第一章 电磁场基本理论
麦克斯韦方程
浙江大学信息与电子工程学院
《高等电磁波理论》
1
2
Andre Marie Ampere
(1775-1836)
螺旋管的磁场
I
B
B
长导线的磁场
安培定律（1826年）
3
Michael Faraday
(1791-1867)
B B
磁场随时间变化
Vgen Vgen
B
面积随时间变化
Vgen
N
S
N S
法拉第定律（1831年）
4
Faraday’s law of induction
The law of all sea and all land—
No lies, no deceit, no corruption
In this law so complete and so grand!
Our children will sing it in chorus –
“Circulation of vector cap E,”
Yes they’ll sing as they march on before us,
“Equals negative d by dt
Of –
Magnetic flux through a surface,”
© 2001 Walter Fox Smith
法拉第定律之歌
They’ll conclude as we strike up the band.
We’ll mark all our coins with our purpose --
“On Maxwell’s equations we stand!”
It’s Faraday’s law of induction
That allows us to generate pow’r.
It gives voltage increase or reduction --
We could sing on and on for an hour!. .
矢量电场积分
= 穿过表面磁通量
的时间微分
赋予“力量”--电压增减
5
Inside, outside, count the lines to tell –
If the charge is inside, there will be net flux as well.
If the charge is outside, be careful and you’ll see
The goings in and goings out are equal perfectly.
If you wish to know the field precise,
And the charge is symmetric,
you will find this law is nice –
Q upon a constant – eps’lon naught they say –
Equals closed surface integral of E dot n dA.
© 2001 Walter Fox Smith
高斯定律（1832）
闭合曲面的电通量积分
= 内部电荷总量 × 常系数
《高斯定律之歌》
“收支”平衡
6
James Clerk Maxwell
(1831-1879)
麦克斯韦-安培定律（1860）
平板电容的失效
E
路径 l
I I
曲面 S1
曲面 S2
加个位移电流试试
7
Mr. Ampere’s magical, mystical, wonderful law!
Of Maxwell’s equations, it is the longest and
strangest of all!
On the left side, he wrote circulation
Of magnetic field, ‘cause it was neat.
On the right hand side of his equation –
Mu-naught I – he thought it was complete.
Decades later, Maxwell saw disaster,
Although he thought of Ampere as a saint –
In between the plates of a capacitor
The right side’s zero, but the left side ain’t!
安培定律之歌
To fix this problem, he added to the right side
Displacement current, a brand new quantity!
It started mu-naught eps’lon-naught and
ended by The time derivative of phi-sub-E.
And so to Maxwell the myst’ry was revealed –
He saw how light could move through empty space.
The changing B-field made the changing E-field,
And vice-a-versa, all at the perfect pace.
两位科学家-同一个定理
© 2001 Walter Fox Smith
8
电磁“相遇”
《电场情歌》
© 2001 Walter Fox Smith
相遇前
电场：始正终负 磁场：自我闭合
负能量
加锁
内耗
相遇后
电变生磁 磁变生电
互相扶持
齐头并进
9
麦克斯韦方程组
James Clerk Maxwell
(1831-1879)
积分形式
电磁场可以传播
光是一种电磁场
电子工程拉开序幕
10
麦克斯韦方程组（微分形式）
矢量分析
梯度（gradient）
散度（divergence）
旋度（curl）
梯度定理：
Gauss定理：
Stokes定理：
麦克斯韦方程组（自由空间）
（法拉第定律）
（安培定律）
（高斯定律）
（磁高斯定律）
（连续性方程）
形式转化
