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Fundamentals of Electromagnetics for Teaching and Learning: A Two-Week Intensive Course for Faculty in Electrical-, Electronics-, Communication-, and Computer- Related Engineering Departments in Engineering Colleges in India

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Discuss the effect of polarization in a dielectric material, involving polarization charge and polarization current. 5.8. What is the polarization vector? How is it ... – PowerPoint PPT presentation

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Title: Fundamentals of Electromagnetics for Teaching and Learning: A Two-Week Intensive Course for Faculty in Electrical-, Electronics-, Communication-, and Computer- Related Engineering Departments in Engineering Colleges in India


1
Fundamentals of Electromagnetics for Teaching and
Learning A Two-Week Intensive Course for Faculty
in Electrical-, Electronics-, Communication-, and
Computer- Related Engineering Departments in
Engineering Colleges in India
  • by
  • Nannapaneni Narayana Rao
  • Edward C. Jordan Professor Emeritus
  • of Electrical and Computer Engineering
  • University of Illinois at Urbana-Champaign, USA
  • Distinguished Amrita Professor of Engineering
  • Amrita Vishwa Vidyapeetham, India

2
Program for Hyderabad Area and Andhra Pradesh
Faculty Sponsored by IEEE Hyderabad Section, IETE
Hyderabad Center, and Vasavi College of
Engineering IETE Conference Hall, Osmania
University Campus Hyderabad, Andhra Pradesh June
3 June 11, 2009 Workshop for Master Trainer
Faculty Sponsored by IUCEE (Indo-US Coalition for
Engineering Education) Infosys Campus, Mysore,
Karnataka June 22 July 3, 2009
3
  • Module 5
  • Materials and Wave Propagation in Material Media
  • 5.1 Conductors and dielectrics
  • 5.2 Magnetic materials
  • 5.3 Wave equation and solution
  • 5.4 Uniform waves in dielectrics and conductors
  • 5.5 Boundary conditions
  • 5.6. Reflection and transmission of uniform plane
    waves

4
Instructional Objectives
  • 31. Find the charge densities on the surfaces of
    infinite plane
  • conducting slabs (with zero or nonzero net
    surface charge
  • densities) placed parallel to infinite
    plane sheets of charge
  • 32. Find the displacement flux density, electric
    field intensity,
  • and the polarization vector in a dielectric
    material in the
  • presence of a specified charge
    distribution, for simple
  • cases involving symmetry
  • 33. Find the magnetic field intensity, magnetic
    flux density,
  • and the magnetization vector in a magnetic
    material in the
  • presence of a specified current
    distribution, for simple
  • cases involving symmetry

5
Instructional Objectives (Continued)
  • 34. Determine if the polarization of a specified
  • electric/magnetic field in an anisotropic
  • dielectric/magnetic material of
    permittivity/permeability
  • matrix represents a characteristic
    polarization
  • corresponding to the material
  • 35. Write expressions for the electric and
    magnetic fields of a
  • uniform plane wave propagating away from an
    infinite
  • plane sheet of a specified sinusoidal
    current density, in a
  • material medium
  • 36. Find the material parameters from the
    propagation
  • parameters of a sinusoidal uniform plane
    wave in a
  • material medium
  • 37. Find the power flow, power dissipation, and
    the electric
  • and magnetic stored energies associated
    with electric and
  • magnetic fields in a material medium

6
Instructional Objectives (Continued)
  • 38. Determine whether a lossy material with a
    given set of
  • material parameters is an imperfect
    dielectric or good
  • conductor for a specified frequency
  • 39. Find the charge and current densities on a
    perfect
  • conductor surface by applying the boundary
    conditions
  • for the electric and magnetic fields on the
    surface
  • 40. Find the electric and magnetic fields at
    points on one side
  • of a dielectric-dielectric interface, given
    the electric and
  • magnetic fields at points on the other side
    of the interface
  • 41. Find the reflected and transmitted wave
    fields for a given
  • field of a uniform plane wave incident
    normally on a
  • plane interface between two material media

7
  • 5.1 Conductors
  • and Dielectrics
  • (EEE, Secs. 4.1, 4.2 FEME, Sec. 5.1)

8
Materials
Materials contain charged particles that under
the application of external fields respond
giving rise to three basic phenomena known as
conduction, polarization, and magnetization.
While these phenomena occur on the atomic or
microscopic scale, it is sufficient for our
purpose to characterize the material based on
macroscopic scale observations, that is,
observations averaged over volumes large compared
with atomic dimensions.
8
9
  • Material Media can be classified as
  • (1) Conductors
  • and Semiconductors
  • (2) Dielectrics
  • (3) Magnetic materials magnetic property
  • Conductors and Semiconductors
  • Conductors are based upon the property of
    conduction, the phenomenon of drift of free
    electrons in the material with an average drift
    velocity proportional to the applied electric
    field.

electric property
10
In semiconductors, conduction occurs not only by
electrons but also by holes vacancies created
by detachment of electrons due to breaking of
covalent bonds with other atoms. The conduction
current density is given by
Ohms Law at a point
11
The effect of conduction is taken into account
explicitly by using J Jc on the right side of
Maxwells curl equation for H.
conductors semiconductors
12
Ohms Law
Ohms Law
Resistance
13
5-12
  • D4.1
  • (a) For cu,
  • (b)

14
  • (c) From

15
  • Conductor in a static electric field

16
Plane conducting slab in a uniform electric field
5-15
5-15
rS e0E0
rS e0E0
rS e0E0
rS e0E0
rS e0E0
rS e0E0
17
5-16
  • P4.3
  • (a)

18
5-17
  • (b)

(1)
(2)
Write two more equations and solve for the four
unknowns.
19
5-18
Solving the four equations, we obtain
20
Dielectrics
are based upon the property of polarization,
which is the phenomenon of the creation of
electric dipoles within the material.
Electronic polarization (bound electrons are
displaced to form a dipole)
Dipole moment p Qd
21
Orientational polarization (Already existing
dipoles are acted upon by a torque)
Direction into the paper.
Ionic polarization (separation of positive and
negative ions in molecules)
22
The phenomenon of polarization results in a
polarization charge in the material which
produces a secondary E.
11
23
Plane dielectric slab in a uniform electric field
24
Polarization Current (in the time-varying case)
25
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26
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27
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28
5-27
The effect of polarization needs to be taken into
account by adding the contributions from the
polarization charges and the polarization
current to the right sides of Maxwells equations.

For free space,
29
5-28
For dielectrics,
Where P is the polarization vector, or the dipole
moment per unit volume. Rearranging,
where now,
30
Thus, to take into account the effect of
polarization, we define the displacement flux
density vector, D, as
vary with the material, implicitly
taking into account the effect of polarization.
31
5-30
As an example, consider
Then, inside the material,
32
D4.3
For 0 lt z lt d,
(a)
33
5-32
(b)
(c)
34
5-33
Isotropic Dielectrics
D is parallel to E for all E.
Anisotropic Dielectrics
D is not parallel to E in general. Only for
certain directions (or polarizations) of E is D
parallel to E. These are known as characteristic
polarizations.
35
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36
5-35
D4.4
(a)
37
5-36
(b)
38
5-37
(c)
39
Review Questions
  • 5.1. Distinguish between bound electrons and free
    electrons
  • in an atom.
  • 5.2. Briefly describe the phenomenon of
    conduction.
  • 5.3. State Ohm law valid at a point, defining
    conductivity.
  • How is conduction current taken into
    account in
  • Maxwells equations?
  • 5.4. Discuss the formation of surface charge at
    the boundaries
  • of a conductor placed in a static electric
    field.
  • 5.5. Briefly describe the phenomenon of
    polarization in a
  • dielectric material. What are the
    different kinds of
  • polarization?
  • 5.6. What is an electric dipole? How is its
    strength defined?

40
Review Questions (Continued)
  • 5.7. Discuss the effect of polarization in a
    dielectric material,
  • involving polarization charge and
    polarization current.
  • 5.8. What is the polarization vector? How is
    it related to the
  • electric field intensity?
  • 5.9. Discuss how the effect of polarization in
    a dielectric
  • material is taken into account in
    Maxwells equations.
  • 5.10. Discuss the revised definition of the
    displacement flux
  • density and the permittivity concept.
  • 5.11. What is an anisotropic dielectric material?
    When can an
  • effective permittivity be defined for an
    anisotropic
  • dielectric material?

41
Problem S5.1. Finding the electric field due to
a point charge in the presence of a conductor
42
Problem S5.1. Finding the electric field due to a
point charge in the presence of a conductor
(Continued)
43
Problem S5.2. Finding D, E, and P for a line
charge surrounded by a cylindrical shell of
dielectric material
44
Problem S5.3. Expressing an electric field in
terms of the characteristic polarizations of an
anisotropic dielectric
45
5.2 Magnetic Materials (EEE, Sec. 4.3 FEME, Sec.
5.2)

46
Magnetic Materials
are based upon the property of magnetization,
which is the phenomenon of creation of magnetic
dipoles within the material.
Diamagnetism
A net dipole moment is induced by changing the
angular velocities of the electronic orbits.
Dipole moment m IA an
47
Paramagnetism
Already existing dipoles are acted upon by a
torque.
Other Ferromagnetism, antiferromagnetism, ferrima
gnetism
48
The phenomenon of magnetization results in a
magnetization current in the material which
produces a secondary B.
49
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50
Magnetization Current
51
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52
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53
5-52
5-52
The effect of magnetization needs to be taken
into account by adding the contributions from the
magnetization current to the right sides of
Maxwells equations.
For nonmagnetic materials,
54
5-53
For magnetic materials,
where M is the magnetization vector, or the
magnetic dipole moment per unit volume.
55
5-54
Rearranging,
where now
56
Thus, to take into account the effect of
magnetization, we define the magnetic field
intensity vector, H, as
mr and m vary with the material, implicitly
taking into account the effect of magnetization.
57
5-56
As an example, consider
Then inside the material,
58
5-57
5-57
D4.6
For 0 lt z lt d,
(a)
59
(b)
(c)
60
Materials and Constitutive Relations
Summarizing,
Conductors
Dielectrics
Magnetic materials
E and B are the fundamental field vectors.
D and H are mixed vectors taking into account the
dielectric and magnetic properties of the
material implicity through ? and m,
respectively.
??
61
Review Questions
  • 5.12. Briefly describe the phenomenon of
    magnetization in a
  • material. What are the different kinds
    magnetization?
  • 5.13. What is a magnetic dipole? How is its
    strength defined?
  • 5.14. Discuss the effect of magnetization in a
    magnetic
  • material, involving magnetization
    current.
  • 5.15. What is the magnetization vector? How is
    it related to
  • the magnetic flux density?
  • 5.16. Discuss how the effect of magnetization in
    a magnetic
  • material is taken into account in
    Maxwells equations.
  • 5.17. Discuss the revised definition of the
    magnetic field
  • intensity and the permeability concept.
  • 5.18. Summarize the constitutive relations for a
    material
  • medium.

62
Problem S5.4. Finding H, B, and M for a wire of
current surrounded by a cylindrical shell of
magnetic material
63
5.3 Wave Equation and Solution (EEE, Sec. 4.4
FEME, Sec. 5.3)
64
5-63
Maxwells equations for a material medium
65
5-64
Waves in Material Media
66
Combining, we get
Define
Then
Wave equation
67
5-66
Solution
68
attenuation
attenuation
a attenuation constant, Np/m
b phase constant, rad/m
69
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70
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71
5-70
72
5-71
Summarizing,
Conversely,
73
5-72
Characteristics of Wave Propagation
The quantity ? characterizes attenuation, which
is a function of frequency. The quantity vp
characterizes phase velocity, which is a
function of frequency, giving rise to dispersion.
The complex nature of results in phase
difference between the electric and magnetic
fields.
74
5-73
75
Three-dimensional depiction of wave propagation
76
5-75
5-75
E5.1
Solution
77
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78
5-77
79
5-78
80
Power Flow and Energy Storage
5-79
A Vector Identity
For
Poynting Vector
81
Poyntings Theorem for Material Medium
Magnetic stored energy density
Power dissipation density
Source power density
Electric stored energy density
82
Interpretation of Poyntings Theorem
5-81
Poyntings Theorem for the material medium says
that the power delivered to the volume V by the
current source J0 is accounted for by the power
dissipated in the volume due to the conduction
current in the medium, plus the time rates of
increase of the energies stored in the electric
and magnetic fields, plus another term, which we
must interpret as the power carried by the
electromagnetic field out of the volume V, for
conservation of energy to be satisfied.
83
5-82
In the case of the infinite plane sheet of
current, work is done by an external agent
(source) for the current to flow, and
represents the power density (per unit
volume) associated with this work.
84
Review Questions
  • 5.19. Summarize Maxwells equations for a
    material medium.
  • 5.20. What is the propagation constant in a
    material medium?
  • Discuss the significance of its real and
    imaginary parts.
  • 5.21. What is the intrinsic impedance of a
    material medium?
  • Discuss the significance of its complex
    nature.
  • 5.22. Discuss the consequence of the frequency
    dependence
  • of the phase velocity in a material
    medium.
  • 5.23. Discuss the solution for the
    electromagnetic field due to
  • to an infinite plane current sheet of
    sinusoidally time-
  • varying current density embedded in a
    material medium.
  • 5.24. How would you obtain the electromagnetic
    field due
  • to a current sheet of nonsinusoidally
    time-varying
  • current density embedded in a material
    medium?

85
Review Questions (Continued)
  • 5.25. State and discuss Poyntings theorem for a
    material
  • medium.
  • 5.26. What are the power dissipation density, the
    electric
  • stored energy density, and the magnetic
    stored energy
  • density associated with an
    electromagnetic field in a
  • material medium?

86
Problem S5.5. Finding the magnetic field and
material parameters from a specified electric
field
87
Problem S5.6. Finding E and H for a current
sheet of nonsinusoidal current density in a
material medium
88
Problem S5.7. For showing that the time average
powers delivered to, and dissipated in, a medium
are the same
89
5.4 Uniform Plane Waves in Dielectrics and
Conductors (EEE, Sec. 4.5 FEME, Sec. 5.4)
90
5-89
5-89
Special Cases
Case 1. Perfect dielectric
Behavior same as in free space except that ?0 ?
? and ?0 ? ?.
91
5-90
For materials with nonzero conductivity, there
are two special cases, depending on the
relationship between and ?? . The quantity
/?? is known as the loss tangent.
From
it can be seen that /?? is the ratio of the
amplitudes of the conduction current density and
the displacement current density in the material.

92
5-91
Case 2. Imperfect Dielectric
Behavior essentially like in a perfect dielectric
except for attenuation.
93
5-92
Case 3. Good Conductor
Behavior much different from that in a
dielectric.
94
5-93
Characteristics of wave propagation in a good
conductor
Skin effect Concentration of fields near the
skin of the conductor. Skin depth, ? Distance
in which fields are attenuated by the factor e?1,
that is, ?? 1.
Ex For copper,
95
5-94
5-94
Even at a low frequency of 1 MHz, ? 0.066 mm.
This explains the phenomenon of shielding by
good conductors, such as copper, aluminum, etc.
96
5-95
. Furthermore,
the lower the frequency, the smaller is the
ratio. Coupled with the fact that this property
makes low frequencies more suitable for
communication with underwater objects.
Ex For sea water,
The value of the ratio of
the two wavelengths for f 25 kHz is 1/134.
97
5-96
For copper,
Even at a frequency of 1012 Hz, this is equal
to 0.369 ?, a very low value. In fact, if we
note that
we see that
Hence, for the same electric field, the magnetic
field inside a good conductor is much larger than
that inside a dielectric.


98
5-97
Case 4. Perfect Conductor
  • No waves can penetrate into a perfect conductor.
  • No time-varying fields inside a perfect
    conductor.

99
Review Questions
  • 5.27. What is loss tangent? Discuss its
    significance.
  • 5.28. What is the condition for a material to be
    a perfect
  • dielectric? How do the characteristics
    of wave
  • propagation in a perfect dielectric
    medium differ from
  • those of wave propagation in free space?
  • 5.29. What is the condition for a material to be
    an imperfect
  • dielectric? What is the significant
    feature of wave
  • propagation in an imperfect dielectric
    as compared to
  • that in a perfect dielectric?
  • 5.30. What is the condition for a material to be
    a good
  • conductor? Give two examples of
    materials that behave
  • as good conductors for frequencies up to
    several
  • gigahertz.
  • 5.31. What is skin effect? Discuss skin depth,
    giving some
  • numerical values.

100
Review Questions (Continued)
  • 5.32. Why are low-frequency waves more suitable
    than high-
  • frequency waves for communication with
    underwater
  • objects?
  • 5.33. What is the consequence of the low
    intrinsic impedance
  • of a good conductor as compared to that
    of a dielectric
  • medium having the same e and µ.
  • 5.34. Why can there be no time-varying fields
    inside a perfect
  • conductor?

101
Problem S5.8. Plotting field variations for an
infinite plane sheet current source in a perfect
dielectric medium
102
Problem S5.9. Calculating parameters for good
conductor materials to satisfy specified
conditions
103
5.5 Boundary Conditions (EEE, Sec. 4.6 FEME,
Sec. 5.5)
104
Why boundary conditions?
Medium 1
Medium 2
Inc. wave
Trans. wave
Ref. wave
105
5-104
Maxwells equations in integral form must be
satisfied regardless of where the contours,
surfaces, and volumes are.
Example
C3
C2
C1
Medium 1
Medium 2
106
Boundary Conditions
5-105
???????????
?????????????
??
107
5-106
Example of derivation of boundary conditions
Medium 1
Medium 2
108
or,
109
Summary of boundary conditions
110
Perfect Conductor Surface
(No time-varying fields inside a perfect
conductor. Also no static electric field may be
a static magnetic field.) Assuming both E and H
to be zero inside, on the surface,
111
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112
Dielectric-Dielectric Interface
113
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114
5-113
D4.11
At a point on a perfect conductor surface,
and
pointing away from the surface. Find . D0 is
positive.
(a)
115
and
pointing toward the surface. D0 is positive.
(b)
116
E5.2
(a)
117
5-116
(b)
(c)
118
Review Questions
  • 5.35. What is a boundary condition? How do
    boundary
  • conditions arise and how are they
    derived?
  • 5.36. Summarize the boundary conditions for the
    general case
  • of a boundary between two arbitrary
    media, indicating
  • correspondingly the Maxwells equations
    in integral
  • form from which they are derived.
  • 5.37. Discuss the boundary conditions on the
    surface of a
  • perfect conductor.
  • 5.38. Discuss the boundary conditions at the
    interface
  • between two perfect dielectric media.

119
Problem S5.10. For application of boundary
conditions on a perfect conductor surface
120
Problem S5.11. Applying boundary conditions at a
dielectric interface in the presence of a point
charge
121
Problem S5.11. Applying boundary conditions at a
dielectric interface in the presence of a point
charge (Continued)
122
Problem S5.12. For application of boundary
conditions on a the surface of a magnetic material
123
  • 5.6 Reflection and Transmission
  • of Uniform Plane Waves
  • (EEE, Sec. 4.7 FEME, Sec. 5.6)

124
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125
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126
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127
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128
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129
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130
Review Questions
  • 5.35. Discuss the determination of the reflected
    and
  • transmitted wave fields of a uniform
    plane wave
  • incident normally onto a plane boundary
    between two
  • material media.
  • 5.36. Define reflection and transmission
    coefficients for a
  • uniform plane wave incident normally
    onto a plane
  • boundary between two material media.
  • 5.37. Discuss the reflection and transmission
    coefficients for
  • the special case of two perfect
    dielectric media.
  • 5.38. What is the consequence of a wave incident
    on a perfect
  • conductor?

131
Problem S5.13. Normal incidence of uniform plane
waves on interface between free space and water
132
Problem S5.14. Eliminating reflection of uniform
plane waves from a dielectric slab between two
media
133
Problem S5.14. Eliminating reflection of uniform
plane waves from a dielectric slab between two
media (Continued)
134
The End
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