ENE 325 Electromagnetic Fields and Waves

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ENE 325Electromagnetic Fields and Waves
Lecture 1 Electrostatics
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Syllabus

• Dr. Rardchawadee Silapunt, rardchawadee.sil_at_kmutt.
  ac.th
• Lecture 930pm-1220pm Wednesday, Rm. CB41004
• Office hours By appointment
• Textbook Fundamentals of Electromagnetics with
  Engineering Applications by Stuart M. Wentworth
  (Wiley, 2005)

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Course Objectives
This is the course on beginning level
electrodynamics. The purpose of the course is to
provide junior electrical engineering students
with the fundamental methods to analyze and
understand electromagnetic field problems that
arise in various branches of engineering
science.
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Prerequisite knowledge and/or skills

• Basic physics background relevant to
  electromagnetism
• charge, force, SI system of units basic
  differential and
• integral vector calculus
• Concurrent study of introductory lumped circuit
  analysis

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Course outline

• Introduction to course
• Review of vector operations
• Orthogonal coordinate systems and change of
  coordinates
• Integrals containing vector functions
• Gradient of a scalar field and divergence of a
  vector field

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• Electrostatics
• Fundamental postulates of electrostatics and
  Coulomb's Law
• Electric field due to a system of discrete
  charges
• Electric field due to a continuous distribution
  of charge
• Gauss' Law and applications
• Electric Potential
• Conductors in static electric field
• Dielectrics in static electric fields
• Electric Flux Density, dielectric constant
• Boundary Conditions
• Capacitor and Capacitance
• Nature of Current and Current Density

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• Electrostatics
• Resistance of a Conductor
• Joules Law
• Boundary Conditions for the current density
• The Electromotive Force
• The Biot-Savart Law

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• Magnetostatics
• Amperes Force Law
• Magnetic Torque
• Magnetic Flux and Gausss Law for Magnetic
  Fields
• Magnetic Vector Potential
• Magnetic Field Intensity and Amperes Circuital
  Law
• Magnetic Material
• Boundary Conditions for Magnetic Fields
• Energy in a Magnetic Field
• Magnetic Circuits
• Inductance

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• Dynamic Fields
• Faraday's Law and induced emf
• Transformers
• Displacement Current
• Time-dependent Maxwell's equations and
  electromagnetic wave equations
• Time-harmonic wave problems, uniform plane waves
  in lossless media, Poynting's vector and theorem
• Uniform plane waves in lossy media
• Uniform plane wave transmission and reflection
  on normal and oblique incidence

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Grading

• Homework 20
• Midterm exam 40
• Final exam 40

Vision Providing opportunities for intellectual
growth in the context of an engineering
discipline for the attainment of professional
competence, and for the development of a sense
of the social context of technology.
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Examples of Electromagnetic fields

• Electromagnetic fields
• Solar radiation
• Lightning
• Radio communication
• Microwave oven
• Light consists of electric and magnetic fields.
  An electromagnetic wave can propagate in a
• vacuum with a speed velocity c2.998x108 m/s
• c f?
• f frequency (Hz)
• ? wavelength (m)

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Vectors - Magnitude and direction

• 1. Cartesian coordinate system (x-, y-, z-)

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Vectors - Magnitude and direction

• 2. Cylindrical coordinate system (?, ?, z)

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Vectors - Magnitude and direction

• 3. Spherical coordinate system (?, ?, ?)

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Manipulation of vectors

• To find a vector from point m to n
• Vector addition and subtraction
• Vector multiplication
• vector ? vector vector
• vector ? scalar vector

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Ex1 Point P (0, 1, 0), Point R (2, 2, 0)

• The magnitude of the vector line from the origin
  (0, 0, 0) to point P
• The unit vector pointed in the direction of
  vector

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Ex2 P (0,-4, 0), Q (0,0,5), R (1,8,0), and S
(7,0,2)

• a) Find the vector from point P to point Q
• b) Find the vector from point R to point S

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• c) Find the direction of

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Coulombs law

• Law of attraction positive charge attracts
  negative charge
• Same polarity charges repel one another
• Forces between two charges

Coulombs Law
Q electric charge (coulomb, C)?0 8.854x10-12
F/m ?
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Electric field intensity

• An electric field from Q1 is exerted by a force
  between Q1 and Q2 and the magnitude of Q2
• or we can write

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Electric field lines
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Spherical coordinate system

• orthogonal point (r,?, ?)
• r a radial distance from the origin to the
  point (m)
• ? the angle measured from the positive axis (0
  ? ? ? ?)
• ? an azimuthal angle, measured from x-axis (0 ?
  ? ? 2?)

A vector representation in the spherical
coordinate system
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Point conversion between cartesian and spherical
coordinate systems
A conversion from P(x,y,z) to P(r,?, ?) A conversion from P(r,?, ?) to P(x,y,z)


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Unit vector conversion (Spherical coordinates)




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Find any desired component of a vector
Take the dot product of the vector and a unit
vector in the desired direction to find any
desired component of a vector.
differential element volume dv
r2sin?drd?d? surface vector

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Ex3 Transform the vector field
into spherical components and variables
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Ex4 Convert the Cartesian coordinate point P(3,
5, 9) to its equivalent point in spherical
coordinates.
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Line charges and the cylindrical coordinate system

• orthogonal point (?, ?, z)
• ? a radial distance (m)
• ? the angle measured from x axis to the
  projection of the radial line onto x-y plane
• z a distance z (m)

A vector representation in the cylindrical
coordinate system
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Point conversion between cartesian and
cylindrical coordinate systems
A conversion from P(x,y,z) to P(r,?, z) A conversion from P(r,?, z) to P(x,y,z)


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Unit vector conversion (Cylindrical coordinates)




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Find any desired component of a vector
Take the dot product of the vector and a unit
vector in the desired direction to find any
desired component of a vector.
differential element volume dv
?d?d?dz surface vector
(top)

(side)
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Ex5 Transform the vectorinto cylindrical
coordinates.
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Ex6 Convert the Cartesian coordinate point P(3,
5, 9) to its equivalent point in cylindrical
coordinates.
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Ex7 A volume bounded by radius ? from 3 to 4 cm,
the height is 0 to 6 cm, the angle is 90?-135?,
determine the volume.