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Field Theory (Electromagnetics)

Kod Kursus: KEEE 1123

Dr Suhana Mohd. Said

Room11, 7th Floor, Menara Kejuruteraan

Telephone: 7967 5399

Meeting times: Monday 2.30-3.30

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Course contents

Minggu Lecture title

1 Introduction to Electromagnetism, Historicalperspective and current applications

2 Vector Analysis: Cartesian, Cylindrical and

Spherical Coordinate System

3 Vector Analysis: Gradient, integration,

divergence and curl

4 Introduction to electrostatics : Basic postulates.

Calculation of Electric Field Intensity using

integration and Gauss’ law.5 Electrical Potential and Electrical Materials

6 Boundary Conditions for two adjacent electrical

materials

7 Capacitors and Capacitance

8 Electrostatic energy and forces. Laplace and

Poisson equations

9 Charge movement in a conductor carrying asteady current

10 Introduction to magnetostatics : Basic

postulates, calculation of magnetic flux density

using Biot Savart law

11  Ampere’s law to calculate magnetic flux density

12 Magnetic materials and mechanism for

magnetisation

13 Inductors and inductance

14 Magnetostatic energy, force and torque

15 Revision

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Course requirements

Related course: Vector Analysis (KXEX 2245)

Reference books:

1. D.K. Cheng, Fundamentals of Engineering

Electromagnetics (Second Edition)

2. Matthew Sadiku, Elements of Electromagnetics,

Third Edition3. C.L Paul, K.W. Whites, S.A. Nasar, Introduction to

Electromagnetic Fields

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Aims of the course

In order to understand the concept of electromagnetism.What is electromagnetism?

• The study of electrical charges in their static and

dynamic states.

• Electrical field and magnetic field

• These fields are interrelated.

Why is it necessary to study electromagnetism?

There are situations where circuit analysis is not sufficient

in order to solve problems concerning electrical ciruits:

•  A straight wire has an inductance value. But

inductances are usually related with electrical coils.

• The volume of a transistor radio is varies with its

position in a room. But circuit theory implies that the

volume should remain constant regardless of the

position of the radio within the room.

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The historical background of

electromagnetic theory

1. Electrostatics:

• Benjamin Franklin(1706-1790)/Joseph

Priestley(1733-1804) explained the relationship

between static electrical charges:

• Charles de Coulomb (1736-1806)

• Karl Frederick Gauss (1777-1855) – divergence

theory and Gauss’ law.

2. Magnetism:

• Plato dan Socrates realised the magnetic

properties of the loadstone, which is able to

attract iron.

• Gilbert (1540-1603) suggested that the earth

was a giant magnetic sphere.

• Henry Cavendish (1773) – the inverse square

law rule which explained the force within a

magnetic field.

2

21

d 

mm F  

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3. Magnetism and electric currents• Hans Christian Oersted (1820) –a wire carrying a

current could deflect a compass•  Andre Ampere (1775-1836) – a force exists

between two current-carrying wires

• Jean-Baptiste Biot and Felix Savart – Biot-Savartlaw

4. Relationship between electric and magnetic fields• Faraday (1791-1867), in 1831, realised that a

time-varying magnetic field induced an electricfield.

• James Clerk Maxwell (1831-1879) was a

mathematician who unified the subjects of theoryand magnetism.

•  Also demonstrated that light was anelectromagnetic wave

• Maxwell derived four well-known equations whichare still widely used to explain and apply

electromagnetic phenomena. For example, inradio antennas, electro-optic devices andelectrical transmission lines.

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Properties of electrical charges

Electrical charges are the fundamental element in currents.

•Comprise of either positive or negative charges. Like charges

attract, opposite charges repel.

•In nature, the sum of charges is neutral.

Principle of conservation of charge: it is not possible to create

or annihilate positive (or negative) charges without creating/annihilating an equal amount of negative or positive charges.

•Charge symmetry. For every positively charged elementary

particle, there exists an identical elementary particle that is

negatively charged.

For example, electrons and positrons, protons and antiprotons

•Charges are quantised. The minimum amount of charge

•Possessed by an elementary particle is that of an electron:

e=1.6x10-19 C (C=Coulomb)

 All charges are integer multiples of the value e stated above.

•Whatever has charge has mass. Therefore electricity is a forof energy (from E=mv2).The lightest charged particle is:

melektron=9.1091x10-31kg.

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Charges within an electromagnetic field

• The presence and movement of charges produce

electric and magnetic fields.

• The quantities of electric and magnetic fields are

directional – vectors are needed!

• Static charges produce an electrostatic field.

• Moving charges produce

•  A steady flow of electric charges produce a

magnetostatic field.

• Charge flow at a non-constant rate will produce

magnetic and electric fields.

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The concept of fields:

• Can be either a scalar field or a vector field.

Example of a scalar field:

Temperature variation within a room.

For example, the room temperature is T1 for all the pointsconnected by the contour line T1. The values oftemperature at different points in the room aredependent on the position and time.

z

x

y

T1

T2

T3

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Example of a vector field:

Fluid flow within a constricted pipe.

Fluid flow has direction and magnitude(rate of flow).

The value of the vector (i.e. fluid flow) is a function of

position and time, and can be written as:

F(x,y,z, t)

z

x

y

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The electric field

• Charge q1 produces an electric field.

• The electric field from q1 influences q2 via an electric

field. 2 separate problems need to be solved:

a) The field from the presence of chargesb) The forces from the charges, as a result of the

electric field

• The response from the movement of q1 will be

realised by charge q2, via the electric field.

q1

q2

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The definition of an electric field

• E=F/q0 (1)

Where E, F are vectors, q0 is scalar.

q0 is a test charge, and F is the electostatic forcewhich acts upon this test charge.

• The size for q0 needs to be as small as possible, sothat it does not disturb the value of, E, which needsto be measured. Therefore,

Equation (1) can be written as:

(2)

• Therefore, the electric field is the limit where thesize of the test charge approaches zero.

• The density of charges within the test charge canbe written as .

3 dimensions: volume charge density

2 dimensions: surface charge density

1 dimension: line charge density

00  0

lim

q F 

q E 

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Lines of force

• Used to sketch the force lines.

• The tangent to the lines of force give the value of E, the

electric field, at that point.

• The number of the lines of force in a unit area is

proportional to the magnitude of E. For example,closely spaced lines of force indicate a high value of

electric field.

+

+

+

+

+

+

+

+

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Example of charges in an electrostatic

field.

+ + + + + + + + + +P

+ + + + + + + + + +P

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A sketch of lines of force for a charge in

an electrostatic field.

-

-

-

-

-

+Q

P

-

-

-

-

-

+Q

P

-

-

-

-

-

+Q

P

--

-

-

-

+Q

P

--

-

-

-

+Q

P

--

-

-

-

+Q

P

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Units and basic quantities in

electromagnetic theory

Basic SI units

Basic quantities in electromagnetic theory

Quantity Unit Abbreviation

Length meter m

Mass kilogram kg

Time seconds s

Current ampere A

Field Quantity Symbol Unit

Electric Electric Field

Intensity

E V/m

Electric Flux Density D C/m2

Magnetic Magnetic FluxDensity

B T

Magnetic Field

Intensity

H  A/m

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Universal constants in electromagnetic

theory

Constant Symbol Value (in free

space_ 

Speed of

light

c 3x108 ms-1

Permittivity   0 8.854x10-12

Fm-1 (Faradper meter)

Permeability   0 4x10-7 Hm-1

(Henry per

meter)

Permittivity, 0,relates the electric flux density, D,and electric field intensity, E.

D=0E

Permeability, 0, relates the magnetic flux density, B,

and the magnetic field intensity, H.

B= 0H

0 and 0 are related to c by the equation:

00

1

  

c