Electromagnetic Theory (ECM515) Ali Othman Universiti Teknologi MARA Pulau Pinang HP No: 019-4260206 BKBA 4.7(04-382 2507)/BP 7.15 (04-382 2827) https://sites.google.com/site/ecoursef

Why Study Electromagnetics (EM)? EM is a branch of physics or electrical engineering in which electric and magnetic phenomena are studied. An EM is made up of interdependent electric and magnetic fields, which is the case when the fields are varying with time, that is, they are dynamic. An electric field is a force field that acts upon material bodies by virtue of their property of charge, just as a gravitational field is a force field that acts upon them by virtue of their property of mass. A magnetic field is a force field that acts upon charges in motion. EM is all around us. In simple terms, every time we turn a power switch on, every time we press a key on our computer keyboard, or every time we perform a similar action involving an everyday electrical device, EM comes into play. It is the foundation for the technologies of electrical and elctronic engineering, spanning the entire electromagnetic spectrum, from dc to light, from the electrically and magnetically based (elctromechanics) technologies to the electronics technologies to the photonics technologies. As such, in the context of engineering education, it is fundamental to the study of electrical and electronic engineering.

Course Outcomes Solve all the properties of electrostatic and magnetic field in different materials and apply the properties in calculating electric and magnetic potential, capacitance and inductance. Apply Maxwell equation and explain the induced EMF using Faraday’s and Lenz’s Law. Identify the properties of material that give impact to the wave propagation. Chapter 1 Vector Analysis (3h) Chapter 2 Electrostatic Field (12h) Chapter 3 Magnetostatic Field (12h) Chapter 4 Time Varying Field & Maxwell’s Equations (6h) Chapter 5 Plane Wave Propagations (6h)

Recommended as a Textbook Title : Elements of electromagnetics Author : Matthew N. O. Sadiku Edition : 5, illustrated Publisher : Oxford University Press, Incorporated, 2010 Original from : the University of California Digitized : 2 Feb 2011 ISBN : 0195387759,9780195387759 Length : 845 pages Recommended as a Textbook

Chapter 1 Vectors Analysis Objectives: Define Vector, Unit Vector, Direction and Distance between two points, Perpendicular & Parallel Vectors, Vector Math (+,-,, x) Coordinate Systems (Cartesian, Cylindrical, Spherical) Integrals (Line, Surface, Volume)

Scalars and Vectors Scalar – a quantity that has only magnitude. i.e., time (t) ; mass (m) ; distance (d) ; temperature (T) Vector – a quantity that has both magnitude and direction. i.e., velocity ( ) ; force ( ) ; displacement ( ) Field – a function that specifies a particular quantity everywhere in a region. (if the quantity is a scalar/vector, the field is said to be a scalar/vector field.

Vectors, Unit Vector Example of Vector Magnitude Direction of unit vector Note that

Adding and Subtracting Vectors Let us consider 2 vectors (A and B)

Direction and Distance between 2 points Let us consider 2D (P1 and P2) If we want to find

Direction and Distance between 2 points Example Q : If A = 10ax - 4ay + 6az and B = 2ax + ay, find: the component of A along ay, (ay = -4) the magnitude of 3A - B, (35.74) 3A - B = 3(10, - 4 , 6) - (2, 1, 0) = (30,-12,18) - (2, 1,0) = (28,-13,18) (c) a unit vector along A + 2B. Let C = A + 2B = (10, - 4 , 6) + (4, 2, 0) = (14, - 2 , 6) A unit vector along C is :

Direction and Distance between 2 points Q : Points P and Q are located at (0, 2, 4) and ( - 3 , 1, 5). Calculate: (a) The position vector P (b) The distance vector from P to Q (c) The distance between P and Q (d) A vector parallel to PQ with magnitude of 10

Vector Multiplication When two vectors A and B are multiplied, the result is either a scalar or a vector depending on how they are multiplied. Thus there are two types of vector multiplication: Scalar (or dot) product: A • B Vector (or cross) product: A X B

Dot Product Scalar (or dot) product: A • B

Cross Product 2. Vector (or cross) product: A X B normal to both A and B

Right Hand Rule (RHR) 2. Vector (or cross) product: A X B The direction of is taken as the direction of the RHR

Another form of Right Hand Rule 2. Vector (or cross) product: A X B

1. Coordinate Systems Rectangular (Cartesian) The 3 unit vectors are orthogonal each other

2. Cylindrical Coordinate System

3. Spherical Coordinate System Specific limit

Differential Elements of Line, Surface, Volume - Rectangular Formula Line Surface Volume

Line Integral (Scalar form) Let consider line of charge Formula Line Surface Volume

Line Integral (Vector form) Let consider line of current in z direction (total amps) Formula Line Surface Volume

Surface Integral Let consider uniform charge distribution of the surface. Formula Line Surface Volume

Surface Integral Let consider non-uniform charge distribution of the surface. Formula Line Surface Volume

Surface Integral (Summary) What changes? Define the formula to use. Define uniform or non- uniform. Set up integral. Formula Line Surface Volume

Volume Integral Formula Line Surface Volume

Differential Elements of Line, Surface, Volume - Cylindrical Coordinate System Formula Line Surface Volume