CHAPTER 1 VECTOR ALGEBRA ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press Scalars and Vectors A scalar is a quantity that has only magnitude A vector is a quantity that has magnitude and direction A field is a function that specifies a particular quantity everywhere in a region. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press Unit Vector ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press FIGURE 1.1 (a) Unit vectors ax, ay, and az, (b) components of A along ax, ay, and az. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press Vector Addition and Subtraction ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press FIGURE 1.2 Vector addition C = A + B: (a) parallelogram rule, (b) head-to-tail rule. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press FIGURE 1.3 Vector subtraction D = A - B: (a) parallelogram rule, (b) head-to-tail rule. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press Position and Distance Vectors The position vector of point P The distance vector is the displacement of one point to another ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press FIGURE 1.4 Illustration of position vector rP = 3ax + 4ay + 5az. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press FIGURE 1.5 Distance vector rPQ. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press Example: ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press Example: ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press FIGURE 1.6 For Example 1.3. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press Vector Multiplication ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press FIGURE 1.7 The cross product of A and B is a vector with magnitude equal to the area of the parallelogram and direction as indicated. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press FIGURE 1.8 Direction of A B and an using (a) the right-hand rule and (b) the right-handed-screw rule. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press FIGURE 1.9 Cross product using cyclic permutation. (a) Moving clockwise leads to positive results. (b) Moving counterclockwise leads to negative results. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press FIGURE 1.10 Components of A along B: (a) scalar component AB, (b) vector component AB. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press Example 1.4 ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press Example 1.5 ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press Example 1.6 FIGURE 1.11 For Example 1.6. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press Example 1.7 FIGURE 1.12 For Example 1.7. ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press ELEMENTS OF ELECTROMAGNETICS, 6/e MATTHEW N. O. SADIKU Copyright © 2014 by Oxford University Press
