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# 01 Sadiku Ch01

```CHAPTER 1
VECTOR ALGEBRA
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 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 &copy; 2014 by Oxford University Press
Unit Vector
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 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 &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
Vector Addition and Subtraction
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 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 &copy; 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 &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 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 &copy; 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 &copy; 2014 by Oxford University Press
FIGURE 1.5 Distance vector rPQ.
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
Example:
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
Example:
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
FIGURE 1.6 For Example 1.3.
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
Vector Multiplication
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 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 &copy; 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 &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 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 &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 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 &copy; 2014 by Oxford University Press
Example 1.4
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
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Example 1.5
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 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 &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 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 &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
ELEMENTS OF ELECTROMAGNETICS, 6/e
MATTHEW N. O. SADIKU
Copyright &copy; 2014 by Oxford University Press
```