E11麥克斯韋方程組

1、Chapter 11 Displacement current Maxwells equations 1 Maxwells electromagnetic theory 2 Maxwells equations3 Electromagnetic wave 4 Examples經(jīng)典電磁理論的奠基人 , 氣體動(dòng)理論創(chuàng)始人之一. 提出了有旋場(chǎng)和位移電流的概念 , 建立了經(jīng)典電磁理論 , 并預(yù)言了以光速傳播的電磁波的存在. 在氣體動(dòng)理論方面 , 提出了氣體分子按速率分布的統(tǒng)計(jì)規(guī)律.麥克斯韋（18311879）英國(guó)物理學(xué)家 1865 年麥克斯韋在總結(jié)前人工作的基礎(chǔ)上，提出完整的電磁場(chǎng)理論，他的主要貢獻(xiàn)是

2、提出了“有旋電場(chǎng)”和“位移電流”兩個(gè)假設(shè)，從而預(yù)言了電磁波的存在，并計(jì)算出電磁波的速度（即光速）. ( 真空中 )1 Maxwells electromagnetic theory1 Maxwells first supposition-curl electric fieldFaraday:The total field at a point in space:Maxwell：Electrostatic field Curl electric field or induced electric field Electrostatic field:（1）The difference betwee

3、n electrostatic field and induced electric field：實(shí)質(zhì): 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 位移電流麥克斯韋對(duì)電磁場(chǎng)理論的重大貢獻(xiàn)的核心是

4、位移電流的假說(shuō)，它是將安培環(huán)路定理應(yīng)用于含有電容的交變電路中出現(xiàn)矛盾而引出的。（1） Amperes circuital theoremConstant current：Amperes law states that the same equation holds if the plane circular region is replaced by any surface having C as its boundary. 通過(guò)以環(huán)路為周界所有曲面的電流相等，與曲面形狀、位置無(wú)關(guān)。CAmperes circuital theorem fails in the circuit shown in

5、 right Fig: 在研究含有電容(capacitor)的交變電流電路時(shí)，應(yīng)用安培環(huán)路定理就會(huì)出現(xiàn)矛盾。穩(wěn)恒情況下得到的安培定理不能用于交變電路中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 hemispherical surface. Th

6、e electric flux is given by （2） The correction of Amperes circuital theoremThe supposition of displacement current 矛盾是由電流變化造成的，即傳導(dǎo)電流在交變電容電路中不再連續(xù)；如果假設(shè)在變化的電容器中有另一種電流存在，整個(gè)電路的電流就又連續(xù)了。在電容器中無(wú)傳導(dǎo)電流但有變化的電場(chǎng)，有電位移。Maxwell argued that this buildup of electric flux could be just whats needed to correct Amperes eq

7、uation. The flux is related to the current flowing into the region by equation:+-IIABMaxwell 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 either real current, I,

8、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 currentsThe same: 二者都可產(chǎn)生磁場(chǎng)The difference： 1 位移電流的實(shí)質(zhì)是變化的電

9、場(chǎng)而非電荷的定向移動(dòng) 2 位移電流不僅在導(dǎo)體中而且在介質(zhì)和真空中存在。3 位移電流不產(chǎn)生焦耳熱。2 Maxwells equationsMeaning: 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 changing magnetic flux creates a

10、n electromotive force.The integral shape of Maxwells equationsMeaning: 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 electric currents or by changing electr

11、ic flux.Appendix:(1) Maxwells equations in free space:(2) Differential shape(3) Matter equation（4）the boundary condition電磁場(chǎng)邊值條件Isotropy當(dāng)界面兩邊為介質(zhì)時(shí)：Free charge facial density Conducting current facial density 3 Electromagnetic wave1 Electromagnetic waveA changing magnetic field can produce an electric

12、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.變化的電場(chǎng)和變化的磁場(chǎng)相互激發(fā)，在空間傳播開(kāi)來(lái)，形成電磁波。已發(fā)出去的電磁波即使波源消失，波仍將繼續(xù)存在并向前傳播。電磁波是電磁振蕩在空間的傳播。Electromagnetic waves tra

13、vel depending on: (1) A changing magnetic field can produce an electric field. (2) A changing electric field can produce a magnetic field.正是在這兩個(gè)基本假說(shuō)的基礎(chǔ)上，麥克斯韋預(yù)言了電磁波的存在。2 The characteristics of electromagnetic wavesExample for electric dipole ：任意時(shí)刻t空間某點(diǎn)的E、 H：PThe characteristics of electromagnetic wav

14、es(1) Electric and magnetic field oscillations propagate in phase E和B都作正弦或余弦的周期性變化，且相位相同(2) E and H are perpendicular, and the both vectors are perpendicular to the direction of propagation of waves電磁波是橫波electromagnetic waves are transverse waves(3) The relationship of E and H：(4) Velocity ：(5) Poyn

15、ting 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單位時(shí)間內(nèi)垂直通過(guò)傳播方向上單位面積的能量Poynting vector3 Hertzs experimentundergoing acceleration radiate electromagnetic waves, as predicted by Maxwell. 振子諧振腔E

16、missionIncept AB感應(yīng)圈A、B是兩段共軸的黃銅桿，它們是振蕩偶極子的兩半，A、B中間留有一個(gè)火花間隙，間隙兩邊桿的端點(diǎn)上焊有一對(duì)磨光的黃銅球，振子的兩半聯(lián)接到感應(yīng)圈的兩極上，當(dāng)充電到一定程度間隙被火花擊穿時(shí)，兩段金屬桿連成一條導(dǎo)電通路，這時(shí)它相當(dāng)于一個(gè)振蕩偶極子，在其中激起高頻的振蕩。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 為了探測(cè)由振子發(fā)射出來(lái)的電磁波，赫茲采用了一個(gè)圓形銅環(huán)，在其中也留有端點(diǎn)球狀的火花間隙。間隙的距離可利用螺旋作微小的調(diào)節(jié)。這種接收裝置稱為諧振器。將諧振器放在距振子一定的距離之外，適當(dāng)?shù)剡x擇其方位，并使之與振子諧振。在發(fā)現(xiàn)振子的間隙有火花跳過(guò)的同時(shí)，諧振器的間隙也有火花跳過(guò)。赫茲利用振蕩偶極子進(jìn)行了許多實(shí)驗(yàn)，不僅證實(shí)了振蕩偶極子能發(fā)射電磁波，并且證實(shí)