Dielectric materials are able to transmit electric force without conduction. When an external electric field is applied to a dielectric material, it induces several types of polarization within the material. The main types are electronic, ionic, orientational, and space charge polarization. Electronic polarization occurs due to the displacement of nuclei and electrons within atoms. Ionic polarization is the displacement of cations and anions in ionic solids. Orientational polarization is the alignment of permanent molecular dipoles in materials like CH3Cl. Space charge polarization results from the accumulation of charges at interfaces in multiphase materials. The total polarization of a material is the sum of these contributions and results in an increased electric flux density and relative permittivity compared to vacuum

1. Dielectric Materials

2. Dielectric properties
• Dielectric: Ability to transmit electric force without conduction.
• Non-dielectric materials- Metals and semiconductors: E is transferred
by conduction of charge carriers
• Dielectric materials – Insulators: No charge carriers, no conduction, E
transferred by electrical polarization

3. Electric flux
• Application of external E to dielectric forms electric lines flowing
inside material from +ve to –ve, know as Electric flux.
• Gauss’s theorem: Total electric flux emanating from a closed surface
is equal to total charge enclosed by that surface.
ϕ =
𝑖=1
𝑛
𝑄𝑖 = 𝐷. 𝑑𝑆

4. Electric flux density
• ϕ – total electric flux under influence of external E
• Qi (Coulombs) = Q1, Q2, Q3, ………………, Qn= Charges enclosed by the
surface Q can be +ve or –ve
• D is the electric flux density (Coulombs/m2) at center of surface
element represented by the outwardly directed vector dS.

5. Electric field strength
• The electric field strength E at any point in dielectric materials, is the
electric force per unit charge.
𝐹 = 𝑒𝐸
𝐸 =
𝐹
𝑒
or
𝐹
𝑞
• For an isotropic and homogeneous material E is related to D as:
𝑫 = 𝜀0𝜀𝑟𝑬

6. Permittivity/Dielectric constant
• ε0 = 8.854 x 10-12 Farad/m = Dielectric constant or permittivity of a
vacuum.
• εr = Relative permittivity of the material
• Dimensionless
• Depends on atomic structure of the material
• 1 for vacuum
• >1 for all other substances
• Permittivity - the ability of a material to store electrical energy within
the material.

7. Measurement of relative permittivity (εr)
• Consider a parallel plate condenser under E
• Area of the plates =A, distance between plates = d
• Charge per unit area of plates = +q
• Electric flux flows from +ve to –ve in a direction
perpendicular to the plates
• By Gauss theorem, the magnitude of electric flux
density D = q

8. Measurement of relative permittivity (εr)
Electric field strength
𝐸 =
𝐷
𝜀0𝜀𝑟
=
𝑞
𝜀0𝜀𝑟
If the applied voltage is V, for homogeneous field
𝐸 =
𝑉
𝑑
𝑉 = 𝐸𝑑

9. Measurement of relative permittivity (εr)
The Capacitance C of the condenser:
𝐶 =
𝑄
𝑉
Q = total charge enclosed by parallel plates (Coulombs) = qA
V = Applied voltage (Volts)
C = Capcitance (Farad)
“1 Farad is the capacitance which stores a one-coulomb charge
across a potential difference of one volt.”

10. Measurement of relative permittivity (εr)
Therefore,
𝐶 =
𝑞𝐴
𝐸𝑑
= 𝜀0𝜀𝑟
𝐴
𝑑
For vacuum εr=1, So
𝐶𝑣𝑎𝑐 = 𝜀0
𝐴
𝑑

11. Measurement of relative permittivity (εr)
The ratio
𝐶
𝐶𝑣𝑎𝑐
= 𝜀𝑟
• The relative permittivity of a dielectric material can be determined
by measuring the capacitance of a parallel plate condenser with
and without the dielectric material.
• εr quantifies how much the electric field within a material is
reduced compared to the electric field in a vacuum when the same
external voltage is applied.

12. Q- relative permittivity (εr)
• What is the relative permittivity of metals? And Why?

13. Electrical polarization in dielectric materials
• Electric dipole: represents a pair of equal and opposite electric
charges separated by a certain distance.

14. Electrical dipole moment
• The electric dipole moment of a neutral system of charges Qi is
defined as:
𝜇 =
𝑖
𝑄𝑖𝑟𝑖
where 𝑟𝑖 is the position vector drawn from origin of a coordinate
system to the position of the charge 𝑄𝑖 (+ve or –ve).
• Unit – Coulomb-m

15. Electrical dipole moment
• Simple form:
Choosing the –Q at origin of the coordinate system, the magnitude of
electric dipole moment is = Qd in the direction from –Q to +Q.

16. Electrical polarization
• When an external electric field is applied to a dielectric material, it
carries dipole moment per unit volume, which is called as
polarization of that dielectric material.
• “Electrical polarization is a measure of dipole moment carried by a
unit volume of dielectric under the influence of electric field.”
• It is directly proportional to relative permittivity of the material and
applied field strength and is measured in Coulomb/m2.

17. Electrical polarization
• Consider for an isotropic and homogeneous dielectric inside a
parallel plate, the flux density:
𝑫 = 𝜀0𝜀𝑟𝑬
• Now suppose, a volume element dxdydz
is cutout from the dielectric.

18. Electrical polarization
• The homogeneous field inside the dielectric is
distorted and is no longer homogeneous due
to presence of the cavity of volume dxdydz.
• To produce a homogeneous field in the
presence of cavity,
𝐸𝑖 = 𝐸𝑜 = 𝐸
𝐸𝑖 = Field strength inside cavity=𝐷𝑖 𝜀0
𝐸𝑜 = Field strength outside cavity= 𝐷𝑜 𝜀0𝜀𝑟

19. Electrical polarization
• The flux densities,
𝐷𝑖 𝜀0 = 𝐷𝑜 𝜀0𝜀𝑟 = 𝐷 𝜀0𝜀𝑟
𝐷𝑜 𝐷𝑖 = 𝜀𝑟 or 𝐷𝑖 = 𝐷𝑜 𝜀𝑟
• Hence, if the flux density inside the cavity is made 𝜀𝑟 times as small
as flux density outside the cavity, we can get a homogeneous field
in the presence of the cavity.

20. Electrical polarization
• Gauss theorem: 𝑖=1
𝑛
𝑄𝑖 = 𝐷. 𝑑𝑆
“A change in flux density can at a surface can only be
achieved if the surface carries an electric charge.”
• To reduce 𝐷𝑜 to 𝐷𝑖 after crossing the
surface, a charge density of –( 𝐷𝑜 - 𝐷𝑖 )
Coulomb/m2 should be provided

21. Electrical polarization
• So, we place –(𝐷𝑜-𝐷𝑖)dydz on left side and
+(𝐷𝑜-𝐷𝑖)dydz on right side of the cavity.
• The dipole moment becomes
𝜇 = 𝐷𝑜 − 𝐷𝑖 𝑑𝑥𝑑𝑦𝑑𝑧
• Since, 𝐷𝑜 𝐷𝑖 = 𝜀𝑟 , the dipole moment
becomes,
𝜇 = 𝐷𝑖 𝜀𝑟 − 1 𝑑𝑥𝑑𝑦𝑑𝑧
𝜇 = 𝜀𝑜 𝜀𝑟 − 1 𝐸𝑑𝑥𝑑𝑦𝑑𝑧

22. Electrical polarization
𝜇 = 𝜀𝑜 𝜀𝑟 − 1 𝐸𝑑𝑥𝑑𝑦𝑑𝑧
Polarization = Dipole moment per unit
volume,
So,
𝜇
𝑑𝑥𝑑𝑦𝑑𝑧
= 𝜀𝑜 𝜀𝑟 − 1 𝐸
𝑃 = 𝜀𝑜 𝜀𝑟 − 1 𝐸
𝐷 = 𝜀𝑜𝐸 + 𝑃

23. Electrical polarization
Q - How can we measure the electrical polarization of a dielectric
material?

24. Electrical polarization
Q - Calculate the electrical polarization of a barium titanate crystal
subject to a voltage of 10mV, which, when inserted in a parallel plate
condenser of area 10mm x 10mm and distance of separation of 2
mm, gives a capacitance of 1nF.

25. Types of Electrical polarization
• Depending on atomic mechanism in the presence of external
electric field:
• Electronic polarization: result of the displacement of the positively charged
nucleus and the (negative) electrons of an atom in opposite directions.

26. Electronic polarization
• On applying a field, the electron cloud around the nucleus readily shifts
towards the positive end of the field.
• Such a shift results in a dipole moment within the atom, as a certain distance
now separates the nucleus and the centre of the electron cloud.
• The extent of this shift is proportional to the field strength.
• As the dipole moment is defined as the product of the charge and the shift
distance, it is also proportional to the field strength.
• The constant of proportionality is called the electronic polarizability αe of the
atom.
• 𝑃 = 𝑁𝛼𝑒𝐸, where N = atoms/m3,E = Applied field
• For the inert gases, this polarizability increases with increasing volume of the
atom.
• Electronic polarizability is independent of temperature.
• Monoatomic gases exhibit only this kind of polarization.

27. Ionic polarization
• Ionic polarization occurs when an electric field is applied to an ionic
solid, due to which the cations and anions get displaced in opposite
directions.
• The ionic polarizability is due to this shift of the ions relative
toother oppositely-charged neighbors.
• Ionic polarization is also independent of temperature.

28. Orientational polarization
• Occurs in chemical compounds in which positive and negative charges
do not coincide with each other such as CH3Cl.
• These molecules carry a dipole moment even in the absence of an
electric field.
• When an electric field is applied on such molecules, they tend to align
themselves in the applied field.
• The polarization due to this alignment is called orientation polarization
• It is dependent on temperature. With increasing temperature, the
thermal energy tends to randomize the alignment.

29. Space charge polarization
• Occurs due to the accumulation of charges at the electrodes or at
the interfaces in a multiphase material.
• The ions diffuse over appreciable distances in response to the
applied field, giving rise to a redistribution of charges in the
dielectric medium.

30. Total polarization
• The total polarization of a material is the sum of the contributions
from the various sources described above:
𝑃𝑡𝑜𝑡𝑎𝑙 = 𝑃𝑒 + 𝑃𝑖 + 𝑃𝑜 + 𝑃𝑠