1. Lecture 7
Dielectrics

2. Lecture Objective
In this unit you will learn
What dielectrics are, and how they make capacitors more effective.
Dielectric Polarization
Principal Properties of Dielectrics

3. What is a dielectric?
The word is coined in the mid 19th century from two English words:
Origin
English di
electric
dielectric
Literal meaning: ‘across which electricity is transmitted (without conduction).’

4. What is a dielectric?
Dielectrics are insulators, plain and simple. The two words refer to the same class of materials, but are of different origin and are used preferentially in different contexts.
Since charges tend not to move easily in nonmetallic solids it's possible to have "islands" of charge in glass, ceramics, and plastics. The latin word for island is insula, which is the origin of the word insulator. In contrast, charges in metallic solids tend to move easily — as if someone or something was leading them. The latin prefix con or com means "with". A person you have bread with is a companion. (The latin word for bread is panis.) To take something with you on the road is to convey it. (The latin word for road is via.) The person you travel with who leads the way or provides safe passage is a conductor. (The latin word for leader is ductor.) A material that provides safe passage for electric charges is a conductor.

5. What is a dielectric?
Inserting a layer of nonmetallic solid between the plates of a capacitor increases its capacitance. The greek prefix di or dia means "across". A line across the angles of a rectangle is a diagonal. (The greek word for angle is gonia — γωνία.) The measurement across a circle is a diameter. (The greek word for measure is metron — μέτρον.) The material placed across the plates of a capacitor like a little nonconducting bridge is a dielectric.
Alternatively, a dielectric (insulator) is a medium which possess no (or very few) free electrons to provide currents due to an impressed electric field.
Electrical insulators obviously must have a very low conductivity, or high resistivity, to prevent the flow of current.
Porcelain, alumina, cordierite, mica, glasses and plastics are examples of insulators.

6. Capacitance Of A Parallel-plate Capacitor
A "charged" capacitor can store charge. When a capacitor is being charged, negative charge is removed from one side of the capacitor and placed onto the other, leaving one side with a negative charge (-Qo) and the other side with a positive charge (+Qo). V

7. Capacitance Of A Parallel-plate Capacitor
Consider two plane parallel metal plates, each of area A and separated a distance d apart in air. If the plates have equal and opposite charge densities + and -, then the magnitude of the electric field at any point in the space between the two plates is
Qo = σA
Therefore, capacitance of the structure in air is +σ E V d -σ
Units of capacitance: Coulomb/Volt = Farad

8. Observations
From the equation for capacitance
we note that the capacitance can be increased:
by decreasing the distance d between the plates,
by increasing the area A.
Note, however, that there is a practical limit on how small a value of d we can use. Practically, for any separation d, the maximum voltage that can be applied across the capacitor plates without causing a discharge depends on the dielectric strength of the dielectric.

9. Capacitance Of A Parallel-plate Capacitor
Consider next the effect of inserting an insulating material between the two plates. As a slab of insulating material is inserted between the plates, there is an external current flow indicating that more charge is stored on the plates. Let Q be charge on the plates with a dielectric medium after the capacitor has finished charging. The capacitance of the structure is now
Defining
where Q > Qo.
we can write
Thus, the insertion of the dielectric material into the capacitor has increased its capacitance by a factor r !

10. Summary
Introducing a dielectric into a capacitor decreases the electric field, which decreases the voltage, which increases the capacitance.
A capacitor with a dielectric stores the same charge as one without a dielectric, but at a lower voltage. Therefore a capacitor with a dielectric in it is more effective.

11. (a) What will be the change in capacitor voltage?
Worked Example
A particular capacitor has a capacitance of 4.7 nF in the absence of any dielectric filling. The capacitor is charged to 150 V and then, in an electrically isolated condition, it is filled with a dielectric of relative permittivity r = 3.
(a) What will be the change in capacitor voltage?
(b) How much extra electric charge is now needed to restore the original voltage?
Solution
V0 = 150 V
+Q0
-Q0
Air-filled capacitor

12. Dielectric-filled capacitor New value of capacitance
Solution +Q -Q
Dielectric-filled capacitor V
New value of capacitance
New value of voltage drop across capacitor
Change in voltage,
V =150 – 50 =100 V
Charge stored by capacitor when voltage restored to 150 V is
Therefore, extra charge needed is

13. Worked Example
A parallel-plate capacitor is charged through a battery of 50 volt, The capacitor is now disconnected with battery and a dielectric slab is inserted in the gap between the plates. If the potential difference is reduced to half that of the original, find the dielectric constant of the slab.
Solution
V0 = 50 V
+Q0
-Q0
Air-filled capacitor

14. Dielectric-filled capacitor
Solution +Q -Q
Dielectric-filled capacitor V
When a dielectric is inserted into the capacitor, the capacitance becomes
New value of voltage drop across capacitor
Therefore, solving for r in the above equation, we obtain

15. Physics of Dielectric Polarization
Earlier we have see that introducing a dielectric into a capacitor decreases the electric field inside the capacitor, which decreases the voltage, which in turn increases the capacitance.
Let us now investigate the physics behind the increase in capacitance caused by the introduction of a dielectric into a capacitor
Consider two oppositely charged metal plates in a vacuum, as shown in the figure below. The force Fo that attracts the two plates towards each other is given by E0
Electric field in vacuum Q1 Q2
The electric field that is established in the space between the two metal plates is

16. Physics of Dielectric Polarization
Suppose now a dielectric is inserted to completely fill the space in between the two metal plates. The force attracting the two metal plates is now E
Electric field in dielectric Q1 Q2
and the electric field in the dielectric is
Thus, the insertion of a dielectric material in the space between the two metal plates has caused to the electric field in dielectric to be reduced by r.
What caused the electric field to be reduced? To answer this question, we need to look at the microscopic level, i.e., what happens to the atoms and molecules when an electric field is applied to a dielectric.

17. Physics of Dielectric Polarization
When an electric field is applied to a dielectric material, the atoms and molecules inside the dielectric material are stretched to align with the applied field, i.e. become “polarized”. When a dielectric is polarized, the dipole moments of the molecules in the dielectric are partially aligned with the external field Eo. This polarization causes an induced charge on the opposite side. The induced surface charge give rise to an induced electric field Ei in the direction opposite the external field Eo.

18. Physics of Dielectric Polarization
The net electric field in the dielectric is given by:
E = Eo - Ei
So, polarization of the dielectric causes a reduction in the net electric field within the dielectric, which decreases the voltage, which increases the capacitance. E0 Ei +σ -σ
σi
σi

19. Electric Dipole Moment
An electric dipole is a pair of point charges with equal magnitude & opposite sign
The electric dipole moment of anything — be it an atom stretched in an external electric field, a polar molecule, or two oppositely charged metal spheres — is defined as the product of charge and separation. In the simple case of two point charges, one with charge +q and the other one with charge −q, the electric dipole moment p is: +q -q d
p = q d
where d is the displacement vector pointing from the negative charge to the positive charge. Thus, the electric dipole moment vector p points from the negative charge to the positive charge. 
The SI unit of dipole moment is coulomb-meter, which has no special name.

20. Worked Example
Calculate the electric dipole moment of a hydrogen atom given that the Bohr radius (the distance between the proton and electron in a hydrogen atom in its ground state) is 5.29 x m.
Solution
The electric dipole moment for a pair of opposite charges of magnitude q is defined as the magnitude of the charge times the distance between them and the defined direction is toward the positive charge.  So, for this one, where
q = e = x C and
d = 5.29 x nm
we obtain
p = qd = x x 5.29 x =8.512 x C.m p
The dipole moment p has a direction that points from the electron to the proton.

21. Polar and Non-polar Molecules
Polarization occurs in both polar and non-polar materials.
Polar dielectric material is composed of molecules that have a permanent electric dipole moment due to their molecular structure e.g., water molecules. In the absence of an externally applied electric field, the permanent dipoles are randomly oriented and so the net dipole moment is zero.
Water is a polar molecule because of the way the atoms bind in the molecule such that there are excess electrons on the Oxygen side and a lack or excess of positive charges on the Hydrogen side of the molecule.

22. Non-polar molecules
Non-polar dielectric material is composed of atoms or molecules that have no electric dipole moment.
A pair of covalent-bonded nitrogen atoms form a non-polar molecule. A nitrogen atom has 5 electrons in its outer shell. Two nitrogen atoms will each share three electrons to form three covalent bonds and make a nitrogen molecule.
There are no ions present (no + or – charges) in nitrogen gas because the electrons are shared, not transferred from one atom to another.
Nitrogen molecule

23. Polarization By Stretching
Induced Polarizations
Dielectric polarization occurs when a dipole moment is formed in an insulating material because of an externally applied electric field.
There are two principal methods by which a dielectric can be polarized: stretching and rotation.
Stretching
Stretching an atom or molecule results in an induced dipole moment added to every atom or molecule.
Polarization By Stretching

24. Polarization by Rotation
Rotation occurs only in polar molecules — those with a permanent dipole moment like the water molecule shown in the diagram below.
Without field
With field
Polarization by Rotation

25. Induced Polarization Types
Electronic Polarizability
In the absence of an applied electric field, the positively charged nucleus is surrounded by a spherical electron cloud with equal and opposite charge. Outside the atom, the electric field is zero.
In the presence of an applied electric field, the electron cloud is distorted such that it is displaced in a direction (w.r.t. the nucleus) opposite to that of the applied electric field.
electron
cloud
electron
cloud
nucleus
nucleus
Eapp

26. Electronic Polarizability
The net effect is that each atom becomes a small charge dipole which affects the total electric field both inside and outside the material.

27. Ionic Polarizability
Ionic polarization is a mechanism that contributes to the relative permittivity of a material. This type of polarization typically occurs in ionic crystal elements such as NaCl, KCl, and LiBr.  There is no net polarization inside these materials in the absence of an external electric field because the dipole moments of the negative ions are canceled out with the positive ions. However, when an external field is applied, the ions become displaced, which leads to an induced polarization. Figure below shows the displacement of ions due to this external electric field.    

28. Ionic Polarizability
The net effect is that each ionic molecule is a small charge dipole which aligns with the applied electric field and influences the total electric field both inside and outside the material.

29. 3. Orientational Polarization of Polar Molecules
In the absence of an applied electric field, the polar molecules are randomly oriented such that the net dipole moment within any small volume is zero.
This induction is caused by the opposite direction of the electric force on the negative and positive charges of a molecule, which displaces the centre of the relative charge distributions and produces an induced electric dipole moment. E
Without field
These molecules can be induced to have a dipole moment under the influence of an external electric field.
With field

30. 3. Orientational Polarization of Polar Molecules
The net effect is that each polar molecule is a small charge dipole which aligns with the applied electric field and influences the total electric field both inside and outside the material.

31. dielectric constant εr
The Dielectric Constant
material
dielectric constant εr
vacuum 1
air
rubber
glass
5-10
NaCl
5.9
ethanol
25.8
water
81.1
barium titanate
we can understand this much better. For air epsilon close to 1. Only electronic polarisation and low density.
Rubber and glass higher density but not really ionic. On the other hand, shifts of charges thinkable. NaCl ionic but not so much more either. Liquids with permanent dipoles rather high.
barium titanate really high but let’s talk about this later.
For air epsilon close to 1. Only electronic polarisation and low density.
Rubber and glass higher density but not really ionic. On the other hand, shifts of charges thinkable.
NaCl ionic but not so much more either.
Liquids with permanent dipoles rather high.
Barium titanate really high. 31

32. Interaction of Electromagnetic Field with Matter
An alternating voltage applied to a dielectric material produces an oscillating electric field inside the material. This alternating field interacts with the dipoles and causes them to rotate and align themselves with the field. As time passes, the electric field reverses its direction, and the dipoles must rotate again to remain aligned with the correct polarity. As they rotates, energy is lost through the generation of heat (friction) as well as the acceleration and deceleration of the rotational motion of the dipoles.
Figure showing the rotation of a polar diatomic molecule under ac field excitation.

33. Because of the frequency dependence of the dielectric constant, εr is in general a complex quantity which can be expressed in the form
Under dc conditions, the imaginary term is zero and so
Under ac field excitation, the degree to which the dipole is out of phase with the incident electric field and the losses that ensue determine how large the imaginary part of the permittivity is as a function of material and frequency. The larger the imaginary part, the more energy is being dissipated through motion, and the less energy is available to propagate past the dipole. Thus, the imaginary part of the relative permittivity directly relates to loss in the system.

34. The typical behavior of real and imaginary part of the permittivity as a function of frequency is show in the following figure.
Frequency dependence of dielectric permittivity for an ideal dielectric material.

35. As can be seen in the figure, the relative permittivity of material is related to a variety of physical phenomena that contribute to the polarization of the dielectric material. In the low frequency range the εr is dominated by the influence of ion conductivity. The variation of permittivity in the microwave range is mainly caused by dipolar relaxation, and the absorption peaks in the infrared region and above, are mainly due to atomic and electronic polarizations.

36. Principal Dielectric Properties
1. Dielectric constant, ’
High for charge storage device e.g. capacitor
Low for faster signal transmission (speed ~ 1/)
2. Dielectric (energy) loss, ”
High for microwave heating
Low for signal transmission
3. Dielectric strength
High for most insulating applications

37. Capacitor with lossless Dielectric
When a perfect insulation is subjected to alternating voltage, it is like applying alternating voltage to a perfect capacitor. In a perfect capacitor the charging current would lead the applied voltage by 90° exactly. This means that there is no power loss in the insulation.

38. Capacitor with lossy Dielectric
In most insulating materials there is a definite amount of dissipation of energy when an insulator is subjected to alternating voltage. This dissipation of energy is called dielectric loss.
Consider a capacitor with a lossy dielectric.
Impedance of circuit
Thus, admittance (Y = 1/Z)

39. The admittance can be written in the form
where
and
Thus, the simplest model for a capacitor with a lossy dielectric is as a capacitor C’ with a perfect dielectric in parallel with a resistor R ( = 1/G) giving the power dissipation.

40. The current now leads the voltage by a very little less than 90°, where the difference δ (Greek letter delta) is termed the dielectric loss angle, as seen in the figure below.
The fraction of the maximum energy lost each cycle, divided by 2 is termed the ‘loss factor’ and its value is given by tan δ (‘tan delta’). From the phasor diagram
The loss tangent represents how lossy the material is for ac signals.

41. Dielectric loss
(because IR = Icos]
(because )
Therefore,
(using )
where V = applied voltage in volts, A = area of the electrode
f = supply frequency in Hz, d = thickness of dielectric medium
0 = is the absolute permittivity of the medium

42. Power loss per unit volume
(using vol = Ad )
Power loss per unit volume in terms of applied electric field E,
(using E = V/d )

43. Table 1: Some typical values of dielectric parameters
Table 1 shows some typical values of dielectric constant and loss factor. The AC values are measured at 1MHz.
Table 1: Some typical values of dielectric parameters
material r
tan δ
air
1.0006
polycarbonate
2.3
0.0012
FR-4
4.4
0.035
alumina
8.8
barium titanate
1200+
0.01

44. Dielectric Heating
Dielectric heating, also known as electronic heating, RF heating, high-frequency heating is the process in which a high-frequency alternating electric field, or radio wave or microwave electromagnetic radiation heats a dielectric material.
The material to be heated is placed between two electrodes (which act as capacitor plates) and forms the dielectric component of a capacitor (see illustration). The electrodes are connected to a high-voltage source of 2-90-MHz power, produced by a high-frequency vacuum-tube oscillator.
Basic assembly for dielectric heating

45. The resultant heat is generated within the material, and in homogeneous materials is uniform throughout. Dielectric heating is a rapid method of heating and is not limited by the relatively slow rate of heat diffusion present in conventional heating by external surface contact or by radiant heating.
This technique is widely employed industrially for preheating in the molding of plastics, for quick heating of thermosetting glues in cabinet and furniture making, for accelerated jelling and drying of foam rubber, in foundry core baking, and for drying of paper and textile products. Its advantages over conventional methods are the speed and uniformity of heating, which offset the higher equipment costs. Because of the absence of high thermal gradients, an improved end-product quality is usually obtained.

46. Worked Example
A piece of insulating material is to be heated by dielectric heating. The size of the piece is 10 x 10 x 3 cm3. A frequency of 30 MHz is used and the power absorbed is 400 W. Determine the voltage necessary for heating and the current that flows in the material. The material has a permittivity of 5 and a power factor of 0.05.

47. Solution The capacitance offered by the material is given by
where 0 = 8.85 x 10-12, r = 5, and A = 10 x 10 x 10-4 = 0.01 m2.
Therefore,
From the phasor diagram,
Thus,

48. The power loss,
Therefore,
Solving for V in the above equation, we obtain
Total current:

49. Dielectric strength
All insulating materials fail at some level of applied voltage, and ‘dielectric strength’ is the voltage a material can withstand before breakdown occurs.
The theoretical dielectric strength of a material is an intrinsic property of the bulk material and is dependent on the configuration of the material or the electrodes with which the field is applied.
The "intrinsic dielectric strength" is measured using pure materials under ideal laboratory conditions.
At breakdown, the electric field frees bound electrons. If the applied electric field is sufficiently high, free electrons from background radiation may become accelerated to velocities that can liberate additional electrons during collisions with neutral atoms or molecules in a process called avalanche breakdown.

50. Dielectric strength
Breakdown occurs quite abruptly (typically in nanoseconds), resulting in the formation of an electrically conductive path and a disruptive discharge through the material.
For solid materials, a breakdown event severely degrades, or even destroys, its insulating capability.

51. Factors affecting apparent dielectric strength
it increases slightly with increased sample thickness.
it decreases with increased operating temperature.
it decreases with increased frequency.
for gases (e.g. nitrogen, sulfur hexafluoride) it normally decreases with increased humidity.
for air, dielectric strength increases slightly as humidity increases

52. Corona
Another failure mode related to voltage stress failure is ‘corona’, which is ionisation under voltage stress of air inside or at the interfaces of insulating materials. Breakdown occurs at edges, points, interfaces, voids or gaps at voltages which depend on the materials and part geometries.
Corona erodes the insulator surface by electron bombardment, associated heat, and sometimes secondary effects from the formation of chemical oxidising agents such as ozone and oxides of nitrogen. This effect begins immediately, and even fractions of a second of exposure at AC voltages near to breakdown will significantly reduce the breakdown strength. Corona-induced breakdown will also occur at lower voltages, but the time required will be longer.

53. Corona discharge on insulator string of a 500 kV transmission line.

54. Dielectric Stress in a Single-Core Cable
Under operating conditions, the insulation of a cable is subjected to electrostatic forces. This is known as dielectric stress. The stress at any point in a cable is in fact the potential gradient (or electric intensity) at that point.
Consider a single-core cable with a core diameter d and internal sheath diameter D. As proven earlier, the electric intensity at a distance r from the centre of the cable is
volts/m
By definition, electric intensity is equal to potential gradient. Therefore, potential gradient |dV/dr| at a distance r metres from the cable is

55. Now, potential difference V between conductor and sheath is
Thus, we obtain

56. It is clear that potential gradient varies inversely as the radius r
It is clear that potential gradient varies inversely as the radius r. Therefore, potential gradient will be maximum when r is minimum i.e. when r = d/2 or at the surface of the conductor. On the other hand, potential gradient will be minimum at r = D/2 or at sheath surface. Therefore, maximum potential gradient is
(Putting x = d/2)
The minimum stress occurs at the sheath and its value is given by

57. Worked Example
A 33 kV single-core cable has a conductor diameter of 1 cm and a sheath of inside diameter 4 cm. Find the minimum and maximum stress in the insulation.
Solution
The maximum stress occurs at the conductor surface and its value is given by:
Here V = 33 kV (rms); d = 1 cm; D = 4 cm.

58. Solution
Substituting the values in the previous expression, we get
The minimum stress occurs at the sheath and its value is given by

59. END