1. Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by
Nannapaneni Narayana Rao
Edward C. Jordan Professor of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
Distinguished Amrita Professor of Engineering
Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India

2. 1.1
Vector Algebra

3. (1) Vectors (A) vs. Scalars (A)
Magnitude and direction Magnitude only Ex: Velocity, Force Ex: Mass, Charge
(2) Unit Vectors have magnitude unity denoted by symbol a with subscript
Useful for expressing vectors in terms of their components.

4. (3) Dot Product is a scalar
A • B = AB cos a B
Useful for finding angle between two vectors.

5. (4) Cross Product is a vector
A B = AB sin a B
is perpendicular to both A and B.
Useful for finding unit vector perpendicular to two vectors. an

6. where
(5) Triple Cross Product
in general.

7. (6) Scalar Triple Product
is a scalar.

8. Volume of the parallelepiped

9. D1.2 A = 3a1 + 2a2 + a3
B = a1 + a2 – a3
C = a1 + 2a2 + 3a3
(a) A + B – 4C
= (3 + 1 – 4)a1 + (2 + 1 – 8)a2
+ (1 – 1 – 12)a3
= – 5a2 – 12a3

10. (b) A + 2B – C
= (3 + 2 – 1)a1 + (2 + 2 – 2)a2
+ (1 – 2 + 3)a3
= 4a1 + 2a2 – 4a3
Unit Vector =

11. (c) A • C =
= 10
(d) =
= 5a1 – 4a2 + a3

12. A • (B C) = (3a1 + 2a2 + a3) • (5a1 – 4a2 + a3) = 3 5 + 2 (–4) + 1 1
(e)
= 15 – = 8
Same as
A • (B C) = (3a1 + 2a2 + a3) • (5a1 – 4a2 + a3)
= (–4)
= 15 – 8 + 1
= 8

13. P1.5
D = B – A ( A + D = B)
E = C – B ( B + E = C)
D and E lie along a straight line.

14. What is the geometric interpretation of this result?

15. Another Example
Given
Find A.

16. To find C, use (1) or (2).