1 Electromagnetics I EELE 3331 Dr Assad AbuJasser

1 Electromagnetics I (EELE 3331) Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

2 Assad Abu-Jasser, Ph. D Electric Power Engineering The Islamic University of Gaza ajasser@iugaza. edu. ps site. iugaza. edu. ps/ajasser Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

3 Chapter 2 Coordinate Systems and Transformation Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

4 Introduction Orthogonal and Nonorthogonal Systems Orthogonal System coordinates are mutually perpendicular Cartesian (Rectangular), Circular Cylindrical, Spherical Nonorthogonal System coordinates are not mutually perpendicular hard to work with and with little or no practical use Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

5 Coordinate Systems Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

6 Cartesian Coordinates (x, y, Z) Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

7 Circular Cylindrical Coordinates Components Transformation Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

8 Spherical Coordinates (r, Ѳ, φ) Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

9 Spherical Coordinates Components Transformation Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

10 Unit Vector Transformation Cylindrical to Spherical Problem 2. 9 Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

11 Coordinate Systems Distance between Two Points Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

12 Example 2. 1 Given point P(-2, 6, 3) and vector A=yax+(x+z)ay, express P and A in cylindrical and spherical coordinates. Evaluate A at P in the cartesian, cylindrical, and spherical systems. Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

13 Example 2. 2 Express the vector B=(10/r)ar+rcosѲaѲ+aφ in cartesian and cylindrical coordinates. Find B(-3, 4, 0) and B(5, π/2, -2) Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

14 Constant-Coordinate Surfaces x=constant y=constant z=constant Dr. Assad Abu-Jasser - EE Department - IUGaza ρ=constant r=constant Ф=constant Ѳ=constant z=constant Ф=constant Electromagnetics I

15 Example 2. 3 Two uniform vector fields are given by E=-5 aρ+10 aφ+3 az and F= =aρ+2 aφ-6 az calculate: (a) |E×F| (b) The vector component of E at P(5, π/2, 3) parallel to x=2, z=3 (c) The angle E makes with the surface z=3 at P Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

16 Example 2. 4 Given a vector field D=rsinφar-(1/r)sinѲcos. ФaѲ+r 2 aφ. Determine: (a) D at P(10, 150 o, 330 o) (b) The component of D tangential to the spherical surface r=10 at P (c) A unit vector at P perpendicular to D and tangential to the cone Ѳ=150 o Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I

17 End Of Chapter Two Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I