ρ = ρf +
ρb
According to Gauss' law in differential form

E is the total electric field due to both types (bound and free) charges.
and Rearranging the expression and substituting


This is the differential form of Gauss Law in dielectrics. D is termed as the electric
displacement. D has the same dimensions as (dipole moment per unit volume).
Above law can be written in terms of E using relation ==>
The other equation in electrostatics remains unchanged in dielectrics.
According to the divergence theorem the differential form changes to integral form
as

The flux of D out of a closed surface S is equal to the total free charge enclosed
within that surface. Thus the statement of Gauss’s Law in integral form can be
obtained from differential form. It can be derived from first principles also.

9. Types of polarization
1. Electronic or Atomic Polarization
This involves the separation of the centre of the electron cloud around an atom
with respect to the centre of its nucleus under the application of electric field.

2. Ionic Polarization
This happens in solids with ionic bonding which automatically have dipoles but
which get cancelled due to symmetry of the crystals. Here, external field leads to
small displacement of ions from their equilibrium positions and hence inducing a
net dipole moment.

3. Dipolar or Orientation Polarization
This is primarily due to orientation of molecular dipoles in the direction of applied
field which would otherwise be randomly distributed due to thermal
randomization.

10. 4. Interface or Space Charge Polarization
This involves limited movement of charges resulting in alignment of charge dipoles
under applied field. This usually happens at the grain boundaries or any other
interface such as electrode-material interface.

11. Clausius Mossotti Relation
The Clausius-Mossotti equation for dielectric matter consisting of atoms or (non-
polar) molecules is

where ε0 is the electrical permittivity of the vacuum and N is the number of atoms or
molecules per volume.

Derivation
Consider a dielectric with number density N (number of particles per unit volume) in
an external electric field E. The sum of E and an internal field Eint induces a
dipole pind on each particle. The polarization vector P is the sum of the induced
dipoles,

From the relation between P, the electric displacement D, and the electric
field E follows

To get an expression for pind, we consider a single particle (molecule or atom) in a
little spherical cavity inside the dielectric. It is shown below that the total field inside
this cavity can be approximated by

Now,

Further,


On Simplifying we get,