SEE 2523 Theory Electromagnetic

Chapter 1 Electromagnetic Introduction and Vector Analysis

You Kok Yeow Contents 1. Introduction the Electromagnetic Study

Brief Flow Chart for Electromagnetic Study

2. Revision on Vector

Basic Law of Vector

Vector Multiplication

3. Orthogonal Coordinate Systems

Length, Area and Volume in Cartesian Coordinates

Length, Area and Volume in Cylindrical Coordinates

Length, Area and Volume in Spherical Coordinates Brief Flow Chart for Electromagnetic Study

Electromagnetic Fields

Static Fields Dynamic Fields (Time Independence) (Time Dependence)

Electrostatics Magnetostatics Electric Fields Magnetic Fields

Phenomenon Electromagnetic Wave

Electromagnetics (EM) is a branch of physics or electrical engineering in which electric and magnetic phenomena are studied Basis of Electromagnetic Laws

Description Study Chapter Critical Experiment

Gauss’s Law Charge and Electric Electrostatic / Charge repel and attract different charges. (electric fields) fields Electric fields Comply with the inverse square law. Charge on an insulated conductor moves outward surface.

Gauss’s Law Magnetic fields Magnetostatic Confirmed that only exist magnetic dipole. (magnetic Magnetic fields (naturedly no magnetic monopole) fields)

Faraday’s Law The electrical effect Magnetic The bar magnet is pushed through a closed of a changing induction loop of wire will produce a current in the loop. magnetic fields

Ampere’s Law The magnetic effect Magnetic fields The current in the wire produces a magnetic of a changing field close to the wire. electric fields Basic Law of Vector (1)  1. A vector A has a  a) magnitude A  A

b) direction specified by a unit vector aˆ Magnitude A 2. A vector    A aAˆ A  aˆ A aˆ  aˆA 1

3. The unit vector aˆ is given by  A aˆ   A  A  A Basic Law of Vector (2) Example  The vector A may be represented as:   A  xˆAx  yˆAy zˆAz A  xˆ3 yˆ2zˆ6

The magnitude of  A  A Basic vector A  32  22  62 2 2 2  Ax  Ay  Az  7

The direction of  6 A aˆ  xˆ3  yˆ2  zˆ6 A aˆ  7 2 xˆA  yˆA  zˆA  x y z  xˆ0.429 yˆ0.286 zˆ0.857 3 2 2 2 Ax  Ay  Az

Components of vector Vector Multiplication (1)

1. There are two types of vector multiplication:   a) Scalar (or dot) product A B   b) Vector (or cross) product A B   2. The dot product of two vectors A and B is expressed as:   A B  AB cos  where  is the smaller angle between A and

  3. If A  Ax , Ay , Az  and B  Bx , By , Bz 

  A B  Ax Bx  Ay By  Az Bz Vector Multiplication (2)   4. Two vectors A and B are said to be orthogonal (perpendicular)   with each other, if A B  0

 5. The cross product of two vectors A and is expressed as:   A B  AB sin aˆn

where aˆ n is a unit vector normal to the plane containing and

  6. If A  Ax , Ay , Az  and B  Bx , By , Bz 

aˆ aˆ aˆ   x y z A B  Ax Ay Az

Bx By Bz

 Ay Bz  Az By aˆ x  Az Bx  Ax Bz  aˆ y  Ax By  Ay Bx aˆ z   Vector Multiplication (3) A B The cross product

Current

aˆn

  Direction of A B field lines 

Magnetic field Motion of force

Current Orthogonal Coordinate Systems

Z Z Z

P (x, y, z) P (ρ, Ø, z) P (ρ, Ø, θ) θ z z Y Y Y ρ ρ x Ø Ø y X X X   x2  y2  z 2 x   cos x   cos

1 y y   sin y   sin   tan x z  z z   cos x 2  y 2   tan 1 z z  z Cartesian Cylindrical Spherical Length, Area and Volume in Cartesian Coordinates Z A B C D

dl

G F dz H E dy dx z dv  dxdydz  dS  zˆ dxdy ABCD dS  xˆ dydz 0 Y HCDE dSFBDE  yˆ dxdz x  y dl  xˆdx yˆdy  zˆdz dl2  dx2  dy2  dz2 X P point is expanded from ( x, y, z ) to ( x+dx, y+dy, z+dz ). Length, Area and Volume in Cylindrical Coordinates Z G B

F dz A dl C ρ dØ

E  dρ dS  ˆ d dz ABCD D dv   d d dz

 z dS  ˆd dz 0 ADEF ρ Y  dS AFGB  zˆ  d d Ø  dl  ˆ d ˆdzˆdz

X dl2  d 2   2 d 2 dz2

P point is expanded from (ρ, Ø, z ) to (ρ+dρ, Ø +dØ, z+dz ). Length, Area and Volume in Spherical Coordinates Z ρ sinθ dØ dρ A B

ρ dθ G C F D dl θ H E

0 Y dv   2 sin d d d Ø ρ  2 dS ABCD  ˆ  sin d d  ˆ dSCDEH    sin d d  X ˆ dS BCHG    d d  dl  ˆ d ˆdˆ sind dl2  d 2   2 d 2   2 sin 2  d 2 P point is expanded from (ρ, θ, Ø) to (ρ+dρ, θ+dθ, Ø+dØ ). The electromagnetic (static) problem cases

The problems most often encountered Coordinate Electrostatic Cases Magnetostatic Cases

Cartesian - Any uniform charge distribution using a - The current flowing on the horizontal scale of cartesian coordinates. infinite extent plane.

Cylindrical - Uniform charge distribution on cylindrical - The current flowing in circumference. conductor. - The current flowing in an infinite - Uniform charge distribution on the infinite straight line. length of line. - The current flows in the solenoid and - Uniform charge distribution on the infinite toroid. extent horizontal plane.

- Uniform charge distribution on the horizontal circle plane.

- Uniform charge distribution on the circle line.

Spherical - Uniform charge distribution on the surface - Problem for the case of spheres less of a sphere. found.

- Uniform charge distribution of the point. References

J. A. Edminister. Schaum’s outline of Theory and problems of electromagnetics, 2nd Ed. New York: McGraw-Hill. 1993.

M. N. O. Sadiku. Elements of Electromagnetics, 3th Ed. U.K: Oxford University Press. 2010.

F. T. Ulaby. Fundamentals of Applied Electromagnetics, Media ed. New Jersey: Prentice Hall. 2001.

Bhag Singh Guru and Hüseyin R. Hiziroglu. Electromagnetic Field Theory Fundamentals, 2nd Ed. U.K.: Cambridge University Press. 2009.

W. H. Hayt. Jr. Engineering Electromagnetics, 5th Ed. New York: McGraw-Hill. 2009.