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PPT – 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 PowerPoint presentation | free to download - id: 4dd09b-ZWEyY

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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

- 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

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

- 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

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

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

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

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

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

- 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

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

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

Ohms Law

Ohms Law

Resistance

5-12

- D4.1
- (a) For cu,
- (b)

- (c) From

- Conductor in a static electric field

Plane conducting slab in a uniform electric field

5-15

5-15

rS e0E0

rS e0E0

rS e0E0

rS e0E0

rS e0E0

rS e0E0

5-16

- P4.3
- (a)

5-17

- (b)

(1)

(2)

Write two more equations and solve for the four

unknowns.

5-18

Solving the four equations, we obtain

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

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)

The phenomenon of polarization results in a

polarization charge in the material which

produces a secondary E.

11

Plane dielectric slab in a uniform electric field

Polarization Current (in the time-varying case)

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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,

5-28

For dielectrics,

Where P is the polarization vector, or the dipole

moment per unit volume. Rearranging,

where now,

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.

5-30

As an example, consider

Then, inside the material,

D4.3

For 0 lt z lt d,

(a)

5-32

(b)

(c)

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.

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5-35

D4.4

(a)

5-36

(b)

5-37

(c)

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?

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?

Problem S5.1. Finding the electric field due to

a point charge in the presence of a conductor

Problem S5.1. Finding the electric field due to a

point charge in the presence of a conductor

(Continued)

Problem S5.2. Finding D, E, and P for a line

charge surrounded by a cylindrical shell of

dielectric material

Problem S5.3. Expressing an electric field in

terms of the characteristic polarizations of an

anisotropic dielectric

5.2 Magnetic Materials (EEE, Sec. 4.3 FEME, Sec.

5.2)

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

Paramagnetism

Already existing dipoles are acted upon by a

torque.

Other Ferromagnetism, antiferromagnetism, ferrima

gnetism

The phenomenon of magnetization results in a

magnetization current in the material which

produces a secondary B.

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Magnetization Current

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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,

5-53

For magnetic materials,

where M is the magnetization vector, or the

magnetic dipole moment per unit volume.

5-54

Rearranging,

where now

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.

5-56

As an example, consider

Then inside the material,

5-57

5-57

D4.6

For 0 lt z lt d,

(a)

(b)

(c)

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.

??

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.

Problem S5.4. Finding H, B, and M for a wire of

current surrounded by a cylindrical shell of

magnetic material

5.3 Wave Equation and Solution (EEE, Sec. 4.4

FEME, Sec. 5.3)

5-63

Maxwells equations for a material medium

5-64

Waves in Material Media

Combining, we get

Define

Then

Wave equation

5-66

Solution

attenuation

attenuation

a attenuation constant, Np/m

b phase constant, rad/m

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5-70

5-71

Summarizing,

Conversely,

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.

5-73

Three-dimensional depiction of wave propagation

5-75

5-75

E5.1

Solution

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5-77

5-78

Power Flow and Energy Storage

5-79

A Vector Identity

For

Poynting Vector

Poyntings Theorem for Material Medium

Magnetic stored energy density

Power dissipation density

Source power density

Electric stored energy density

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.

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.

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?

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?

Problem S5.5. Finding the magnetic field and

material parameters from a specified electric

field

Problem S5.6. Finding E and H for a current

sheet of nonsinusoidal current density in a

material medium

Problem S5.7. For showing that the time average

powers delivered to, and dissipated in, a medium

are the same

5.4 Uniform Plane Waves in Dielectrics and

Conductors (EEE, Sec. 4.5 FEME, Sec. 5.4)

5-89

5-89

Special Cases

Case 1. Perfect dielectric

Behavior same as in free space except that ?0 ?

? and ?0 ? ?.

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.

5-91

Case 2. Imperfect Dielectric

Behavior essentially like in a perfect dielectric

except for attenuation.

5-92

Case 3. Good Conductor

Behavior much different from that in a

dielectric.

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,

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.

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.

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.

5-97

Case 4. Perfect Conductor

- No waves can penetrate into a perfect conductor.
- No time-varying fields inside a perfect

conductor.

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.

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?

Problem S5.8. Plotting field variations for an

infinite plane sheet current source in a perfect

dielectric medium

Problem S5.9. Calculating parameters for good

conductor materials to satisfy specified

conditions

5.5 Boundary Conditions (EEE, Sec. 4.6 FEME,

Sec. 5.5)

Why boundary conditions?

Medium 1

Medium 2

Inc. wave

Trans. wave

Ref. wave

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

Boundary Conditions

5-105

???????????

?????????????

??

5-106

Example of derivation of boundary conditions

Medium 1

Medium 2

or,

Summary of boundary conditions

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,

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Dielectric-Dielectric Interface

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5-113

D4.11

At a point on a perfect conductor surface,

and

pointing away from the surface. Find . D0 is

positive.

(a)

and

pointing toward the surface. D0 is positive.

(b)

E5.2

(a)

5-116

(b)

(c)

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.

Problem S5.10. For application of boundary

conditions on a perfect conductor surface

Problem S5.11. Applying boundary conditions at a

dielectric interface in the presence of a point

charge

Problem S5.11. Applying boundary conditions at a

dielectric interface in the presence of a point

charge (Continued)

Problem S5.12. For application of boundary

conditions on a the surface of a magnetic material

- 5.6 Reflection and Transmission
- of Uniform Plane Waves
- (EEE, Sec. 4.7 FEME, Sec. 5.6)

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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?

Problem S5.13. Normal incidence of uniform plane

waves on interface between free space and water

Problem S5.14. Eliminating reflection of uniform

plane waves from a dielectric slab between two

media

Problem S5.14. Eliminating reflection of uniform

plane waves from a dielectric slab between two

media (Continued)

The End