Dielectric Properties of Insulating Materials, in Material Science different material used in Power system as Insulators and their required properties and applications.

1. Unit No.1
Dielectric Properties of
Insulating Materials
1

2. Static Field
• Electric and magnetic fields are invisible lines of force generated
by natural phenomena such as the Earth’s magnetic field or
lightning, but also by human activities, mainly through the use of
electricity.
• An electric field is the force field created by the attraction and
repulsion of electric charges (the cause of electric flow), and is
measured in volts per meter (V/m).
• A magnetic field is a force field created by a magnet or as a
consequence of the movement of the charges (flow of electricity).
The magnitude (intensity) of a magnetic field is usually measured
in Tesla (T or mT)
• A static electric field (also referred to as electrostatic field) is
created by charges that are fixed in space;
• A static magnetic field is created by a magnet or charges that
move as a steady flow (as in appliances using direct current).
2

3. 3

4. 4

5. 5

6. 6

7. 7

8. Dielectric Parameters
Dielectric:-
• when charge storage in the main function such as non- conducting
materials are called Dielectric
• All dielectric materials are insulating but all insulating materials are not
Dielectic.
• Electrical Energy can be stored with minimum dissipation are called
Dielectric materials. e.g. Paper, Mica, Glass
• Dielectric is an insulating material which can be polarized by an Electric
field.
Dipole Moment:-
• Two Charges of equal magnitude but opposite polarity & separated by
distance ‘d’ a dipole moment.
• Its denoted by ‘μ’ = qX d
• Its unit is coulomb meter or Debye.
• Dipole Moment is vector quantity.
• It is directed from –ve charge to +ve charge.
8

9. • Dielectric Constant :- ‘ϵ’ –
• An electrical insulating material (a dielectric) equal to the ratio of the
capacitance of a capacitor filled with the given material to the capacitance of
an identical capacitor in a vacuum without the dielectric material.
There are two types :-
• A) Relative Permittivity :- A parallel plate capacitor having area of each plate
‘a’m² & distance between plates be ‘d’m. the dielectric medium between plates
is vacuum.
• The capacitance given by,
𝐶𝑜 = 𝑎
∈ 𝑜
𝑑
Where, 𝜖𝑜 = 8.85 ∗ 10¹²𝐹/𝑚.
• B) Absolute Permittivity:- the electric field density D is directly proportional
to electric field intensity E.
𝐷 ∝ 𝐸 , 𝐷 = ∈ 𝐸
∈ =
𝐷
𝐸
also ∈ =∈ 𝑜 ×∈ 𝑟
• ϵo – permittivity of free space = 8.85 ∗ 10¹²𝐹/𝑚
• ϵr – Relative permittivity of material. Air or Vacuum =1
9

10. Material Єr
Glass 3.3
Mica 3.8
Paper 2 – 2.5
Bakelite 5.6
Rubber 2.3 – 3.5
Extra Oil 2
Porcelain 4 -- 7
Distilled Water 81
10

11. Polarization
• Polarization :- It is defined as electric dipole moment per unit
volume.
𝑃 =
𝑑𝑖𝑝𝑜𝑙𝑒 𝑚𝑜𝑚𝑒𝑛𝑡
𝑣𝑜𝑙𝑢𝑚𝑒
=
𝜇
𝑣
=
𝑐𝑜𝑙𝑢𝑚𝑏−𝑚
𝑚³
• Dielectrics are two types :-
• Polar Dielectric :- Dipoles are present in random directions inside
the material so net dipole moment in material is zero in absence of
an electric field.
• When external electric field applied the dipoles are aligned in the
direction of applied field.
• Non Polar Dielectric :- the dielectric which are polarized only when
they are placed in an electric field are known as Non polar dielectric.
11

12. 12

13. Mechanisms of polarization
 Electronic Polarization (Pe):-This polarization is due to
displacement of negative charge cloud with respect to
positive nucleus of an atom when electric field is applied
to it shifting of electron cloud in a dipole moment.
• This polarization in gases dielectrics, so that dielectric
constant of all gases are nearly equal to unity.
• Electronic polarization is given by,
𝑃𝑒 = 𝑁. ∝ 𝑒. 𝐸 − − 1
𝑃𝑒 = 𝑋𝑜. 𝜖𝑜. 𝐸 − − 2
Xo- Susceptibility of dielectric
𝑋𝑜 =
𝑃𝑜
∈ 𝑜. 𝐸
− − 3
But
𝑋𝑜 + 1 =∈ 𝑟
13

14. ∈ 𝑟 = 1 +
𝑃𝑜
∈ 𝑜. 𝐸
∈ 𝑟 = 1 +
𝑁. ∝ 𝑜. 𝐸
∈ 𝑜. 𝐸
∈ 𝑟 = 1 +
𝑁. ∝ 𝑜
∈ 𝑜
−− −4
∈ 𝑟 = 1 +
𝑁4𝜋 ∈ 𝑜𝑅3
∈ 𝑜
since, ∝ 𝑒 = 4𝜋 ∈ 𝑜𝑅3
∈ 𝑟 = 1 +
𝑁 ∝ 𝑒
∈ 𝑜
– radius of atom
14

15. Electronic Polarization
15

16. Ionic Polarization(Pi):- Ionic polarization takes place due to
shifting of charged ions when an electric field is applied to ionic
crystals. Positive ions relative to negative ions causes an induced
dipole moment μi given by,
𝜇𝑖 = 𝛼𝑖 . 𝐸
• Where, αi- ionic polarizability
• Ionic polarization is given by
𝑃𝑖 = 𝑁𝛼𝑖 𝐸
16

17. Orientation or Dipolar Polarization (Po):-
• The absence of external electric field, orientation of these dipoles is
in random which results in complete cancellation of each other
effect.
• When an electric field is applied , dipoles rotate about their axis of
symmetry to align with applied electric field, this orientation is
through small angle.
• Dielectric constant of water is 80 & solid ice is only 10.
• The orientation polarization is given by,
17

18. 𝑃𝑜 = 𝑁𝛼𝑜 𝐸
𝑃𝑜 = 𝑁
𝜇2
3 𝑘𝑇
𝐸
𝑠𝑖𝑛𝑐𝑒, 𝛼𝑜 =
𝜇2
3𝑘𝑇
∴ 𝑃𝑜 = 𝑁 × 𝛼𝑜 × 𝐸
𝑤ℎ𝑒𝑟𝑒, 𝑇 − 𝑇𝑒𝑚𝑝. 𝑖𝑛 ˚𝑘
𝑁 − 𝑁𝑜. 𝑜𝑓 𝑎𝑡𝑜𝑚𝑠 𝑝𝑒𝑟 𝑚3
𝑘 − 𝐵𝑜𝑙𝑡𝑧𝑚𝑎𝑛𝑛′ 𝑠 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
= 1.38 × 10¯²³𝐽/°𝑘
18

19. 19

20. Total Polarization :-
• In a material which can experience all forms of
polarization the total polarization,
𝑃 = 𝑃𝑒 + 𝑃𝑖 + 𝑃𝑜
• Total polarizability is equal to sum of electronic,
ionic,& orientation polarizabilies.
𝛼 = 𝛼𝑒 + 𝛼𝑖 + 𝛼𝑜
= 𝛼𝑒 + 𝛼𝑖 +
𝜇2
3𝑘𝑇
• The total polarization of a polyatomic gas,
𝑃 = 𝑃𝑒 + 𝑃𝑖 + 𝑃𝑜
= 𝑁𝑜. 𝐸 (∝ 𝑒 +∝ 𝑖 +∝ 𝑜)
20

21. Clausius Mossotti Equation:-
• The solid dielectric are those materials which are build up of single type of
atoms they exibit only electronic polarization.
• So for such materials
𝑃𝑖 = 𝑃𝑜 = 0
𝑃 = 𝑃𝑒
∴ 𝑃 = 𝑁𝛼𝑒. 𝐸𝑖 −− −1
• Where αe- electronic polarizability
• Ei – internal field.
• For cubic symmetry structure atoms, internal field is given by,
𝐸𝑖 = 𝐸 +
𝑃
3 ∈ 𝑜
−− −2
∴ 𝑃 = 𝑁𝛼𝑒 𝐸 +
𝑃
3𝜖𝑜
−− −3
∴ 𝑃 = 𝜖𝑜 𝜖𝑟 − 1 𝐸 −− −4
Equating equation (3) & (4),
∈ 𝑜 ∈ 𝑟 − 1 𝐸 = 𝑁𝛼𝑒 𝐸 +
𝑃
3𝜖𝑜 21

22. ∈ 𝑜 ∈ 𝑟 − 1 𝐸 = 𝑁 ∝ 𝑒[𝐸 +
∈ 𝑜 ∈ 𝑟 − 1 𝐸
3 ∈ 𝑜
]
∈ 𝑜 ∈ 𝑟 − 1 𝐸 = 𝑁 ∝ 𝑒 𝐸 [1 +
∈ 𝑟 − 1
3
]
∈ 𝑜 ∈ 𝑟 − 1 = 𝑁 ∝ 𝑒 [
3 +∈ 𝑟 − 1
3
]
∈ 𝑜 ∈ 𝑟 − 1 = 𝑁 ∝ 𝑒 [
∈ 𝑟 + 2
3
]
∈ 𝐫 − 𝟏
∈ 𝐫 + 𝟐
=
𝐍𝛂𝐞
𝟑𝛜𝐨
−− −𝟓
• Assumptions in Clausius Mossotti equation:-
1. To elemental solid dielectric only having cubic crystal structure.
2. The polarizability of molecule is isotropic.
3. Polarization of molecule is by elastic displacement only.
4. Absence of short range interactions.
5. Єr- Dimand – 5.68, Silicon – 12, Germanium – 16 etc.
22

23. Piezo- Electric Materials
• Piezoelectricity provides mechanism for converting
electrical energy into mechanical stress or strain and
vise versa.
• The materials which convert mechanical strain applied
to them into electrostatic charges on the faces of
crystal are called piezo electric material and this
phenomenon is called piezo electricity.
• Piezo electric effect is nothing but production of
electricity by applying pressure.
• There are two effects of piezo electricity
A) Inverse piezo electric effect
B) Direct piezo electric effect
23

24. 24

25. 25

26. a) Inverse Piezo electric effect:-
• when an electric field is applied to dielectric it becomes
polarized due to which nuclei & electrons geometric
position.
• Mechanical deformation of dielectric by external electric
field is called inverse piezoelectric effect.
• If alternating voltage is applied between the two opposite
faces of the crystal it vibrates with the frequency of the
field.
26

27. 27

28. 28

29. 29

30. b) Direct piezo electric effect:-
• The production of electric polarization by
applications of mechanical stress is known as direct
piezoelectric effect.
• If mechanical pressure on crystal is altered, a
varying voltage which is proportional to mechanical
pressure is produced by the crystal.
• The voltage generated can be as small as fraction of
voltage or can be thousands of volt depending on
the piezoelectric material & pressure applied.
• e.g. ammonium phosphate, quartz, rochette salt,
barium titanate (BaTio3) piezoelectric properties.
30

31. 31

32. • Applications:-
1. For conversion of mechanical stress into electric
signal such as transducer , oscillators, multi
vibrators, strain gauges etc.
2. Piezo electric semiconductors are used to
transform electromagnetic vibration into audio
signal at very high frequency.
3. Piezo electric materials serves as a source of ultra
sonic waves at sea they can be used to measure
depth, the distance to shore the position of ice
barges and submarines.
4. Inverse piezoelectric effect is used in Quartz
watches which keep accurate time.
32

33.  Pyro Electric Materials :-
• A pyro electric material is one which exhibits polarization in
absence of can electric field & changes its polarization an
heating.
• This effect is represented by equation,
∆𝑃 = 𝜆Δ𝑇
Where ∆𝑃 – change in polarization on raising the temp. Δ𝑇
𝜆- Pyro electric coefficient
Δ𝑇 – change in Temp.
• The heat absorbed by the pyro electric crystal increases the
temp.by Δ𝑇 which induced a change ∆𝑃 in its polarization.
• The changes ∆𝑃 gives rise to change Δ𝑉
𝑖𝑛 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑡ℎ𝑎𝑡 𝑐𝑎𝑛 𝑏𝑒 measured with voltmeter across the
crystal.
33

34.  Application:-
• Pyro electric crystals are widely used as infrared detectors.
• Any infrared radiation that can raise the temp.of the crystal
even by (1/1000) of a degree can be change or detected.
 Ferro-electric Materials:-
• The materials which polarization in absence of external
electric field & it may be switched in direction by application
of external electric field are called as a ferroelectric material.
• For dielectric materials , polarization P is a linear function of
applied electric field E, Pα E so ordinary dielectric are also
called Linear dielectric.
• For Ferro electric materials polarization is not unique function
of applied electric field E, the relationship between P & E is
nonlinear so there materials are also called as non-linear
dielectric.
34

35.  Dielectric Loss:-
• The absorption of electrical energy by dielectric material to
AC supply is called Dielectric loss.
• The dielectric loss by AC field results in dissipation of
electrical energy in form of heat in the material, an ideal
dielectric does not absorb any electric energy.
• Consider a parallel plate capacitor ‘C’ having plate area ‘a’m²
& separated by distance ‘d’m.
• Let the dielectric having permittivity of 𝜖 be filled between
the plates.
• Let sinusoidal voltage be applied to the resultant current is
given by,
𝐼 = 𝐼𝑟 + 𝑗𝐼𝑑
=
𝑣
𝑟
+
𝑗𝑤
1
𝑐𝑣
=
v
r
+ jwcv −−− −1
35

36. Where, Ir- conduction current
Id- displacement current
• The resultant current I lags behind displacement current Id by an
angle δ, called dielectric loss angle.
• However for a lossy dielectric total current is
𝐼 = 𝐼𝑟 + 𝑗𝐼𝑑
• The angle δ= (90-ø) is called dielectric loss angle.
• For phasor diagram,
𝑡𝑎𝑛𝛿 =
𝐼𝑟
𝐼𝑑
= 𝑙𝑜𝑠𝑠 𝑡𝑎𝑛𝑔𝑒𝑛𝑡 −− −2
• The dielectric loss is given by,
𝑃 = 𝑉𝐼 𝑐𝑜𝑠𝜙 −− −3
𝑃 = 𝑉𝐼 cos 90 − 𝛿
= 𝑉𝐼 𝑠𝑖𝑛𝛿 − − 4
Phasor diagram, 𝑐𝑜𝑠𝛿 =
𝐼𝑑
𝐼
∴ 𝐼 =
𝐼𝑑
𝑐𝑜𝑠𝛿
− −5
36

37. Putting eq.5 in eq.4 we get,
𝑃 = 𝑉
𝐼𝑑
𝑐𝑜𝑠𝛿
. 𝑠𝑖𝑛𝛿 = 𝑉. 𝐼𝑑. 𝑡𝑎𝑛𝛿
But,
𝐼𝑑 =
𝑉
𝑋𝑐
−− −6
∴ 𝑃 = 𝑉.
𝑉
𝑋𝑐
. 𝑡𝑎𝑛𝛿
=
𝑉2
𝑋𝑐
. 𝑡𝑎𝑛𝛿
=
𝑉2
1
2𝜋𝑓𝑐
. 𝑡𝑎𝑛𝛿
= 2𝜋𝑓𝑐. 𝑉2
. 𝑡𝑎𝑛𝛿 −− −7
Where, V- applied AC voltage
δ – dielectric loss angle
P – dielectric loss, tanδ – loss tangent
C- capacitance of parallel plate.
37

38. • The dielectric power loss is directly proportional to
frequency , square of supply voltage, capacitance
and loss tangent.
 Significance of loss tangent:-
• Dielectric loss occurring in form of heat so it called
dissipation factor i.e. electric power loss.
• Greater the value of tan δ, large will be dielectric
loss.
• tan δ depends on temp. & freq.
• tan δ indicates good or bad insulator.
38

39. • Problems:-
1. Two parallel plate 0.15*0.30m² in area are separated by a dielectric of
thickness 0.06m dielectric constant Ɛr=5.4. the capacitance so formed is
connected to a 400v d.c.supply calculate a) the capacitance of the plates
of capacitors. b) the charge on the plates of capacitor. c) the electric field
intensity in the dielectric. d) the energy stored in conductor as well as
energy stored in polarizing the dielectric.
Sol.:- Given data, a= 0.15*0.30m² v= 400v, d= 0.06m, Ɛr= 5.4
a) Capacitance of parallel plate capacitor is ,
𝐶 =
𝑎 ∗∈ 𝑜 ∗∈ 𝑟
𝑑
=
0.15 ∗ 0.30 8.85 ∗ 10¯¹² ∗ 5.4
0.06
= 3.585 ∗ 10¯11 𝐹𝑎𝑟𝑎𝑑.
b) Charge
𝑄 = 𝐶 ∗ 𝑉
= 3.585 ∗ 10⁻11 ∗ 400
= 1.432 ∗ 10⁻8
𝑐𝑜𝑙𝑢𝑚𝑏
c) Electric field intensity
𝐸 =
𝑉
𝑑
=
400
0.06
= 6666.67 𝑣/𝑚
39

40. d) Energy stored in condenser
𝐸 = 𝑤 =
1
2
∗ 𝐶 ∗ 𝑉2
=
1
2
∗ 3.585 ∗ 10−11 ∗ 4002
= 2.864 ∗ 10−6
𝐽
C𝑜 =
𝐶
∈ 𝑟
=
3.585 ∗ 1011
5.4
= 0.6638 ∗ 10⁻¹¹
Energy stored in polarizing the
dielectric is,
𝑊′
=
1
2
𝐶 − 𝐶𝑜 𝑉²
=
1
2
3.585 − 0.6638 ∗ 10−11
∗ 4002
= 23.3688 ∗ 10−7 𝐽𝑜𝑢𝑙𝑒.
2. When sodium chloride crystal is
subjected to an electric field of
1000v/m. the resultant
polarization is 4.3*10⁻⁸C/m².
calculate the relative permittivity
of sodium chloride crystal.
Sol.:- Given data,
Polarization
𝑃 =∈ 𝑜 ∈ 𝑟 − 1 𝐸
∴
𝑃
∈ 𝑜. 𝐸
=∈ 𝑟 − 1
∴∈ 𝑟 = 1 +
𝑃
∈ 𝑜 ∗ 𝐸
= 1 +
4.3 ∗ 10−8
8.85 ∗ 10−12 1000
∈ 𝑟 = 5.86
40

41. 3) Calculate the electronic
polarizability of Argon atom, given
∈ 𝑟 = 1.0024and NTTP &
N=2.7*10²⁵ atom/m³.
Sol.:-
𝑃 =∈ 𝑜 ∈ 𝑟 − 1 ∗ 𝐸
𝑎𝑙𝑠𝑜, 𝑃 = 𝑁 𝛼𝑒 𝐸
𝑁𝛼𝑒𝐸 =∈ 𝑜 ∈ 𝑟 − 1 ∗ 𝐸 ∴ 𝛼𝑒
=
∈ 𝑜 ∈ 𝑟 − 1
𝑁
=
8.85 ∗ 10−12 ∗ 1.0024 − 1
2.7 ∗ 1025
= 7.9 ∗ 10−40 𝐹 − 𝑚2
4) A parallel plate has capacitance of
5μF. The dielectric has permittivity
Ɛr=100, for an applied voltage of
1000V.
Sol.:-
1) Energy stored in capacitor,
𝑊 =
1
2
𝐶𝑉²
=
1
2
∗ 5 ∗ 10−6
∗ 1000 2
= 2.5𝐽
𝐶𝑜 =
𝐶
∈ 𝑟
=
5
100
= 0.05 ∗ 10−6 𝐹
2) Energy stored in polarizing the
dielectric
𝑊′ =
1
2
𝐶 − 𝐶𝑜 𝑉2
=
1
2
5 − 0.05 ∗ 10002 ∗ 10−6
= 2.475𝐽
41