4/27/21

EEE528: Advanced
Electromagnetic Fields and Waves
A 1st Semester Course in the EEE Undergraduate Programme
Lecture 1
Dr. J.G. Kolo and Dr. A. Daniyan
Slide 1

EEE528: Advanced Electromagnetic Fields

• and Waves
Instructors
– Dr. J. G. Kolo, Room 212, First Floor, SEET Building
Jgkolo@futminna.edu.ng
– Dr. A. Daniyan, EEE 007, Electrical Engineering Complex
a.daniyan@futminna.edu.ng

• Text Books
1. Sadiku Mathew N.O.,“Elements of Electromagnetics”, Oxford University Press
Inc, New Delhi, 2009
2. William H. Hayt and Jr John A. Buck, “Engineering Electromagnetics”, Tata
McGraw-Hill Publishing Company Ltd, New Delhi, 2008
Slide 2

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Course Overview
• Maxwell’s Equations:
– Displacement Current, Maxwell’s Equations in Final Forms, Time - Harmonics Fields.
• Electromagnetic Wave Propagation:
– Waves in General, Wave Propagation in Lossy Dielectrics, Plane Waves in Lossless
Dielectrics, Plane Waves in Free Space, Plane Waves in Good Conductors, Wave
Polarization, ‘Power and Poynting Vector’.
• Transmission Lines:
– Transmission Line Parameters, Transmission Line Equations, ‘Input Impedance, Standing
Wave Ratio and Power’, The Smith Chart, Applications of Transmission Lines.
• Wave Guides:
– Rectangular Waveguides, Transverse Magnetic (TM) Modes, Transverse Electric (TE)
Modes, Wave Propagation in the Guides.

Slide 3

Review of Electromagnetic Laws in Static

States.
• Electrostatic Fields:
– Coulomb’s Law and Field Intensity,
– Electric Field Intensity, Electric Flux Density,
– Gauss’s Law
– Application of Gauss’s Law,
– Electric Potential,
– An Electric Field Dipole and Flux Lines,
– Energy Density in Electrostatic Fields.

Slide 4

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Review of Electromagnetic Laws in Static

States.
• Magnetostatic Fields:
– Biot-Savart's Law,
– Ampere's Circuit Law
– Applications of Ampere's Law,
– Magnetic Flux Density
– Maxwell's Equation,
– Maxwell's Equations for Static Fields,
– Magnetic Scalar and Vector Potentials.

Slide 5

Introduction
• Electromagnetic wave consists of oscillating electric and
magnetic fields in certain directions
• They propagate through free space at the velocity of light
• Electromagnetic Waves are 3 dimensional propagation of
vibrations of electric and magnetic fields.
• Remember, Electric fields and magnetic fields are vector
fields.
• Electromagnetic Waves are transverse in nature. Waves are
basically two types
– transverse and
– longitudinal. Slide 6

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Introduction
• The example of longitudinal waves are acoustic waves
(sound). They are longitudinal because the direction of
propagation of wave is along the direction of vibration

• Transverse Waves are so called because in this type the

direction of propagation of wave is perpendicular or
transverse to the direction of vibration.

Note; vibrations are also called disturbances, undulation, oscillation, ripples and
wiggles in various usage of waves. Electromagnetic waves are transverse
undulations of electric and magnetic fields. Slide 7

Introduction
• Transverse nature of
electromagnetic waves
• The vector field B vibrates
E
along y-direction whereas
the vector field E vibrates
along x-direction. x
• The wave cruises along the
z-direction. z
• Thus the EM wave is vector y
in nature in addition to
being transverse.
B

Slide 8

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Introduction

• Electromagnetic Waves are a set of phenomena broadly

categorized as
• Gamma rays,
• X-rays,
• Ultraviolet Rays,
• Visible light,
• Infra-red Rays,
• Microwaves and
• Radio waves.

Slide 9

The EM Spectrum

ØVarious types of electromagnetic waves make up the EM

spectrum.
ØThere is no sharp division between one kind of EM wave
and the next.
ØAll forms of the various types of radiation are produced
by the same phenomenon – accelerating charges.

Slide 10

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The EM Spectrum
• Note the overlap between types of waves
• Visible light is a small portion of the spectrum.
• Types are distinguished by frequency or wavelength

Slide 11

The EM Spectrum
• Electromagnetic waves can have any wavelength; we have
given different names to different parts of the
electromagnetic spectrum.

Slide 12

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The Electromagnetic Spectrum

Slide 13

The Electromagnetic Spectrum

Slide 14

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The Electromagnetic Spectrum

Slide 15

Notes on the EM Spectrum

•Radio Waves
– Wavelengths of more than 104 m to about 0.1 m
– Used in radio and television communication systems
•Microwaves
– Wavelengths from about 0.3 m to 10-4 m
– Well suited for radar systems
– Microwave ovens are an application

Slide 16

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Notes on the EM Spectrum, 2

•Infrared waves
– Wavelengths of about 10-3 m to 7 x 10-7 m
– Incorrectly called “heat waves”
– Produced by hot objects and molecules
– Readily absorbed by most materials
•Visible light
– Part of the spectrum detected by the human eye
– Most sensitive at about 5.5 x 10-7 m (yellow-green)
Slide 17

More About Visible Light

•Different wavelengths correspond to different colors.
•The range is from red (λ ~ 7 x 10-7 m) to violet (λ ~4 x 10-7 m).

Slide 18

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Visible Light, cont

Slide 19

Notes on the EM Spectrum, 3

•Ultraviolet light
– Covers about 4 x 10-7 m to 6 x 10-10 m
– Sun is an important source of uv light
– Most uv light from the sun is absorbed in the stratosphere by
ozone
•X-rays
– Wavelengths of about 10-8 m to 10-12 m
– Most common source is acceleration of high-energy electrons
striking a metal target
– Used as a diagnostic tool in medicine
Slide 20

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Notes on the EM Spectrum, final

•Gamma rays
– Wavelengths of about 10-10 m to 10-14 m
– Emitted by radioactive nuclei
– Highly penetrating and cause serious damage when absorbed
by living tissue
•Looking at objects in different portions of the spectrum
can produce different information.

Slide 21

DEL OPERATOR

• The del operator, written ▽, is the vector differential

operator.
• In Cartesian coordinates,
• This vector differential operator, otherwise known as the
gradient operator, is not a vector in itself, but when it
operates on a scalar function, for example, a vector
ensues. The operator is useful in defining

Slide 22

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DEL OPERATOR

• The del operator is useful in defining

1. The gradient of a scalar ▽, written as ▽ ▽
2. The divergence of a vector A, written as ▽ · A
3. The curl of a vector A, written as ▽ X A
4. The Laplacian of a scalar ▽, written as ▽2▽

Slide 23

MAXWELL’S EQUATIONS

• Electric and magnetic phenomena at the macroscopic

level are described by Maxwell’s equations, as published
by Maxwell in 1873.
• Maxwell's equations describe how electric charges and
electric currents create electric and magnetic fields.
• They also describe how an electric field can generate a
magnetic field, and vice versa.

Slide 24

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MAXWELL’S EQUATIONS Contd…

Slide 25

MAXWELL’S EQUATIONS Contd…

Slide 26

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MAXWELL’S EQUATIONS Contd…

Slide 27

MAXWELL’S EQUATIONS Contd…

• The sources of the electromagnetic field are the currents

M¯ and J¯ and the electric charge density ρ.
• The magnetic current M¯ is a fictitious source in the
sense that it is only a mathematical convenience:
– the real source of a magnetic current is always a loop of electric
current or some similar type of magnetic dipole, as opposed to
the flow of an actual magnetic charge (magnetic monopole
charges are not known to exist).

Slide 28

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MAXWELL’S EQUATIONS Contd…

• In free-space, the following simple relations hold between
the electric and magnetic field intensities and flux
densities:

Slide 29

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