University of Utah Introduction to Electromagnetics Lecture 14: Vectors and Coordinate Systems Dr. Cynthia Furse University of Utah Department of Electrical and Computer Engineering 1

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

Vector, Unit Vector 3

Adding and Subtracting Vectors 4

Direction and Distance between two points 5

Dot Product 6

Projection of A on B 7

Cross Product 8

Perpendicular Vectors 9

Right Hand Rule 10

Another Form of R Hand Rule 11

Coordinate Systems Rectangular (Cartesian) 12

Cylindrical Coordinate System 13

Spherical Coordinate System 14

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

Line Integral 16 From Table 3-1:

Surface Integral 17 From Table 3-1:

Volume Integral 18 From Table 3-1:

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

Line Integral 20 From Table 3-1:

Surface Integral 21 From Table 3-1:

Volume Integral 22 From Table 3-1:

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

Line Integral 24 From Table 3-1:

Surface Integral 25 From Table 3-1:

Volume Integral 26 From Table 3-1:

Vector Transformation 27

Distance Between Points 28 From Table 3-2:

29

30