*ENE 325Electromagnetic Fields and WavesLecture 1 Electrostatics

*SyllabusDr. Rardchawadee Silapunt, rardchawadee.sil@kmutt.ac.thLecture: 9:30pm-12:20pm Wednesday, Rm. CB41004Office hours :By appointmentTextbook: Fundamentals of Electromagnetics with Engineering Applications by Stuart M. Wentworth (Wiley, 2005)

*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.

Course Objectives

* 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

Prerequisite knowledge and/or skills

*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

Course outline

*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

*Electrostatics:

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

*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

*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

*Homework 20% Midterm exam 40% Final exam 40%GradingVision: 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.

*Examples of Electromagnetic fieldsElectromagnetic fields Solar radiationLightningRadio communicationMicrowave oven

Light consists of electric and magnetic fields. An electromagnetic wave can propagate in a vacuum with a speed velocity c=2.998x108 m/s

c = ff = frequency (Hz) = wavelength (m)

*Vectors - Magnitude and direction 1. Cartesian coordinate system (x-, y-, z-)

*Vectors - Magnitude and direction 2. Cylindrical coordinate system (, , z)

*Vectors - Magnitude and direction 3. Spherical coordinate system (, , )

* Manipulation of vectorsTo find a vector from point m to n

Vector addition and subtraction

Vector multiplication vector vector = vector vector scalar = vector

*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

*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

*c) Find the direction of

*Coulombs lawLaw of attraction: positive charge attracts negative chargeSame polarity charges repel one anotherForces between two chargesCoulombs LawQ = electric charge (coulomb, C) 0 = 8.854x10-12 F/m

*Electric field intensityAn electric field from Q1 is exerted by a force between Q1 and Q2 and the magnitude of Q2

or we can write

*Electric field lines

*Spherical coordinate systemorthogonal 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:

*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)

*Unit vector conversion (Spherical coordinates)

*differential element

volume: dv = r2sindrdd

surface vector: Take the dot product of the vector and a unit vector in the desired direction to find any desired component of a vector.Find any desired component of a vector

*Ex3 Transform the vector field into spherical components and variables

*Ex4 Convert the Cartesian coordinate point P(3, 5, 9) to its equivalent point in spherical coordinates.

*Line charges and the cylindrical coordinate systemorthogonal point (, , z) = a radial distance (m) = the angle measured from x axis to the projection of the radial line onto x-y planez = a distance z (m)A vector representation in the cylindrical coordinate system:

*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)

*Unit vector conversion (Cylindrical coordinates)

*differential element

volume: dv = dddz

surface vector: (top)(side)Take the dot product of the vector and a unit vector in the desired direction to find any desired component of a vector.Find any desired component of a vector

*Ex5 Transform the vectorinto cylindrical coordinates.

*Ex6 Convert the Cartesian coordinate point P(3, 5, 9) to its equivalent point in cylindrical coordinates.

*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.