ece208 engineering electromagnetics class no. 1822

Electromagnetic Engineering

Dr. Tanmaya Kumar Das

C.V. Raman Global University, Bhubaneswar

Department of Electronics and Communication Engineering

▪ To provide the basic skills required to understand engineering applications involving

electromagnetic fields and its practice in modern communications.

COURSE OBJECTIVE

COURSE OUTCOME

At the end of the Course, the students will be able to analyze and solve the problems related

to:

CO1: Apply concepts of vector algebra and co-ordinate geometry to electromagnetic field

and wave propagation.

CO2: Define and illustrate the problems related to electrostatics and magnetostatics.

CO3: Discuss and solve wave equation and transmission line problems in various media.

CO4: Read voluntarily to enhance the knowledge in electromagnetic.

Unit 1: Co-ordinate systems & Vector Calculus (8 Hrs)

▪ Co-ordinate systems: Cartesian co-ordinates, Vector Calculus: Scalars and Vectors,

Types of vector, vector algebra, Differential length, Area & volume, Line, surface and

volume Integrals, Del operator, Gradient of a scalar, Divergence of a vector & divergence

theorem, curl of a vector & Stoke’s theorem, Laplacian of a scalar. (T1: 1.3-1.7, 2.2, 3.1-

3.8)

▪ Constant co-ordinate surfaces, Components of a vector. (T1: 2.5, 1.8)

SYLLABUS

Text Books:

T1. “Principles of Electromagnetics”, Matthew N. O. Sadiku, OXFORD UNIVERSITY

PRESS, 4th Edition, 2010.

T2. “Electromagnetic Field Theory Fundamentals”, B. Guru, H. Higiroglu, CAMBRIDGE

UNIVERSITY PRESS, 2nd Edition, 2006.

Reference Books:

R1. “Engineering Electromagnetic”, W.H. Hyat, J.A. Buck, Tata Mcgraw Hill Education

Private Limited, 7th Edition, 2012.

R2. “Engineering Electromagnetics”, Jin Au Kong, Amalendu Patnaik, Cengage Learning,

1st Edition, 2011.

R3. “Engineering Electromagnetic”, Nathan Ida, Springer,

Marks Distribution

Attendance+Assi

gnment 10

Experiencial Learning 20

10 Surprise Tests 20 Midsem 20

End Sem (100) 30

What is Electromagnetics?

▪ Why this course is essential?

▪ Where Electromagnetics fit in the curriculum?

What is Electromagnetics?

Content

• Electromagnetics is the study of interaction of fields generated

by (time-varying) charge distributions and currents.

▪ What is a field?

▪ How are fields generated by charges and currents?

▪ How these fields interact?

• Successful completion of this course helps to prepare for

courses in Microwaves, Radar, Antennas, etc.

For the circuit shown below, what will happen?

Answer (s):

▪ Nothing

▪ Current will flow for short time

▪ Outcome depends on length and shape of wire

▪ Outcome depends on frequency of source.

Why EM Theory is necessary?

Nothing:

From circuit background:

▪ Circuit is not closed, Hence current can not flow.

▪ Frequency of source and length of wire does not matter.

For the circuit shown below, what will happen?

Current will flow for short time:

From the earlier Physics course, the wire will get charged and the current will flow

during charging process.

▪ What process charges wire?

▪ What will be the shape of current waveform?

▪ Does the frequency of source matter?

Outcome depends on length and shape of wire:

To a circuit person, the length and shape of wire does not matter.

▪ With the increase in the frequency

of the source, at sufficiently high

frequencies, this wire will actually

cause the voltage across the

resistor to drop to zero.

▪ Both inductance and transmission line are concepts that are not actually developed

from circuit theory.

▪ In circuit theory, if you remember we just are given that we have an inductor, we

have capacitor, we have a resistor, and we are not told how we exactly calculate

these things.

Shape of wire:

▪ Metal plates acts as capacitor and

alter the voltage across register.

▪ Clearly, there is no continuity of the wire between the two plates over here, because

the plate is broken, there is nothing out there that will allow the conduction of

electrons from one wire to another wire.

▪ However, we do know that this situation is exactly that of a capacitor.

▪ Question: what is capacitance and how do we calculate it.

▪ The current will be continuous, i.e. the current going through here must be coming out

as the same current, voltage will be different phase, but the current will be all the same

phase.

▪ So the current that is flowing here at one plate must also be the current that is exiting

the other plate.

▪ Now what exactly goes on in between the two plates is something that Electromagnetic

Theory will help us understand.

Length of wire

▪ In circuit theory again

length of a wire or a

interconnect between

two gates or two circuit

elements does not really

matter.

▪ However, what you observe on a oscilloscope that you put at the far end or at the load

side if you would think, is that the maximum does not really occur at T = 0.

▪ It occurs after a certain time, and this time is L/V.

▪ A source and a load when separated by a long distance, there is some time delay

involved, and this time delay is not taken into account by circuits, whereas this is

explicitly taken into account by electromagnetic theory.

Summary:

▪ A wire is more than just a wire.

▪ It can be inductor, capacitor, or transmission line depending on length and shape of

wire and frequency of source.

▪ Ordinary circuit theory can not account for these effects.

▪ Electromagnetic theory can successfully analyze these effects.

Electromagnetic Spectrum

Force is an external stimulus on an object, that brings about motion of a body

in rest or vice versa, change direction of motion or cause physical contraction

or expansion.

Force is measured in Newtons 1 N = 1 Kg m/s2 (remember Newton’s Laws of

Motion ?)

Energy is the capacity of a physical system or phenomena to carry out work.

It can be in any form, electrical, mechanical, thermal, chemical, nuclear, light,

acoustic etc

Energy is measured in Joules. 1 J = 1 N-m

Power is rate of doing work or energy consumed per unit amount of time.

Power is measured in Watts. 1 W = 1 J/s

Work is energy expended by a force to displace an object by unit distance.

Work has same units as energy

Some Fundamentals

Work is force applied on an object to displace it by a distance.

Work = Force x Distance

Work is also change of energy from one form into another

Work = Energy

By which we can say that Energy = Force x Distance

Power is rate of doing work or rate at which energy is absorbed or

expended.

Power = Energy / time

Similarly can you relate terms such as Momentum, Angular Momentum,

Torque etc ?

We will study the electrical equivalents of the mechanical concepts later

How can we relate them ??

◆ 6th Century BC Thales of Miletus Rubbing fur on

amber would cause an attraction between the two, Origin of

static electricity

◆ 1st Century BC Shephard MagnesMagnetic properties

of some stones

◆ 1600AD William Gilbert Magnetic

bodies and earth as a big magnet

◆ 1663AD Otto von Guericke

electrostatic generating machine

First

◆ 1745AD Pieter van Musschenbroek &

Ewald Georg von Kleist First Capacitor

Timeline and Pioneers

Establishes link◆ 1752AD Benjamin Franklin

between lightning and electricity

Proposes◆ 1767AD Joseph Priestley

electrical inverse-square law

◆ 1785AD Charles-Augustine de Coulomb

Inverse-square law of electrostatics

◆ 1791AD Luigi Galvani Galvanic Battery

Timeline and Pioneers

Alessandro Volta Voltaic Cell (chemical◆ 1799AD

Battery)

◆ 1820AD Hans Christian Oersted Compass needle

deflects when a battery nearby is switched on and off

of wire◆ 1820AD Andre MarieAmpere Coil

carrying current behaves like magnet (Solenoid)

◆ 1826AD Georg Simon Ohm

electrical resistance

Ohm’s Law of

Timeline and Pioneers

Gauss’s Law or◆ 1831AD Carl Friedrich Gauss

Law of Flux densities

Wilhelm Eduard Weber Magnetism and◆ 1831AD

Telegraphy

Law of◆ 1831AD Michael Faraday

electromagnetic induction

◆ 1833AD Heinrich Friedrich Emil Lenz

Increase or decrease of magnetic flux induces

electromotive force

Timeline and Pioneers

◆ 1835AD

Electric relay

Joseph Henry Self inductance,

◆ 1837AD Samuel Morse Telegraphy, Morse Code

◆ 1840AD James Prescott Joule Joule’s Law,

amount of heat produced in a circuit proportional to

product of time, resitance and square of current

◆ 1854 AD Gustav Robert Kirchoff Conservation of

electric charge and energy (Kirchoff’s Voltage, Current

Laws)

Timeline and Pioneers

◆ 1865AD James Clerk Maxwell Maxwell’s

equations linking electricity and magnetism, Father of

electromagnetic theory

Thomas Alva Edison Incandescent◆ 1878AD

light bulb

◆ 1888 AD Heinrich Rudolf Hertz Radio wave

propagation in free space and various media,

experimental verification of Maxwell’s equations

Timeline and Pioneers

◆ 1897AD

electron

Joseph John Thomson Discovery of

◆ 1905AD Albert Einstein

& Special Theory of Relativity

Speed of Light

◆ 1911AD Heike Kammerlingh Onnes

Superconductivity

Timeline and Pioneers

Introduction (Vector & Scalar)

Examples : Mass, Temperature, Distance, Speed, Entropy etc

Chennai is 142 Km from Vellore

➢ What is a Scalar ? A quantity that has magnitude

➢ What is a Vector ?A quantity that has magnitude and

direction

Examples : Weight, Displacement, Velocity, Force etc

Chennai is 142 Km East of Vellore

How is it Denoted ? Small or Capital Letters (italics) such as a, A

How is it Denoted ? Small or Capital Letters (Boldface) such as a, A or with

an arrow overhead Ԧ𝐴

➢What is a Unit Vector ?A quantity that has magnitude of

unity and direction as the

original vector

If A = Ax 𝒂𝒙+Ay 𝒂𝒚+Az 𝒂𝒛 is a vector in Cartesian coordinates then

the magnitude of A = A = 𝐴𝑥2 + 𝐴𝑦

2 + 𝐴𝑧2

X

Y

Ax

Ay

Az

Aa

Z

Unit Vector

The unit vector along A is denoted by:

Unit Vector

➢What is a Position Vector ?Vector defining position of a

point in space with reference to

a fixed point (origin)

Position & Distance Vector

The position vector 𝒓𝒑 (or radius vector) of

point P is defined as the directed distance from

the origin O to P; that is,

➢What is a Distance Vector ?The distance vector is the

displacement from one point to

another.

Position & Distance Vector

If two points P and Q are given by (𝑥𝑃, 𝑦𝑃 , 𝑧𝑃) and

(𝑥𝑄, 𝑦𝑄, 𝑧𝑄 ), the distance vector (or separation

vector) is the displacement from P to Q as shown

in Figure

▪ When two vectors A and B are multiplied, the result is either a scalar or a vector

depending on how they are multiplied. Thus there are two types of vector

multiplication:

Vector Multiplication

1. Scalar (or dot) product: A . B2. Vector (or cross) product: A× B

▪ Multiplication of three vectors A, B, and C can result in either:

3. Scalar triple product: A . (B × C)

or

4. Vector triple product: A × (B × C)

→ →

➢ The Scalar or Dot Product of two vectors A and B is geometrically

defined as the product of the magnitudes of A and B and the cosine of

smaller angle between them (𝜃𝐴𝐵)

A•B = A B cos 𝜃𝐴𝐵

If A = (𝐴𝑥 , 𝐴𝑦, 𝐴𝑧) and B = (𝐵𝑥 , 𝐵𝑦, 𝐵𝑧)

A•B = AxBx +AyBy +AzBz

Vector Multiplication

▪ If A . B = 0, the two vectors A and B are orthogonal or perpendicular.

Vector Multiplication

➢ If C = A – B , then by Law of Cosines

C•C = (A – B) • (A– B) = A2 + B2 – 2 AB Cos

AAA•B = AB A•B = 0

BB

Vector Multiplication

➢The Cross Product of two vectors A and B is A B = AB Sin𝜃𝐴𝐵 ෝ𝒏

n

A

B

n

A

B

Vector Multiplication

= 𝐴𝐵 𝑆𝑖𝑛 𝜃𝐴𝐵𝒂𝒏

where 𝒂𝒏 or ෝ𝒏 is a unit vector normal to the plane containing A and B.

The vector multiplication is called cross product owing to the cross sign; it is also

called vector product because the result is a vector.

◆The Right Hand Rule is employed to find the direction of the

normal to the surface enclosing A and B (or remember the direction

a screw moves, when rotated clockwise or anti-clockwise)

Vector Multiplication

(a) the right-hand rule and (b) the right-handed-screw rule

Vector Multiplication

If A = (𝐴𝑥, 𝐴𝑦, 𝐴𝑧) and B = (𝐵𝑥, 𝐵𝑦 , 𝐵𝑧)

Note that the cross product has the following basic properties:

Note:

Cross product using cyclic permutation. (a) Moving clockwise leads to positive

results. (b) Moving counterclockwise leads to negative results.

Scalar Triple Product

obtained in cyclic permutation.

If A = (𝐴𝑥, 𝐴𝑦, 𝐴𝑧) , B = (𝐵𝑥, 𝐵𝑦, 𝐵𝑧) and C = (𝐶𝑥, 𝐶𝑦, 𝐶𝑧)

Since the result of this vector multiplication is scalar, it is called the scalar triple

product.

Vector Triple Product

obtained in cyclic permutation.

If A = (𝐴𝑥, 𝐴𝑦, 𝐴𝑧) , B = (𝐵𝑥, 𝐵𝑦, 𝐵𝑧) and C = (𝐶𝑥, 𝐶𝑦, 𝐶𝑧)

Since the result of this vector multiplication is scalar, it is called the scalar triple

product.

Given vectors A = 3𝒂𝒙 + 4𝒂𝒚 + 𝒂𝒛 and B = 2𝒂𝒚− 5𝒂𝒛, find the angle between A and B.

Try This

Try This

Try This

▪ A direct application of scalar product is its use in determining the projection (or

component) of a vector in a given direction.

▪ The projection can be scalar or vector.

▪ Given a vector A, we define the scalar component 𝐴𝐵 of A along vector B as:

COMPONENTS OF A VECTOR

▪ The vector component 𝑨𝐵 of A along B is simply the scalar component multiplied by a

unit vector along B; that is,

Fig: Components of A along B: (a) scalar component 𝐴𝐵 , (b) vector component 𝑨𝐵

▪ The vector can be resolved into two orthogonal components: one

component 𝐀B parallel to B, another (𝐀 − 𝐀𝐁) perpendicular to B.

Fig: Components of A along B: (a) scalar component 𝐴𝐵 , (b) vector component 𝑨𝐵

Example

Example

Consider a triangle as shown in the Figure. It is clear that.

For any point P on the line joining 𝑃1 and 𝑃2

▪ This is the vector equation of the straight line joining 𝑃1 and 𝑃2. If 𝑃3 is on

this line, the position vector of 𝑃3 must satisfy the equation; 𝒓3 does satisfy

the equation when 𝜆 = 2.

▪ The shortest distance between the line and point 𝑃4 (3, −1 , 0) is the

perpendicular distance from the point to the line.

1. Let E = 3ay + 4az, F = 4ax – 10 ay + 5az

a. Find the component of E along F

b. Determine a unit vector perpendicular to both E and F

Solve