EKT 241/4: ELECTROMAGNETIC THEORY

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EKT 241/4: ELECTROMAGNETIC THEORY. UNIVERSITI MALAYSIA PERLIS. PREPARED BY: NORDIANA MOHAMAD SAAID dianams@unimap.edu.my. CHAPTER 1 - INTRODUCTION. Electromagnetic Applications. Optical transmission Coaxial transmission line Antenna system High voltage transmission.

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### EKT 241/4:ELECTROMAGNETIC THEORY

UNIVERSITI MALAYSIA PERLIS

dianams@unimap.edu.my

CHAPTER 1 - INTRODUCTION

Electromagnetic Applications
• Optical transmission
• Coaxial transmission line
• Antenna system
• High voltage transmission

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Electrostatic vs. Magnetostatic

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Timeline for Electromagneticsin the Classical Era
• 1785 Charles-Augustin de Coulomb (French) demonstrates that the electrical force between charges is proportional to the inverse of the square of the distance between them.

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Timeline for Electromagneticsin the Classical Era
• 1835 Carl Friedrich Gauss (German) formulates Gauss’s law relating the electric flux flowing through an enclosed surface to the enclosed electric charge.

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Timeline for Electromagneticsin the Classical Era
• 1873 James Clerk Maxwell (Scottish) publishes his “Treatise on Electricity and Magnetism” in which he unites the discoveries of Coulomb, Oersted, Ampere, Faraday and others into four elegantly constructed mathematical equations, now known as Maxwell’s Equations.

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Units and Dimensions
• SI Units
• French name ‘Systeme Internationale’
• Based on six fundamental dimensions

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Multiple & Sub-Multiple Prefixes

Example:

• 4 x 10-12 F becomes

4 pF

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The Nature of Electromagnetism

Physical universe is governed by 4 forces:

• nuclear force
• weak-interaction force
• electromagnetic force
• gravitational force

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The Electromagnetic ForceAnalogy: The Gravitational Force

Where;

m2, m1 = masses R12= distanceG = gravitational constant

= unit vector from 1 to 2

Gravitational force

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The Electric Fields

Coulomb’s law

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Where;

Fe21 = electrical force

q1,q2 = charges

R12 = distance between the two charges = unit vector

ε0 = electrical permittivity of free space

pointing away from charge

The Electric Fields

Electric field intensity, E

due to q

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The Electric Fields

TWO important properties for electric charge:

• Law of conservation of electric charge

2. Principle of linear superposition

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The Electric Fields

Electric flux density, D

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where E = electric field intensityε = electric permittivity of the material

The Magnetic Fields
• Velocity of light in free space, c

where µ0 = magnetic permeability of free space

= 4π x 10-7 H/m

• Magnetic flux density, B

where H = magnetic field intensity

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Permittivity
• Describes how an electric field affects and is affected by a dielectric medium
• Ability of material to polarize in response to field
• Reduce the total electric field inside the material
• Permittivity of free space;
• Relative permittivity

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Permeability
• The degree of magnetization of a material
• Responds linearly to an applied magnetic field.
• The constant value μ0 is known as the magnetic constant, i.e permeability of free space;
• Relative permeability

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The Electromagnetic Spectrum

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Review of Complex Numbers
• A complex number z is written in the rectangular form Z = x ± jy
• x is the real ( Re ) part of Z
• y is the imaginary ( Im ) part of Z
• Value ofj = −1 .
• Hence, x =Re (z) , y =Im (z)

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Forms of Complex Numbers
• Using Trigonometry, convert from rectangular to polar form,
• Alternative polar form,

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Forms of complex numbers
• Relations between rectangular and polar representations of complex numbers.

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Forms of complex numbers

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Complex conjugate
• Complex conjugate, z*
• Opposite sign (+ or -) & with * superscript (asterisk)
• Product of complex number z with its complex conjugate is always a real number;

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Equality
• z1 = z2 if and only if x1=x2 AND y1=y2
• Or equivalently,

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Multiplication in Rectangular Form
• Given two complex numbers z1 and z2;
• Multiplication gives;

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Multiplication in Polar Form
• In polar form,

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Division in Polar Form
• For

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Division in Rectangular Form

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Powers
• For any positive integer n,
• And,

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Powers
• Useful relations

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