E11麦克斯韦方程组

1、Chapter 11 Displacement current Maxwells equations,1 Maxwells electromagnetic theory,2 Maxwells equations,3 Electromagnetic wave,4 Examples,经典电磁理论的奠基人 , 气体动理论创始人之一. 提出了有旋场和位移电流的概念 , 建立了经典电磁理论 , 并预言了以光速传播的电磁波的存在. 在气体动理论方面 , 提出了气体分子按速率分布的统计规律.,麦克斯韦（18311879）英国物理学家,1865 年麦克斯韦在总结前人工作的基础上，提出完整的电磁场理论，他的主要

2、贡献是提出了“有旋电场”和“位移电流”两个假设，从而预言了电磁波的存在，并计算出电磁波的速度（即光速）.,( 真空中 ),1 Maxwells electromagnetic theory,1 Maxwells first supposition-curl electric field,Faraday:,The total field at a point in space:,Maxwell：,Electrostatic field,Curl electric field or induced electric field,Electrostatic field:,（1）,The differ

3、ence between electrostatic field and induced electric field：,实质: A circulating electric field can be created by a changing magnetic field.,Faradays law of electromagnetic induction. A changing magnetic flux creates an electromotive force.,2 Maxwells second supposition -displacement current 位移电流,麦克斯韦

4、对电磁场理论的重大贡献的核心是位移电流的假说，它是将安培环路定理应用于含有电容的交变电路中出现矛盾而引出的。,（1） Amperes circuital theorem,Constant current：,Amperes law states that the same equation holds if the plane circular region is replaced by any surface having C as its boundary. 通过以环路为周界所有曲面的电流相等，与曲面形状、位置无关。,C,Amperes circuital theorem fails in

5、the circuit shown in right Fig: 在研究含有电容(capacitor)的交变电流电路时，应用安培环路定理就会出现矛盾。,稳恒情况下得到的安培定理不能用于交变电路中,On the other hand, because no current is emerging, charge is building up inside, and as a result, electric flux is building up between the capacitor plates, and therefore, flux lines pass through the hem

6、ispherical surface. The electric flux is given by,（2） The correction of Amperes circuital theorem The supposition of displacement current,矛盾是由电流变化造成的，即传导电流在交变电容电路中不再连续；如果假设在变化的电容器中有另一种电流存在，整个电路的电流就又连续了。,在电容器中无传导电流但有变化的电场，有电位移。,Maxwell argued that this buildup of electric flux could be just whats nee

7、ded to correct Amperes equation. The flux is related to the current flowing into the region by equation:,Maxwell thought of the term as representing a kind of fictitious current to complete the circuit that is interrupted by the capacitor. It is called Displacement current,Maxwell reasoned that eith

8、er real current, I, or displacement current , Id, (or both) might flow any given surface, but the sum I+Id that flows into any region must also flow out.,Total current：,To generalize Amperes circuital theorem by replacing I by I+Id,Note :,Displacement and conducting currents,The same: 二者都可产生磁场 The d

9、ifference： 1 位移电流的实质是变化的电场而非电荷的定向移动 2 位移电流不仅在导体中而且在介质和真空中存在。 3 位移电流不产生焦耳热。,2 Maxwells equations,Meaning: Gausss law for electricity. Comes directly from Coulombs law. The electric flux out of a region is proportional to the net charge inside.,Meaning: Faradays law of electromagnetic induction. A cha

10、nging magnetic flux creates an electromotive force.,The integral shape of Maxwells equations,Meaning: Gausss law for magnetism. Because there ere no magnetic monopoles, there is never any net flux out of any region.,Meaning: Maxwell-Ampere law. Circuital magnetic fields are created either by electri

11、c currents or by changing electric flux.,Appendix: (1) Maxwells equations in free space:,(2) Differential shape,(3) Matter equation,（4）the boundary condition 电磁场边值条件,Isotropy,当界面两边为介质时：,Free charge facial density,Conducting current facial density,3 Electromagnetic wave,1 Electromagnetic wave,A chang

12、ing magnetic field can produce an electric field. A changing electric field can produce a magnetic field. Waves arise when these two are combined. The dynamic E and B can be created by each other. This is the essence of the electromagnetic wave. 变化的电场和变化的磁场相互激发，在空间传播开来，形成电磁波。,已发出去的电磁波即使波源消失，波仍将继续存在并

13、向前传播。,电磁波是电磁振荡在空间的传播。,Electromagnetic waves travel depending on: (1) A changing magnetic field can produce an electric field. (2) A changing electric field can produce a magnetic field.,正是在这两个基本假说的基础上，麦克斯韦预言了电磁波的存在。,2 The characteristics of electromagnetic waves,Example for electric dipole ：,任意时刻t空间

14、某点的E、 H：,The characteristics of electromagnetic waves,(1) Electric and magnetic field oscillations propagate in phase E和B都作正弦或余弦的周期性变化，且相位相同,(2) E and H are perpendicular, and the both vectors are perpendicular to the direction of propagation of waves,电磁波是横波electromagnetic waves are transverse waves

15、,(3) The relationship of E and H：,(4) Velocity ：,(5) Poynting vector 波印亭矢量,The Energy density of Electromagnetic fields,Energy flow density能流密度： Poynting vector The energy per unit time (the power) across a unit area 单位时间内垂直通过传播方向上单位面积的能量,Poynting vector,3 Hertzs experiment,undergoing acceleration r

16、adiate electromagnetic waves, as predicted by Maxwell.,振子,谐振腔,Emission,Incept,A,B,感应圈,A、B是两段共轴的黄铜杆，它们是振荡偶极子的两半，A、B中间留有一个火花间隙，间隙两边杆的端点上焊有一对磨光的黄铜球，振子的两半联接到感应圈的两极上，当充电到一定程度间隙被火花击穿时，两段金属杆连成一条导电通路，这时它相当于一个振荡偶极子，在其中激起高频的振荡。,Maxwells spectacular discovery was not verified experimentally until nearly a decade after his death. In 1887, Hertz used a simple method to determine whether electric charges,为了探测由振子发射出来的电磁波，赫兹采用了一个圆形铜环，在其中也留有端点球状的火花间隙。间隙的距离可利用螺旋作微小的调节。这种接收装置称为谐振器。将谐振器放在距振子一定的距离之外，适当地选择其方位，并使之与振子谐振。在发现振子的间隙有火花跳过的同时，谐振器的间隙也有火花跳过。,赫兹利用振荡偶极子进行了许多实验，不仅证实了振荡偶极子能发射电磁波，并且证实这种