麥克斯韋方程拓展內(nèi)涵

1、 麥克斯韋方程拓展內(nèi)涵 麥克斯韋方程拓展內(nèi)涵胡唐錦，深圳大學(xué) 胡 良，深圳市宏源清實(shí)業(yè)有限公司摘要：電動(dòng)勢(shì)可分為兩種：感生電動(dòng)勢(shì)及動(dòng)生電動(dòng)勢(shì)。對(duì)于感生電動(dòng)勢(shì)來(lái)說(shuō)，根據(jù)法拉第感應(yīng)定律，處于含時(shí)磁場(chǎng)的閉電路，由于磁場(chǎng)隨著時(shí)間而改變，會(huì)有感生電動(dòng)勢(shì)出現(xiàn)于閉電路。感生電動(dòng)勢(shì)等于電場(chǎng)沿著閉電路的路徑積分。處于閉電路的帶電粒子會(huì)感受到電場(chǎng)，因而產(chǎn)生電流。對(duì)于動(dòng)生電動(dòng)勢(shì)來(lái)說(shuō)，移動(dòng)于磁場(chǎng)的細(xì)直導(dǎo)線，其內(nèi)部將會(huì)出現(xiàn)動(dòng)生電動(dòng)勢(shì)。處于這導(dǎo)線的電荷，根據(jù)洛倫茲力定律，會(huì)感受到洛倫茲力，從而造成正負(fù)電荷分離至直棍的兩端。這動(dòng)作會(huì)形成一個(gè)電場(chǎng)與伴隨的電場(chǎng)力，抗拒洛倫茲力，直到兩種作用力達(dá)成平衡。關(guān)鍵詞:電場(chǎng)，磁場(chǎng)，感生電

2、動(dòng)勢(shì)，動(dòng)生電動(dòng)勢(shì)，電流，能量，動(dòng)量，量子，杠桿，質(zhì)量，萬(wàn)有引力，質(zhì)量場(chǎng)，作用力，反作用力，杠桿平衡，背景空間，光子，電子，質(zhì)子，中子作者：總工，高工，碩士，副董事長(zhǎng) ,2320051422物理學(xué)研究物質(zhì)，能量，空間及時(shí)間等的內(nèi)涵。1電場(chǎng)及磁場(chǎng)電動(dòng)勢(shì)可分為兩種：感生電動(dòng)勢(shì)及動(dòng)生電動(dòng)勢(shì)。對(duì)于感生電動(dòng)勢(shì)來(lái)說(shuō)，根據(jù)法拉第感應(yīng)定律，處于含時(shí)磁場(chǎng)的閉電路，由于磁場(chǎng)隨著時(shí)間而改變，會(huì)有感生電動(dòng)勢(shì)出現(xiàn)于閉電路。感生電動(dòng)勢(shì)等于電場(chǎng)沿著閉電路的路徑積分。處于閉電路的帶電粒子會(huì)感受到電場(chǎng)，因而產(chǎn)生電流。對(duì)于動(dòng)生電動(dòng)勢(shì)來(lái)說(shuō)，移動(dòng)于磁場(chǎng)的細(xì)直導(dǎo)線，其內(nèi)部將會(huì)出現(xiàn)動(dòng)生電動(dòng)勢(shì)。處于這導(dǎo)線的電荷，根據(jù)洛倫茲力定律，會(huì)感受到洛

3、倫茲力，從而造成正負(fù)電荷分離至直棍的兩端。這動(dòng)作會(huì)形成一個(gè)電場(chǎng)與伴隨的電場(chǎng)力，抗拒洛倫茲力，直到兩種作用力達(dá)成平衡。介質(zhì)在電場(chǎng)（或磁場(chǎng)）的作用下，將被極化（或磁化），從而出現(xiàn)附加電荷及電流。這些附加的電荷及電流，也要激發(fā)電磁場(chǎng)，導(dǎo)致原來(lái)的宏觀電磁場(chǎng)發(fā)生一些改變。對(duì)于極化（介質(zhì)對(duì)電場(chǎng)的響應(yīng)）來(lái)說(shuō)，如果是導(dǎo)電介質(zhì)（導(dǎo)體），存在大量的自由電子可在內(nèi)部自由移動(dòng)。如果是絕緣介質(zhì)（電介質(zhì)），電子被束縛在分子（或原子）范圍內(nèi)，不能夠在宏觀體積內(nèi)自由移動(dòng)。能量最低原理的內(nèi)涵是指勢(shì)能最低；從另一個(gè)角度來(lái)看，就是對(duì)周?chē)囊ψ畲?，因此，也可稱(chēng)為引力最大原理。物質(zhì)為了保持穩(wěn)定，就會(huì)自動(dòng)降低其能量，來(lái)保持平衡。由于，

4、能量最低的狀態(tài)比較穩(wěn)定，體現(xiàn)為能量最低原理。能量最低原理與最小作用量具有相似性。任何滿(mǎn)足邊界條件的連續(xù)函數(shù)x(t)就是路徑；對(duì)于每一條可能的路徑x(t)，都可根據(jù)某個(gè)規(guī)則計(jì)算出相應(yīng)的物理學(xué)量，可稱(chēng)為量子三維常數(shù)作用量（），即，。而最穩(wěn)定的路徑就是那條具有量子三維常數(shù)作用量（）的路徑，即，能量最低原理。，其中，量子三維常數(shù)作用量，量綱，*L(3)T(-3)；，內(nèi)稟空間，量綱，；，能量-動(dòng)量張量，量綱，L(3)T(-3)；，能量，量綱，*L(2)T(-2)；，質(zhì)量，量綱，；，路徑，量綱，L(1)T(0)L(1)T(-1)L(0)T(1)L(1)T(-1）；0，真空電容率，量綱，；Xe，極化率，量綱

5、，L(0)T(0）；E，電場(chǎng)強(qiáng)度，量綱，L(1)T(-2）L(3)T(-2）/L(2)T(0）L(1)T(-1);0， vacuum permittivity, dimension, ;Xe， polarizability, dimension, L(0)T(0);E， electric field strength, dimension, L(1)T(-2)L(3)T(-2)/L(2)T (0)L(3)T(-2）L(1)T(-1）L(1)T(0）L(1)T(-1）L(3)T(-2)L(1)T(-1)L(1)T(0)L(1)T(-1)L(0)T(-1）L(0)T(-1）L(0)T(-1）L(1

6、)T(-1）L(0)T(-1)L(0)T(-1)L(0)T(-1)L(1)T(-1)L(1)T(-1）L(1)T(-1）L(1)T(-1）L(1)T(-1）L(3)T(-2）L(1)T(-1）L(1)T(-1)L(1)T(-1)L(1)T(-1)L(1)T(-1)L(3)T(-2)L(1)T(-1)L(1)T(-1）；0，真空電容率，量綱，；E，電場(chǎng)強(qiáng)度，量綱，L(1)T(-2）L(1)T(-1）L(3)T(-2）L(1)T(-1）L(-2)T(1）L(3)T(-2）L(1)T(-1);0， vacuum permittivity, dimension, ;E， electric field

7、strength, dimension, L(1)T(-2)L(1)T(-1)L(3)T(-2)L(1)T(-1)L(-2)T(1)L(3)T(-2)L(1)T(-1）L(0)T(-1）L(3)T(-2）L(1)T(-1）L(1)T(0）L(1)T(-1）L(1)T(-1)L(0)T(-1)L(3)T(-2)L(1)T(-1)L(1)T(0)L(1)T(-1)L(1)T(-1)L(0)T(-1)L(1)T(-1）L(3)T(-2)L(1)T(-1)L(1)T(-1）L(1)T(-1)L(0)T(-1)L(1)T(-1)L(3)T(-2)L(1)T(-1)L(1)T(-1).第二種情況，如果介質(zhì)

8、是運(yùn)動(dòng)的，并且吸收了光子；則有，The second case, if the medium is moving and absorbs photons;Then there is, Ekn=Q* H=Q（jfC）+QpDt+QVPSp+nf；其中，Ekn,系統(tǒng)的總能量，量綱，*L(2)T(-2）；Q ，總電荷量（有效電荷總量），量綱，；H，輔助磁場(chǎng)（相當(dāng)于電通量），量綱，L(3)T(-2）L(1)T(-1）L(1)T(0）L(1)T(-1）；in,Ekn, the total energy of the system, dimension, *L(2)T(-2);Q ，Total charg

9、e (total effective charge), dimension, ;H， auxiliary magnetic field (equivalent to electric flux), dimension, L(3)T(-2)L(1)T(-1)L(1)T(0)L(1)T(-1)L(1)T(-1）L(1)T(-1）L(1)T(-1）L(0)T(0）；，光子的普朗克常數(shù)，量綱，*L(2)T(-2）L(0)T(-1）L(1)T(-1)L(1)T(-1)L(1)T(-1)L(0)T(0);， Plancks constant of photon, dimension, *L(2)T(-2)

10、L(0)T(-1)-L(3)T(-1）L(3)T(-2）；(Vpfp)，表達(dá)電荷，量綱，；(C2p)，表達(dá)電荷相對(duì)應(yīng)的電場(chǎng)（通量），量綱，；(Vpfp)f，表達(dá)在導(dǎo)線中的相對(duì)磁荷，量綱，-L(3)T(-2）L(3)T(-1）-L(3)T(-1)L(3)T(-2);(Vpfp)， express charge, dimension, ;(C2p)， express the electric field (flux) corresponding to the charge, dimension, ;(Vpfp)f，the relative magnetic charge expressed in

11、the wire, dimension, -L(3)T(-2)L(3)T(-1);(Vpfp)fp，表達(dá)磁荷，量綱，；Cp(2，表達(dá)磁荷相對(duì)應(yīng)的磁場(chǎng)（通量），量綱，。Ve，電子的空間荷，量綱，；Ve,電子內(nèi)稟一維空間速度（信號(hào)速度），量綱，L(1)T(-1）L(0)T(-1）L(1)T(0）L(1)T(0）L(1)T(-1）。(Vpfp)fp，express magnetic charge, dimension, ;Cp(2， express the magnetic field (flux) corresponding to the magnetic charge, dimension, .

12、Ve，the space charge of the electron, dimension, ;Ve， electron intrinsic one-dimensional space velocity (signal velocity), dimension, L(1)T(-1)L(0)T(-1)L(1)T(0)L(1)T(0)L(1)T(-1)L(3)T(-1）L(1)T(-1）L(3)T(-1）/L(2)T(0）L(2)T(0）L(3)T(-1)L(1)T(-1)L(3)T(-1)/L(2)T (0) L(2)T(0)L(3)T(-2）L(1)T(-2）L(3)T(-2）/L(2)T(

13、0）L(2)T(0）L(3)T(-2)L(1)T(-2)L(3)T(-2)/L(2)T (0) L(2)T(0)L(3)T(-2）L(1)T(-2）L(3)T(-2）/L(2)T(0）L(2)T(0）；，負(fù)電荷單元（收斂屬性），量綱，；，真空電容率，量綱，；，電荷數(shù)量（自由電荷及束縛電荷），量綱，L(0)T(0）；，普朗克頻率，量綱，。in, electric flux (divergent property), L(3)T(-2)L(1)T(-2)L(3)T(-2)/L(2)T (0) L(2)T(0);, negative charge unit (convergence property

14、), dimension, ;, vacuum permittivity, dimension, ;, the number of charges (free charge and bound charge), dimension, L(0)T(0);, Planck frequency, dimension, .2電場(chǎng)及磁場(chǎng)的內(nèi)涵對(duì)于電子來(lái)說(shuō)，其表達(dá)式為：For electrons, the expression is: ；其中，表達(dá)一個(gè)負(fù)電荷（收斂屬性），量子化，量綱，；，表達(dá)電通量（發(fā)散屬性），量綱，L(3)T(-2）。in, express a negative charge (con

15、vergence property), quantization, dimension, ;, express electric flux (divergent property), dimension, L(3)T(-2).對(duì)于自旋的電子來(lái)說(shuō)，其表達(dá)式為，F(xiàn)or spin electrons, its expression is, ；其中，表達(dá)電子的磁荷（收斂屬性），量子化，量綱，；，表達(dá)磁通量（發(fā)散屬性），量綱，L(3)T(-1)。in, expressing the magnetic charge of the electron (convergent property), quanti

16、zation, dimension, ;, expressing the magnetic flux (divergent property), dimension, L(3)T(-1).對(duì)于質(zhì)子來(lái)說(shuō)，其表達(dá)式為：For protons, the expression is:；其中，表達(dá)正電荷（收斂屬性），量子化，量綱，；，表達(dá)電通量（發(fā)散屬性），量綱，L(3)T(-2)。in, express positive charge (convergent property), quantization, dimension, ;, expressing electric flux (diverge

17、nt property), dimension, L(3)T(-2).對(duì)于自旋的質(zhì)子來(lái)說(shuō)，其表達(dá)式為，F(xiàn)or spin protons, the expression is, ；其中，表達(dá)質(zhì)子的磁荷（收斂屬性），量綱，；，表達(dá)磁通量（發(fā)散屬性），量綱，L(3)T(-1)。in, express the magnetic charge of proton (convergent property), dimension, ;, expressing the magnetic flux (divergent property), dimension, L(3)T(-1)L(3)T(-1)*L(1)

18、T(-2)L(1)T(-1)L(1)T(0)；，普朗克頻率,量綱，；，普朗克空間,量綱，.in, express magnetic force, dimension, L(3)T(-1)*L(1)T(-2)L(1)T(-1)L(1)T(0);, Planck frequency, dimension, ;， Planck space, dimension, .3麥克斯韋方程的內(nèi)涵麥克斯韋方程表達(dá)了電場(chǎng)，磁場(chǎng)，電荷密度及電流密度等之間聯(lián)系的偏微分方程；其由四個(gè)方程組成：第一，表達(dá)電荷如何產(chǎn)生電場(chǎng)的高斯定律；第二，高斯磁定律；第三，表達(dá)時(shí)變磁場(chǎng)如何產(chǎn)生電場(chǎng)的法拉第感應(yīng)定律；第四，表達(dá)電流及時(shí)變電場(chǎng)

19、如何產(chǎn)生磁場(chǎng)的麥克斯韋-安培定律。3 The meaning of Maxwells equationsMaxwells equations express the partial differential equations of the connection between electric field, magnetic field, charge density, and current density; it consists of four equations: first, Gausss law, which expresses how electric fields are g

20、enerated by electric charges; second, Gausss law of magnetism; third , Faradays law of induction, which expresses how a time-varying magnetic field produces an electric field; fourth, Maxwell-Amperes law, which expresses how a current and a time-varying electric field produce a magnetic field.麥克斯韋方程

21、組乃是由四個(gè)方程共同組成的：第一，高斯定律，該定律體現(xiàn)了電場(chǎng)與空間中電荷分布的關(guān)系；電場(chǎng)線始于正電荷，終止于負(fù)電荷?？赏ㄟ^(guò)計(jì)算穿過(guò)某給定閉曲面的電場(chǎng)線數(shù)量（電通量），可知道包含在該閉曲面內(nèi)的總電荷。更詳細(xì)地說(shuō)，該定律表達(dá)了穿過(guò)任意閉曲面的電通量與該閉曲面內(nèi)的電荷之間的聯(lián)系。Maxwells equations are composed of four equations:First, Gausss law,This law expresses the relationship between the electric field and the distribution of electric

22、 charges in space; electric field lines start with positive charges and end with negative charges.The total charge contained within a given closed surface can be known by counting the number of electric field lines (electric flux) passing through that closed surface. In more detail, the law expresse

23、s the connection between the electric flux through any closed surface and the charge within that closed surface.高斯定律可表達(dá)為：Gausss law can be expressed as: ；其中，電場(chǎng)強(qiáng)度，量綱，L(1)T(-2)L(2)T(0)；，電荷（收斂屬性），量綱，；，真空介電常數(shù)，量綱，；，閉合曲面所包圍的體積，量綱，L(3)T(0)L(1)T(-2)L(2)T(0);, charge (convergence property), dimension, ;, vac

24、uum permittivity, dimension, ;, the volume enclosed by the closed surface, dimension, L(3)T(0)L(0)T(-1)L(3)T(-1)/L(3)T(0)L(0)T(-1)L(3)T(-1)/L(3)T(0) L(3)T(-2)L(3)T(-2).這意味著，穿過(guò)一個(gè)任意的封閉曲面的電場(chǎng)通量正比于其內(nèi)部的電荷量；電場(chǎng)通量（場(chǎng)屬性）從電荷（粒子屬性）出發(fā)后，不可能憑空消失，也不可能憑空產(chǎn)生。也就是說(shuō)，電荷（粒子屬性）與相應(yīng)的電場(chǎng)通量（場(chǎng)屬性）構(gòu)成了一個(gè)整體物質(zhì)（例如，電子）。顯然，該方程的左邊，體現(xiàn)為場(chǎng)屬性；該

25、方程的右邊，體現(xiàn)了荷屬性。此外，假設(shè)，不存在電荷的源頭（無(wú)源場(chǎng)），則進(jìn)入封閉曲面內(nèi)的電通量（）等于離開(kāi)封閉曲面內(nèi)的電通量（）。值得注意是，具有正電屬性的基本粒子（含有正電荷）是基本粒子；具有負(fù)電屬性的基本粒子（含有負(fù)電荷）也是基本粒子，可獨(dú)立存在。值得一提的是，根據(jù)量子三維常數(shù)理論，對(duì)于電子來(lái)說(shuō)，其表達(dá)式為：It is worth mentioning that, according to the quantum three-dimensional constant theory,For electrons, its expression is: ；其中，表達(dá)一個(gè)負(fù)電荷，量子化的，量綱，；，表

26、達(dá)電通量（發(fā)散屬性），量綱，L(3)T(-2)。in, express a negative charge, quantized, dimension, ;, expressing electric flux (divergent property), dimension, L(3)T(-2).假設(shè)有N個(gè)電子包含在閉曲面內(nèi)，則有，第一種情況，總電荷是，量綱，；相對(duì)應(yīng)的穿過(guò)某給定閉曲面的電場(chǎng)線數(shù)量（電通量）是，NC2*p，量綱，L(3)T(-2)。Assuming that there are N electrons contained in the closed surface, there

27、are,In the first case,The total charge is, , dimension, ;The corresponding number of electric field lines (electric flux) passing through a given closed surface is,NC2*p, dimension, L(3)T(-2)L(3)T(-2)L(3)T(-2).換句話(huà)說(shuō)，磁荷（），收斂屬性,量綱，。電通量（），發(fā)散屬性,量綱，L(3)T(-2)。In other words, magnetic charge (), convergence

28、 property, dimension, .Electric flux (), divergence property, dimension, L(3)T(-2)L(1)T(-1)L(3)T(-1)/L(2)T(0)L(2)T(0)L(3)T(-1)L(1)T(-1)L(3)T(-1)/L(2)T (0) L(2)T(0)L(3)T(-1)L(1)T(-1)L(1)T(-1)L(1)T(-1)L(1)T(-1)L(1)T(-1)L(1)T(-1)L(1)T(-2)L(3)T(-2)/L(2)T(0)；，普朗克長(zhǎng)度，量綱，；，閉合曲線，量綱，L(1)T(0)L(3)T(-1)L(2)T(0)L

29、(1)T(-1)L(3)T(-1)/L(2)T(0)L(0)T(1)L(1)T(-2)L(3)T(-2)/L(2)T(0) ;, Planck length, dimension, ;, closed curve, dimension, L(1)T(0)L(3)T(-1)L(2)T(0)L(1)T(-1)L(3)T(-1)/L(2)T(0) L(0)T(1)L(3)T(-2)L(3)T(-2)L(1)T(-1)L(3)T(-1)/L(2)T(0)；，普朗克長(zhǎng)度，量綱，；，閉合曲線，量綱，L(1)T(0)L(1)T(-1)L(2)T(0)L(1)T(-1)；，真空介電常數(shù)，量綱，；，普朗克時(shí)間，

30、量綱，。in, the magnetic field strength,Dimensions, L(1)T(-1)L(3)T(-1)/L(2)T(0) ;, Planck length, dimension, ;, closed curve, dimension, L(1)T(0)L(1)T(-1)L(2)T(0)L(1)T(-1);, vacuum permittivity, dimension, ;, Planck time, dimension, .該公式右邊，第一項(xiàng)，揭示了，電流（I ）可以產(chǎn)生磁場(chǎng)（例如，通電的線圈相當(dāng)于一個(gè)磁鐵）。第二項(xiàng)，揭示了，感應(yīng)磁場(chǎng)在空間環(huán)路上的積累正比于電場(chǎng)

31、通量的變化速度?？傊?，該方程體現(xiàn)了磁通量（）具有守恒性，量綱，L(3)T(-1)L(3)T(-1)L(3)T(-1)。電荷（，收斂屬性）,量綱，；磁通量（，發(fā)散屬性）,量綱，L(3)T(-1)L(3)T(-1)L(3)T(-1).charge (), convergence property , dimension, ;Magnetic flux (), divergence property , dimension, L(3)T(-1)L(1)T(-1)L(3)T(-1)/L(2)T(0)L(2)T(0)L(3)T(-1)L(1)T(-1)L(3)T(-1)/L(2)T (0) L(2)T(

32、0)L(3)T(-1)L(0)T(-1)L(3)T(-1)/L(3)T(0)。，真空介電常數(shù)，量綱，；，普朗克長(zhǎng)度，量綱，；t,時(shí)間，量綱，L(0)T(1)；0,真空磁導(dǎo)率，量綱，；，真空介電常數(shù)，量綱，；J,傳導(dǎo)電流，量綱，L(1)T(-1)L(1)T(-2)L(3)T(-2)/L(2)T(0)L(1)T(-1)L(3)T(-1)/L(2)T(0)L(1)T(-1)L(1)T(-1)L(1)T(0)L(1)T(-1)；0,真空磁導(dǎo)率，量綱，；0，真空介電常數(shù)，量綱，；S，曲面面積，量綱，L(2)T(0)L(1)T(-2)L(3)T(-2)/L(2)T(0)L(1)T(-1)L(1)T(-1)

33、L(0)T(-1)-L(3)T(-1)/L(3)T(0)L(1)T(-1)L(0)T(-1)-L(3)T(-1)/L(3)T(0) L(1)T(-1)L(2)T(0)L(2)T(0)；Qf，在閉合曲面（S）里面的自由電荷，量綱，。in,D, electric displacement, dimension, L(1)T(-1)L(2)T(0)L(2)T(0);Qf, free charge inside the closed surface ( ), dimension, .二，高斯磁定律微分表達(dá)式，Second, Gausss law of magnetismdifferential exp

34、ression, B=0；其中，B，磁場(chǎng)強(qiáng)度，量綱，L(1)T(-1)L(1)T(-1)L(2)T(0)L(2)T(0)L(1)T(-1)L(2)T(0)L(2)T(0)L(1)T(-1)L(1)T(-2)L(1)T(-1)；p，普朗克長(zhǎng)度，量綱，；t，時(shí)間，量綱，L(0)T(1L(1)T(-2)L(1)T(-1);p, Planck length, dimension, ;t, time, dimension, L(0)T(1L(1)T(-2)L(1)T(0)L(1)T(0)；p，普朗克長(zhǎng)度，量綱，；B,穿過(guò)閉合路徑所包圍的曲面（S）的磁通量，量綱，L(3)T(-1)L(0)T(1)L(1)

35、T(-2)L(1)T(0)L(1)T(0);p, Planck length, dimension, ;B, the magnetic flux passing through the surface (S ) enclosed by the closed path, dimension, L(3)T(-1)L(0)T(1)L(3)T(-2)-L(3)T(-1)/L(2)T(0)L(1)T(-1)；p,普朗克長(zhǎng)度，量綱，；t，時(shí)間，量綱，L(0)T(1）L(3)T(-2)-L(3)T(-1)/L(2)T(0), or, L(1)T(-1) ;0, vacuum permeability, di

36、mension, ;D, electric displacement, dimension, L(1)T(-1);p, Planck length, dimension, ;t, time, dimension, L(0)T(1)L(3)T(-2)L(1)T(0)L(1)T(0)L(1)T(-1)L(3)T(-1)L(0)T(1）L(3)T(-2)L(1)T(0)L(1)T(0)L(1)T(-1)L(3)T(-1)L(0)T(1)L(1)T(-2)L(0)T(-1)L(3)T(-1)/L(3)T(0)；0=tp，真空電容率，量綱， ;tp,普朗克時(shí)間，量綱， 。in,E, electric f

37、ield strength, dimension, L(1)T(-2)L(0)T(-1)L(3)T(-1)/L(3)T(0) ;0=tp, vacuum permittivity, dimension, ；tp, Planck time, dimension, 。積分表達(dá)式，Integral expression, SEda = Q0 ；其中，E，電場(chǎng)強(qiáng)度，量綱，L(1)T(-2)L(2)T(0)L(2)T(0)；Q，在閉合曲面（S）里面的總電荷，量綱，；0=tp，真空電容率，量綱， ；tp，普朗克時(shí)間，量綱， 。in,E, electric field strength, dimension

38、, L(1)T(-2)L(2)T(0)L(2)T(0);Q, the total charge in the closed surface (S), dimension, ;0=tp, vacuum permittivity, dimension, ;tp, Planck time, dimension, .二，高斯磁定律微分表達(dá)式，Second, Gausss law of magnetismDifferential Expressions, B=0；其中，B磁場(chǎng)強(qiáng)度，量綱，L(1)T(-1)L(1)T(-1)L(2)T(0)L(2)T(0)L(1)T(-1)L(2)T(0)L(2)T(0)

39、L(1)T(-1)L(1)T(-2)L(1)T(-1)；p，普朗克長(zhǎng)度，量綱，；t，時(shí)間，量綱，L(0)T(1L(1)T(-2)L(1)T(-1);p, Planck length, dimension, ;t, time, dimension, L(0)T(1L(1)T(-2)L(1)T(0)L(1)T(0)；p，普朗克長(zhǎng)度，量綱，；B,穿過(guò)閉合路徑所包圍的曲面（S）的磁通量，量綱，L(3)T(-1)L(0)T(1)L(1)T(-2)L(1)T(0)L(1)T(0);p, Planck length, dimension, ;B, the magnetic flux passing thro

40、ugh the surface ( S) enclosed by the closed path, dimension, L(3)T(-1)L(0)T(1)L(1)T(-1)L(3)T(-1)/L(3)T(0)L(0)T(-1)；0，真空磁導(dǎo)率，量綱，;0，真空電容率（真空介電常量），量綱，;，電場(chǎng)強(qiáng)度，量綱，L(1)T(-2)L(0)T(1)L(1)T(-1)L(3)T(-1)/L(3)T(0)L(0)T(-1) ;0, vacuum permeability, dimension, ;0, vacuum permittivity (vacuum dielectric constant),

41、dimension, ;, electric field strength, dimension, L(1)T(-2)L(0)T(1)L(1)T(-1)L(1)T(0)L(1)T(0)L(3)T(-2)；Q,在閉合曲面內(nèi)的總電荷，量綱，;0,真空磁導(dǎo)率，量綱，;，穿過(guò)閉合路徑所包圍的曲面（S）的總電流，量綱，L(1)T(-1)L(0)T(1)L(1)T(-1)L(1)T(0)L(1)T(0)L(3)T(-2);Q, the total charge in the closed surface, dimension, ;0, vacuum permeability, dimension, ;,

42、the total current passing through the surface ( ) enclosed by the closed path, dimension, L(1)T(-1)L(0)T(1).值得一提是，麥克斯韋方程組的積分形式是表達(dá)電磁場(chǎng)在某一體積（或某一面積內(nèi)）的數(shù)學(xué)模型；而麥克斯韋方程組的微分形式是對(duì)場(chǎng)中每一點(diǎn)而言的。According to the quantum three-dimensional constant theory, Maxwells equations have a reduced expression: SEdS=Q0;SBdS=0;L(Ep

43、)dr=SBtdS;L(B/p)dr=Ienc+00SEtdS=0E+00SEtdS;Pe=QeL(B/p)dr=QeIenc+00SEtdS=Qe0E+00SEtdS；此外，U=RL(B/p)dr=RIenc+00SEtdS=R0E+00SEtdS。從廣義的角度來(lái)看，Pe=QeL(B/p)dr =QeIenc+00SEtdS+(nf)/C=Qe0E+00SEtdS+(nf)/C;in,Pe，動(dòng)量，dimension, *L(1)T(-1);Pe，momentum, dimension, *L(1)T(-1);Qe,有效電荷，dimension, ；Qe, effective charge,

44、dimension, ;E,magnetic field strength, dimension, L(1)T(-1);Q, the total charge in the closed surface, dimension, ;B,magnetic field strength, dimension, L(1)T(-1);0, vacuum permittivity (vacuum dielectric constant), dimension, ;S,the operation surface of surface integral, dimension, L(2)T(0)L(1)T(0)

45、L(1)T(0)L(1)T(0)L(1)T(-1)L(3)T(-2);0, vacuum permeability, dimension, ;t, time, dimension, L(0)T(1).U，電壓，量綱，*L(1)T(-2)L(3)T(-2);U，voltage, dimension, *L(1)T(-2)L(3)T(-2)；，普朗克常數(shù)，量綱，*L(2)T(-2)L(0)T(-1)L(1)T(-1)；n，光子的數(shù)量，量綱，L(0)T(0)。， Plancks constant, dimension, *L(2)T(-2)L(0)T(-1)L(1)T(-1)L(1)T(-1)；，電

46、容率（介電常量），量綱，;，電場(chǎng)強(qiáng)度，量綱，L(1)T(-2)L(1)T(-1);, permittivity (dielectric constant), dimension, ;, electric field strength, dimension, L(1)T(-2)L(1)T(-1)；，磁導(dǎo)率，量綱，;H，輔助磁場(chǎng)（相當(dāng)于電通量），量綱，L(3)T(-2)L(1)T(-1);, permeability, dimension, ;H, auxiliary magnetic field (equivalent to electric flux), dimension, L(3)T(-2

47、)L(3)T(-2)*L(1)T(0)L(1)T(-1)L(2)T(0)L(3)T(-2)*L(1)T(0)L(1)T(-1)L(2)T(0)L(3)T(-1)*L(1)T(-2)L(1)T(0)L(5)T(-3)L(3)T(-2)*L(1)T(0)L(1)T(-1)L(3)T(-1)*L(1)T(-2)*L(1)T(0)L(5)T(-3)L(3)T(-1)*L(1)T(-2)L(1)T(0)L(5)T(-3)L(3)T(-2)*L(1)T(0)L(1)T(-1)L(3)T(-1)*L(1)T(-2)*L(1)T(0) L(5)T(-3).第二大類(lèi)基本粒子（電子及質(zhì)子等）因內(nèi)稟自旋而產(chǎn)生磁矩;

48、而，基本粒子（電子及質(zhì)子等）的內(nèi)稟磁矩的大小都是物理學(xué)常數(shù)。磁矩的方向取決于粒子的自旋方向，例如，如果電子磁矩的測(cè)量值是負(fù)值；這意味著電子的磁矩與內(nèi)稟自旋呈現(xiàn)相反的方向。The second categoryElementary particles (electrons and protons, etc.) generate magnetic moments due to their intrinsic spin; however, the magnitudes of the intrinsic magnetic moments of elementary particles (electro

49、ns, protons, etc.) are all physical constants.The direction of the magnetic moment depends on the spin direction of the particle, for example, if the measured value of the electrons magnetic moment is negative; this means that the electrons magnetic moment is in the opposite direction to its intrins

50、ic spin.電子可表達(dá)為：Electron can be expressed as: C2p =Cp(2)=(Cp)p=Cp=Ve Ve(3) =（Vefe )Ve(2)e = meVe(2)*e .顯然，電子的內(nèi)稟磁矩可表達(dá)為：Obviously, the intrinsic magnetic moment of the electron can be expressed as: =geBSi ;其中，=(Vpfp)fpp，電子的內(nèi)稟磁矩，量綱，*L(1)T(0); ge,電子的朗德因子，量綱，; Si=,電子內(nèi)稟自旋，量綱，; ,普朗克常數(shù)，量綱，*L(2)T(-2); B=(eme)

51、,玻爾磁子，量綱，; e=(Vpfp)，電子的基本電荷，量綱，; me，電子的質(zhì)量，量綱，。in,=(Vpfp)fpp, the intrinsic magnetic moment of the electron,Dimension, *L(1)T(0);ge, the electrons Lande factor, dimension, ;Si=, electron intrinsic spin, dimension, ;, Plancks constant, dimension, *L(2)T(-2);B=(eme), Bohr magneton, dimension, ;e=(Vpfp)

52、, the basic charge of the electron, dimension, ;me, the mass of the electron, dimension, .電阻及電流的內(nèi)涵電阻（R）是表達(dá)導(dǎo)體導(dǎo)電性能的物理量。電阻（R）可由導(dǎo)體兩端的電壓（U）與通過(guò)該導(dǎo)體的電流（I）的比值來(lái)定義，可表達(dá)為，The meaning of resistance and currentResistance (R) is a physical quantity that expresses the electrical conductivity of a conductor. Resistan

53、ce (R) can be defined by the ratio of the voltage across a conductor (U) to the current (I) through that conductor, and can be expressed as, R=U/I ;其中，R，電阻，量綱，;U，電壓，量綱，*L(1)T(-2)L(1)T(-1)。in,R, resistance, dimension, ;U, voltage, dimension, *L(1)T(-2)L(1)T(-1).電阻(R)大小可用來(lái)衡量導(dǎo)體對(duì)電流阻礙作用的強(qiáng)弱（導(dǎo)電性能的好壞）。而，電阻的

54、倒數(shù)(1/R)稱(chēng)為電導(dǎo)()，是表達(dá)導(dǎo)體導(dǎo)電性能的物理量。電阻是揭示導(dǎo)體導(dǎo)電性能的參數(shù);對(duì)于由某種材料制成的柱形均勻?qū)w，其電阻（R）與長(zhǎng)度（L）成正比，而與橫截面積（S）成反比;可表達(dá)為：The resistance (R) can be used to measure the strength of the resistance of the conductor to the current (the quality of the electrical conductivity).However, the reciprocal of resistance (1/R) is called co

55、nductance (), which is a physical quantity that expresses the conductivity of a conductor.Resistance (R) is a parameter that reveals the conductive properties of a conductor; for a cylindrical uniform conductor made of a certain material, its resistance (R) is proportional to its length (L) and inve

56、rsely proportional to its cross-sectional area (S);It can be expressed as: R= LS ；其中，R,電阻，量綱，;，電阻率，量綱，;L，導(dǎo)電材料的長(zhǎng)度，量綱，L(1)T(0)L(2)T(0);，電導(dǎo)，量綱，。in,R, resistance, dimension, ;, resistivity, dimension, ;L, the length of the conductive material, dimension, L(1)T(0)L(2)T(0);, conductance, dimension, .值得一提的

57、是，電阻率（）是由導(dǎo)體的材料及周?chē)鷾囟鹊人鶝Q定，可表達(dá)為：It is worth mentioning that the resistivity () is determined by the material of the conductor and the surrounding temperature, etc. It can be expressed as: =0（1+T）；其中，電阻率，量綱，;0，溫度是0時(shí)的電阻率，量綱，;，為電阻的溫度系數(shù)，量綱，;T，溫度，量綱，L(3)T(-2),或，*L(2)T(-2)L(3)T(0)。, resistivity, dimension, ;

58、0, the temperature is the resistivity at 0, dimension, ;, is the temperature coefficient of resistance, dimension, ;T, temperature, dimension, L(3)T(-2),Or, *L(2)T(-2)L(3)T(0).值得注意的是，半導(dǎo)體與絕緣體的電阻率跟金屬不同，它們與溫度之間不是按線性規(guī)律變化的。當(dāng)溫度升高時(shí)，它們的電阻率會(huì)急劇地減小（體現(xiàn)出非線性變化的性質(zhì)）。It is worth noting that the resistivity of semico

59、nductors and insulators, unlike metals, does not vary linearly with temperature. As the temperature increases, their resistivity decreases sharply (indicating a nonlinear change).電流的本質(zhì)，導(dǎo)體中的自由電荷在電場(chǎng)力的作用下做有規(guī)則的定向運(yùn)動(dòng)可形成電流；而，正電荷定向流動(dòng)的方向就是電流方向。the nature of current,Under the action of electric field force, t

60、he free charges in the conductor can make regular directional movements to form current; however, the direction of directional flow of positive charges is the current direction.電通量（E）是電場(chǎng)的通量，與穿過(guò)一個(gè)曲面的電場(chǎng)線的數(shù)目成正比，是表征電場(chǎng)分布情況的物理量。 電通量（E）與金屬導(dǎo)體中電流（I）具有內(nèi)在的聯(lián)系，其微觀表達(dá)式為：Electric flux (E) is the flux of the electri