工程电磁场第一章解读

Chapter 1 Vector Analysis
1. Vector analysis is the branch of mathematics that was developed to describe quantities that are both directional in nature and distributed over regions of space. 2. The reason for starting our study of electromagnetics with vector analysis 3. The main contents in the chapter
1. Three coordinate systems
Cartesian system or rectangular system Circular cylindrical system Spherical coordinate system
2. The Cartesian coordinate system has three axes
3. In other coordinate systems, points are also located at the common intersection of three surfaces, not necessarily planes, but still normal at the point of intersection. 4. Shown in Fig.1.2c, the coordinate of P is x,y,z respectively and that of Q is x+dx, y+dy, z+dz.
Engineering Electromagnetics
工程电磁场
主讲 彭润玲 讲师
The aim of having this lesson
1. Electromagnetics is both the oldest and most basic branch of electrical engineering 2. It deals with the following questions: What’s electricity? How does it behave? What can it do? How can we control it? 3. So it is essential to understand electromagnetics for us to fully understand the operation of many electrical devices and effects. Transformer Computer wireless communication
7. (r s)( A B) r ( A B) s( A B) rA rB sA sB
Obeys associative and distributive laws 8. A B 0 A B
1.3 The Cartesian Coordinate System
Vector addition---adding the corresponding components
5. Scalar times Vector
If the scalar>0, the vector is changed only with magnitude
If the scalar<0, both magnitude and direction are changed A 1 6. Division of a Vector by a Scalar A s s
1.1 Scalars and Vectors
1. A scalar: a quantity that can be specified by a single number
What’s a scalar? In mathematics---any real quantity In physics---given a physical unit, with physical significance.
2. A vector:
What’s a vector?
3. Scalar and Vector fields
A field is defined as some function of that vector which connects an arbitrary origin to a general point in space.
The rules of vector algebra: addition, subtraction, multiplication by a scalar
Follows the parallelogram law
2. Vectorial addition
Follows the commutative law Follows the associative law
4. Boldface type---Vector and Italic type---Scalar 5. When writing, please draw a line or an arrow over a vector
1.2 Vector Algebra
1. The main contents of this subsection
Mutually normal to each other A right-handed system The intersection of three surfaces x=constant;y=constant;z=constant
1.3 The Cartesian Coordinate System
A ( B C) ( A B) C
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A B B A
1.2 Vector Algebra
3. Vector---two or three components
4. Vector subtraction A B A (B)