电磁场与电磁波课件76238207详解

B
A B
A
矢量的加法
B B
A B
矢量的减法
A
A ( B C ) ( A B) C
第1章 矢量分析
Chapter 1 Vector Analysis
6
（2）Scalar product Vector kA ex kAx ey kAy ez kAz
7
A B en AB sin
When be expressed in coordinate components A B ex ( Ay Bz Az By ) ey ( Az Bx Ax Bz ) ez ( Ax By Ay Bx ) Written in the form of determinant ex e y ez A B Ax Ay Az
第1章 矢量分析
Chapter 1 Vector Analysis
4
Coordinated component of vector
A Ax ex Ay ey Az ez
Ax A cos Ay A cos Az A cos A A(ex cos ey cos ez cos )
A B
Bx
By
Bz
If A // B ，then
A B B A A B AB If A B，then
A B 0
B

AB sin
矢量A 与B 的叉积
A
第1章 矢量分析
Chapter 1 Vector Analysis
第1章 矢量分析
Chapter 1 Vector Analysis
1
Chapter 1: Vector Analysis
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第1章 矢量分析
1.1 Vector Algebra 1.2 Orthogonal Coordinate 1.3 Gradient of scalar field
Chapter 1 Vector Analysis Overview
eA ex cos e y cos ez cos
z
Az
A
Ay
y
Ax
x
第1章 矢量分析
Chapter 1 Vector Analysis
5
2. The rule of vector algebra （1）Vector’s Addition & Subtraction Adding or subtracting two vector lead to the diagonal line of a parallelogram outlined by the given vectors with one neighboring the other In Cartesian： A B ex ( Ax Bx ) ey ( Ay By ) ez ( Az Bz ) Vector’s addition and subtraction follows Commutative Law A B B A Associative Law
2
1.4 Flux and Divergence of vector field
1.5 Circulation and Curl of vector field 1.6 Irrotational/conservative field and commuous/solenoidal
field
1.7 Laplacian operator and Green’s theorem 1.8 Helmholtz’s theorem
第1章 矢量分析
Chapter 1 Vector Analysis
3
1.1 Vector Algebra
1. The Definition of Scalar and Vector Scalar is a physical quantity that is solely described by its size Vector is, on the contrary, a physical quantity that is described not only by its size, but also a direction that expressed by bold letter with arrows Geometric Expression vector denoted by a line segment with direction A Vector’s algebra A eA A eA A Vector’s size A A A Unit vector eA A Constant Vector the vector that both the size and direction are unchanged
（3）Vector’s dot product
B

A B AB cos Ax Bx Ay By Az Bz A B B A Commutative Law A B 0 A // B A B AB AB
A
矢量 A与 B 的夹角
ex e y e y ez ez ex 0 ex ex e y e y ez ez 1
第1章 矢量分析
（4）Vector’s cross product
Chapter 1 Vector Analysis
8
（5）Vector’s hybrid calculation distributive law ( A B) C A C B C ( A B) C A C B C distributive law A ( B C ) B (C A) C ( A B) scalar triple product A ( B C ) ( A C ) B ( A B)C vector triple product