The document discusses foundational concepts in electromagnetics, including vector addition and properties like the associative and distributive laws. It introduces rectangular coordinate systems and vector representations, emphasizing vector fields as functions with magnitude and direction in space. Additionally, it covers the dot product and vector projections.

1. 1-1
Electromagnetics (I)

2. 1-2
Vector Addition
Associative Law:
Distributive Law:

3. 1-3
Rectangular Coordinate System

4. 1-4
Differential Volume Element

5. 1-5
1-5
Vector Representation in Terms of
Orthogonal Rectangular Components

6. 1-6
1-6
Vector Expressions in Rectangular
Coordinates
General Vector, B:
Magnitude of B:
Unit Vector in the
Direction of B:

7. 1-7
1-7
Example

8. 1-8
1-8
Vector Field
We are accustomed to thinking of a specific vector:
A vector field is a function defined in space that has magnitude
and direction at all points:
where r = (x,y,z)

9. 1-9
1-9
The Dot Product
Commutative Law:

10. 1-10
1-10
Vector Projections Using the Dot Product
B • a gives the component of B
in the horizontal direction
(B • a) a gives the vector component
of B in the horizontal direction

11. 1-11
Projection of a vector on another
vector