电磁场知识复习.pdf

文档介绍：电磁场知识复习
一、三维广义正交曲线坐标系
v 1、直角坐标系 A = a x Ax + a y Ay + az Az
z a x ´a y = az
M (x, y, z)
dl1 = h1dx = dx h1 = 1
y dl2 = h2dy = dy h2 = 1
dl3 = h3dz = dz h3 = 1
x dν= dxdydz
v 2、柱坐标系 A = ar Ar + aϕ Aϕ+ a z Az
z ar ´aϕ= a z
M (r,ϕ, z) dl1 = h1dr = dr h1 = 1
dl2 = h2dϕ= rdϕ h2 = r
dl = h dz = dz h = 1
r 3 3 3
ϕ dν= dl1dl2dl3 = rdrdϕdz
1

一、三维广义正交曲线坐标系
A = ar Ar + aθ Aθ+ aϕ Aϕ
v 3、球坐标系 ar ´aθ= aϕ
z
z dl1 = h1dr = dr h1 = 1
dl2 = h2dθ= rdθ h2 = r
θ M (r,θ,ϕ) dl = h dϕ= r sinθdϕ h = r sinθ
r r 3 3 3
ϕ 2
ϕ dν= dl1dl2dl3 = r sinθdrdθdϕ
v 2、柱坐标系 A = ar Ar + aϕ Aϕ+ a z Az
z ar ´aϕ= a z
M (r,ϕ, z) dl1 = h1dr = dr h1 = 1
dl2 = h2dϕ= rdϕ h2 = r
dl = h dz = dz h = 1
r 3 3 3
ϕ dν= dl1dl2dl3 = rdrdϕdz
一、三维广义正交曲线坐标系
A = ar Ar + aθ Aθ+ aϕ Aϕ
v 3、球坐标系 ar ´aθ= aϕ
z
z dl1 = h1dr = dr h1 = 1
dl2 = h2dθ= rdθ h2 = r
θ M (r,θ,ϕ) dl = h dϕ= r sinθdϕ h = r sinθ
r r 3 3 3
ϕ 2
ϕ dν= dl1dl2dl3 = r sinθdrdθdϕ
M (q1, q2 , q3 )
v 4、三维广义坐标系 a1 ´a2 = a3
A = a 1 A1 + a 2 A2 + a3 A3
凡是具有三个坐标变量(q1, q2, q3),
而且其坐标单位矢量a1 ,a2 ,a3相互正 dl1 = h1dq1
交的坐标系.
dl2 = h2dq2
dl3 = h3dq3
dν= dl1dl2dl3
2

二、基本概念和公式
1 ¶u 1 ¶u 1 ¶u
1、梯度: Ñu = a1 + a 2 + a3
h1 ¶q1 h2 ¶q2 h3 ¶q3
¶u ¶u ¶u ¶u
gradu = G = Ñu = a x + ay + az
¶x ¶y ¶z
¶l max
¶u 1 ¶u ¶u
gradu = Ñu Ñu = a r + a + az
¶r ϕ r ¶ϕ¶z
¶u 1 ¶u 1 ¶u
Ñu =