1. University of Utah Introduction to Electromagnetics Lecture 14: Vectors and Coordinate Systems Dr. Cynthia Furse University of Utah Department of Electrical and Computer Engineering www.ece.utah.edu/~cfurse 1

2. Vectors and Coordinate Systems Vector, Unit Vector, Direction and Distance between two points, Perpendicular & Parallel Vectors, Vector Math (+,-,,x) Coordinate Systems (Cartesian, Cylindrical, Spherical) Integrals (Line, Surface, Volume) 2

3. Vector, Unit Vector 3

4. Adding and Subtracting Vectors 4

5. Direction and Distance between two points 5

6. Dot Product 6

7. Projection of A on B 7

8. Cross Product 8

9. Perpendicular Vectors 9

10. Right Hand Rule 10

11. Another Form of R Hand Rule 11

12. Coordinate Systems Rectangular (Cartesian) 12

13. Cylindrical Coordinate System 13

14. Spherical Coordinate System 14

15. Differential Elements of Line, Surface, Volume -- Rectangular 15 From Table 3-1:

16. Line Integral 16 From Table 3-1:

17. Surface Integral 17 From Table 3-1:

18. Volume Integral 18 From Table 3-1:

19. Differential Elements of Line, Surface, Volume -- Cylindrical 19 From Table 3-1:

20. Line Integral 20 From Table 3-1:

21. Surface Integral 21 From Table 3-1:

22. Volume Integral 22 From Table 3-1:

23. Differential Elements of Line, Surface, Volume -- Spherical 23 From Table 3-1:

24. Line Integral 24 From Table 3-1:

25. Surface Integral 25 From Table 3-1:

26. Volume Integral 26 From Table 3-1:

27. Vector Transformation 27

28. Distance Between Points 28 From Table 3-2:

29. 29

30. 30