1. EKT 242/3: ELECTROMAGNETIC THEORY
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CHAPTER 1 - INTRODUCTION

2. What is Electromagnetism?
Electromagnetism - Magnetic forces produced by electricity. Oscillating electrical and magnetic fields.
Electromagnetism - Magnetism arising from electric charge in motion.

3. Electrostatic vs. Magnetostatic
Fields arise from a potential difference or voltage gradient
Fields arise from the movement of charge carriers, i.e flow of current
Field strength:
Volts per meter (V/m)
Amperes per meter (A/m)
Fields exist anywhere as long as there was a potential difference
Fields exist as soon as current flows
We will see how charged dielectric produces an electrostatic fields
We will see how current flows through conductor and produces magnetostatic fields
Example of electrostatics: vigorously rubbing a rubber rod with a piece of fur and bring to a piece of foil – foil will be attracted to the charged rod
Example of magnetostatics:
Current passes through a coil produces magnetic field about each turn of coil – combined will produce two-pole field, south & north pole
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4. Timeline for Electromagnetics in 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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5. Timeline for Electromagnetics in 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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6. Timeline for Electromagnetics in 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
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SI Units
French name ‘Systeme Internationale’
Based on six fundamental dimensions

8. Multiple & Sub-Multiple Prefixes
Example:
4 x F becomes
4 pF
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9. The Nature of Electromagnetism stop here
Physical universe is governed by 4 forces:
nuclear force – strongest of the four but its range is limited to submicroscopic systems, such as nuclei
weak-interaction force – strength is only that of the nuclear force. Interactions involving certain radioactive particles.
electromagnetic force – exists between all charged particles. The dominant force in microscopic systems such as atoms and molecules. Strength is of the order 10-2 of the nuclear force
gravitational force – weakest of all four forces. Strength is of the order that of the nuclear force. Dominant force in macroscopic systems, e.g solar system
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10. The Electromagnetic Force
Gravitational force – between two masses
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Where;
m2, m1 = masses R12 = distance G = gravitational constant
= unit vector from 1 to 2

11. Electric fields
Electric fields exist whenever a positive or negative electrical charge is present.
The strength of the electric field is measured in volts per meter (V/m).
The field exists even when there is no current flowing.
E.g rubbing a rubber sphere with a piece of fur.

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Electric Fields
Electric field intensity, E
due to q
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where = radial unit vector
pointing away from charge

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Electric Fields
Electric flux density, D
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where E = electric field intensity ε = electric permittivity of the material

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Magnetic Fields
Magnetic field arise from the motion of electric charges.
Magnetic field strength (or intensity) is measured in amperes per meter (A/m).
Magnetic field only exist when a device is switched on and current flows.
The higher the current, the greater the strength of the magnetic field.
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Magnetic Fields
Magnetic field lines are induced by current flow through coil.
Magnetic field strength or magnetic field intensity is denoted as H, the unit is A/m.
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north pole
south pole

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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 (unit: Tesla)
where H = magnetic field intensity
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Permittivity
Describes how an electric field affects and is affected by a dielectric medium
Relates to the ability of a material to transmit (or “permit”) an electric field.
Each material has a unique value of permittivity.
Permittivity of free space;
Relative permittivity;
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Permeability
The degree of magnetization of a material that responds linearly to an applied magnetic field.
The constant value μ0 is known as the magnetic constant, i.e permeability of free space;
Most materials have permeability of except ferromagnetic materials such as iron, where is larger than
Relative permeability;
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19. The Electromagnetic Spectrum
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20. Electromagnetic Applications
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21. Review of Complex Numbers
You can use calculator .
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 of
Hence, x =Re (z) , y =Im (z)
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22. Forms of Complex Numbers
Using Trigonometry, convert from rectangular to polar form,
Alternative polar form,
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23. Forms of complex numbers
Relations between rectangular and polar representations of complex numbers.
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24. Forms of complex numbers
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NB: θ in degrees

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Complex conjugate
Complex conjugate, z*
Opposite sign (+ or -) & with * superscript (asterisk)
Product of a complex number z with its complex conjugate is always a real number.
Important in division of complex number.
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Equality
z1 = z2 if and only if x1=x2 AND y1=y2
Or equivalently,
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27. Addition & Subtraction
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28. Multiplication in Rectangular Form
Given two complex numbers z1 and z2;
Multiplication gives;
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29. Multiplication in Polar Form
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Division in Polar Form
For
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Division in Polar Form
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Powers
For any positive integer n,
And,
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Powers
Useful relations
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