12中英文雙語(yǔ)外文文獻(xiàn)翻譯成品對(duì)高斯定理在靜電場(chǎng)中的應(yīng)用及理解

1、<p>　　外文標(biāo)題：Understanding and application of Gauss Theorem in electrostatic field</p><p>　　外文作者：Wang Xiaolan ，Wang Feng, Lanzhigao,Chen Ruian </p><p>　　文獻(xiàn)出處：International Conference on Intel

2、ligence Science and Information Engineering，2011，386-388</p><p>　　英文1078單詞，4865字符，中文1502漢字。</p><p>　　此文檔是外文翻譯成品，無(wú)需調(diào)整復(fù)雜的格式哦！下載之后直接可用，方便快捷！只需二十多元。</p><p>　　原文：Understanding and applic

3、ation of Gauss Theorem in electrostatic field</p><p>　　Wang Xiaolan ，Wang Feng, Lanzhigao,Chen Ruian </p><p>　　Abstract—Correct understanding and mastering electrostatic field of Gauss theorem i

4、s the key part of learning electromagnetism; the field strength E in Gaussian theorem is the total field strength excited by all charges in the space on the closed surface, E=Ein+Eout. The sum of E refers to the algebra

5、sum of charges in the closed surface; When charge distribution has certain symmetry(Spherical symmetry, axial symmetry, plane symmetry ), we can use Gauss theorem to calculate the distrubution of t</p><p>　　

6、Keywords- Gauss theorem; Gaussian surface; Electric field strength; Symmetry</p><p>　　INTRODUCTION</p><p>　　Gauss theorem is both important and difficult part in electrostatic field, and also in

7、 entire Electromagnetic, so understanding and mastering the Gauss theorem is the key of</p><p>　　by the mathematical expression of Gauss theroem learning Electromagnetic.</p><p>　　CONTENT OF GAU

8、SS THEOREM</p><p><b>　　Content:</b></p><p>　　Electrostatic field through any closed surface in the flux of electric field strength equal to the surface surrounded by the algebraic su

9、m of all the charges divided by the dielectric constant of vacuum.</p><p><b>　　Formula:</b></p><p><b>　　Note:</b></p><p>　　1In the Gauss theorem, the closed

10、surface we choose is often called Gauss Surface.</p><p>　　2Applicable scope of Gauss theorem: Electrostatic field; changing electric field.</p><p>　　3Gauss theorem show that electrostatic is act

11、ive field one of the basic properties of eletrostatic field.</p><p>　　UNDERSTANDING OF GAUSS THEOREM</p><p>　　1.The total flux 8e through the closed surface S in electric field is only related w

12、ith charges in the closed surface, and has nothing to do with the charge outside the closed surface, also the distribution of charges in the closed surface.</p><p>　　2. Refers to algebraic sum charge i

13、n the closed surface, if qi is positive charge, the Flux is positive, and negative versa.</p><p>　　3.The field strength E in Gaussian theorem is the total field strength excited by all charges in the space

14、 on the closed surface.</p><p><b>　　Thinking:</b></p><p><b>　　If</b></p><p>　　by the mathematical expression of Gauss theroem,</p><p><b>　

15、　Then:</b></p><p>　　E must equals to 0.</p><p><b>　　Discuss:</b></p><p>　　The power line began with closed surface within positive Charge equals to the power line

16、end with closed surface within negative charge,then the piercing the closed surface of power line and into the closed surface are equal, that is, the total flux is zero through all the closed surface.</p><p>

17、;　　But that doesn’t means the electric field strength E on the closed surface is 0,</p><p><b>　　FOR:</b></p><p>　　1. The field strength on Gaussian surface is the vector sum of field

18、 strength generated by both inside and outside the Gaussian surface, therefore within the Gaussian surface</p><p>　　E=0 can not be completely sure.</p><p>　　2.As in the type E and dS is the scal

19、ar product between</p><p>　　vector and therefore the direction of the two problems exist,if</p><p>　　and dS the side perpendicular to it, there are</p><p><b>　　If</b><

20、;/p><p>　　So it can not be </p><p>　　USE GAUSS THEOREM APPLIED FOR ELETRIC FIELD STRENGTH</p><p>　　When the charge distribution has some symmetry, the Gauss theorem can be applied to f

21、ind the electric field distribution. The following discussion of two cases:</p><p>　　1.Charge distribution is spherical symmetry: that is equidistant to the center of the sphere equal to the surface charge d

22、ensity</p><p>　　2. Electric field distribution: E along the radial direction. E is equal at any concentric spherical surface.</p><p><b>　　Eg1.</b></p><p>　　Find the fiel

23、d strength in and out the uniformly charged sephere with radius R and charge +q.</p><p>　　A:For the charge distribution is spherical symmetry, the field strength it Emerges has spherical symmetry, that is, a

24、s the center of the sphere r points on the sphere equal electric field strength and direction along the radius vector direction, outward.</p><p>　　For the concentric and the Gaussian surface of radius r Obta

25、ined by the Gauss theorem:</p><p>　　When r>R, Gaussian surface surrounding the charge q:</p><p>　　When r< R, no charge within the Gaussian surface:</p><p>　　Electric field dis

26、tribution of a uniformly charged sphere:</p><p>　　The charge distribution has axis symmetry: the charge density equal on the surface equidistant to the axis.</p><p>　　Electric field distribution

27、:</p><p>　　E along the vertical axis in the radial direction;</p><p>　　Any concentric cylindrical surface is equal to the points of E.</p><p><b>　　Eg2</b></p><

28、;p>　　Find infinite uniform electric field strength inside and outside the cylinder. Let cylindrical radius R, along with a charge per unit length of axis is + l</p><p>　　A: The field distribution should a

29、lso be column symmetrcial, the radicial direction, for a charged cylinder coaxial with the cylindrical Gaussian surface height l, radius</p><p>　　r. Obtianed by Gaussian theorem:</p><p>　　CONCLU

30、SION</p><p>　　Summary of the use of Gauss theorem seeking the conditions skills and procedures of field strength.</p><p>　　Condition: field strength has special symmetry: sephrical symmetry, axi

31、al Symmetry,plane symmetry.</p><p>　　If can integrated, we can use Gauss theorem no matter whether there is symmetry of the charge or the Electric field.)</p><p>　　Skills: choose the suitable

32、Gaussian surface, the</p><p>　　integral sign of the electric field strength E can form scalar</p><p>　　raised from the integral sign in.</p><p>　　Procedures:</p><p>　　(

33、1).Analysis the symmetry of field strength</p><p>　　(2).Choose suitable Gaussian surface</p><p>　　(3).Calculate the flux through the Gaussian surface </p><p>　　(4).Applied the Gauss

34、 theorem for electric field strength.</p><p>　　REFERENCES</p><p>　　[1] Ma Wenwei, physical [M].Beijing: Higher education press.2008.</p><p>　　[2] Chen Yincong, new century physics,

35、[M].Shanghai, East China normal University press, 2006.</p><p>　　[3] Shi Chuanzhu, Discussion of Gauss theorem, [J] .Qujing normal university. Press, 2002, 3.</p><p>　　[4] "Findings and Rec

36、ommendations to Enhance Reliability From the Summer of 1999", Final Report, Power Outage Study Team, U. S. Department of Energy, March 2000, p S-2</p><p>　　[5] IntelliTEAM Overview of Operations, "

37、 EnergyLine Systems, Alameda, CA. www.energyline.com</p><p><b>　　譯文：</b></p><p>　　對(duì)高斯定理在靜電場(chǎng)中的應(yīng)用及理解</p><p>　　Wang Xiaolan ，Wang Feng, Lanzhigao,Chen Ruian </p><

38、;p>　　摘要 - 在學(xué)習(xí)電磁學(xué)時(shí)，其重要的一環(huán)是要正確認(rèn)識(shí)和掌握高斯定理的靜電場(chǎng); 高斯定理中電場(chǎng)強(qiáng)度是指封閉曲面空間中所有電荷的總場(chǎng)強(qiáng)度，E = E內(nèi) + E外。 E的總值是指封閉曲面中電荷的總和; 當(dāng)電荷分布具有一定的對(duì)稱(chēng)性（球?qū)ΨQ(chēng)性、軸對(duì)稱(chēng)性、平面對(duì)稱(chēng)性）時(shí)，我們就可以用高斯定理來(lái)計(jì)算電場(chǎng)的分布。</p><p>　　關(guān)鍵詞 - 高斯定理; 高斯曲面; 電場(chǎng)強(qiáng)度; 對(duì)稱(chēng)性</p>&l

39、t;p><b>　　引言</b></p><p>　　高斯定理不僅是靜電場(chǎng)的重要組成部分，而且也是整個(gè)電磁場(chǎng)的重要組成部分，因此通過(guò)高斯定理來(lái)學(xué)習(xí)電磁學(xué)的數(shù)學(xué)表達(dá)式對(duì)理解和掌握高斯定理非常關(guān)鍵。</p><p><b>　　高斯定理的內(nèi)容</b></p><p><b>　　內(nèi)容：</b><

40、;/p><p>　　靜電場(chǎng)通過(guò)任何封閉曲面的電場(chǎng)強(qiáng)度的通量等于由所有曲面的代數(shù)和，它是由所有曲面電荷除以真空介電常數(shù)得出。</p><p><b>　　其表達(dá)式是：</b></p><p><b>　　備注:</b></p><p>　　1在高斯定理中，我們選擇的閉合曲面通常稱(chēng)為高斯曲面。</p&

41、gt;<p>　　2高斯定理的適用范圍：靜電場(chǎng); 改變電場(chǎng)。</p><p>　　3高斯定理表明，靜電是激發(fā)的電場(chǎng)，是靜電場(chǎng)的基本性質(zhì)之一。</p><p><b>　　高斯定理的理解</b></p><p>　　1.電場(chǎng)中通過(guò)封閉曲面S的總流量Фe僅與封閉曲面中的電荷有關(guān)，與封閉曲面外的電荷以及封閉曲面中電荷的分布無(wú)關(guān)。<

42、/p><p>　　2. 指封閉曲面中的電荷的總數(shù)，當(dāng)qi是正電荷，則電磁流量為正，反之亦然。</p><p>　　高斯定理中的電磁場(chǎng)強(qiáng)E是封閉曲面空間中所有電荷激發(fā)的總電磁場(chǎng)強(qiáng)度。</p><p><b>　　思考一下:</b></p><p><b>　　當(dāng)</b></p><p

43、>　　高斯定理的數(shù)學(xué)表達(dá)式為,</p><p><b>　　那么:</b></p><p><b>　　E 必須等于 0.</b></p><p><b>　　探討:</b></p><p>　　正電荷內(nèi)封閉曲面的電力線(xiàn)初始端等于負(fù)電荷內(nèi)封閉曲面的電力線(xiàn)末端，然后穿過(guò)電力

44、線(xiàn)的封閉曲面并進(jìn)入封閉曲面，也就是通過(guò)所有封閉曲面的總通量為零。</p><p>　　但這并不表示著封閉曲面上的電場(chǎng)強(qiáng)度E為0，</p><p><b>　　對(duì)于：</b></p><p>　　1.高斯曲面上的場(chǎng)強(qiáng)是高斯面內(nèi)外產(chǎn)生的場(chǎng)強(qiáng)的向量和，因此在高斯曲面內(nèi)</p><p>　　E=0 不能完全確定。</p&g

45、t;<p>　　E和dS是向量之間的數(shù)積，因此著兩個(gè)問(wèn)題存在方向的問(wèn)題，</p><p><b>　　當(dāng)</b></p><p>　　dS 是垂直它的面, 那么就有：</p><p><b>　　當(dāng)</b></p><p><b>　　則不會(huì)出現(xiàn)：</b><

46、;/p><p>　　高斯定理在電場(chǎng)強(qiáng)度中的應(yīng)用</p><p>　　當(dāng)電荷分布具有某種對(duì)稱(chēng)性時(shí)，可以應(yīng)用高斯定理來(lái)找到電場(chǎng)分布。 以下討論兩種情況：</p><p>　　1.電荷分布是球形對(duì)稱(chēng)：即等距的球體中心等于曲面電荷密度</p><p>　　2.電場(chǎng)分布：E沿半徑方向。 E在任何同心球面上都是相等的。</p><p>

47、;<b>　　例1</b></p><p>　　求出半徑為R和電荷+ q的均勻帶電球內(nèi)外的場(chǎng)強(qiáng)。</p><p>　　答：電荷分布是球?qū)ΨQ(chēng)的，其出現(xiàn)的場(chǎng)強(qiáng)具有球?qū)ΨQ(chēng)性，即球體r的中心指向球體的電場(chǎng)強(qiáng)度和沿半徑向量方向的場(chǎng)外強(qiáng)度相等。</p><p>　　圖一 帶電球結(jié)構(gòu)</p><p>　　半徑為r的同心和高斯曲面，

48、由高斯定理可以得到：</p><p>　　當(dāng) r>R, 高斯曲面環(huán)繞的電荷 q:</p><p>　　當(dāng) r< R, 高斯曲面內(nèi)無(wú)電荷:</p><p>　　圖二 均勻帶電球的電場(chǎng)分布</p><p><b>　　圖三 電場(chǎng)分布</b></p><p>　　電荷分布具有軸對(duì)稱(chēng)性：

49、電荷密度與曲面到軸等距。</p><p><b>　　電場(chǎng)分布：</b></p><p>　　E沿半徑方向的垂直軸線(xiàn);</p><p>　　任何同心圓柱面都等于E點(diǎn)。</p><p><b>　　例2</b></p><p>　　在圓柱體內(nèi)外發(fā)現(xiàn)無(wú)限均勻分布的電場(chǎng)強(qiáng)度。 假設(shè)

50、圓柱形半徑R以及每單位長(zhǎng)度軸的電荷為+ 1</p><p>　　答：場(chǎng)分布也應(yīng)該是沿著半徑柱狀對(duì)稱(chēng)，同軸帶電圓柱體圓柱形高斯曲面高度l，半徑r可用高斯定理求出：</p><p><b>　　圖四 圓柱圖</b></p><p><b>　　圖五 圓柱圖 </b></p><p><b&

51、gt;　　圖六 電場(chǎng)分布</b></p><p><b>　　結(jié)論</b></p><p>　　利用高斯定理總結(jié)求解場(chǎng)強(qiáng)的條件技巧和步驟。</p><p>　　條件：場(chǎng)強(qiáng)具有特殊的對(duì)稱(chēng)性：球?qū)ΨQ(chēng)性，軸對(duì)稱(chēng)性，平面對(duì)稱(chēng)性。</p><p>　　如果能對(duì) 進(jìn)行整合, 則無(wú)論電荷還是電場(chǎng)是否具有對(duì)稱(chēng)性，我們都可

52、以使用高斯定理。）</p><p>　　技巧：選擇合適的高斯面，電場(chǎng)強(qiáng)度E的積分符號(hào)可以從積分符號(hào)中形成標(biāo)量。</p><p><b>　　步驟：</b></p><p>　　（1）分析場(chǎng)強(qiáng)的對(duì)稱(chēng)性</p><p>　?。?）選擇合適的高斯曲面</p><p>　　（3）計(jì)算通過(guò)高斯面的通量<

53、;/p><p>　?。?）在電場(chǎng)強(qiáng)度中應(yīng)用高斯定理</p><p><b>　　參考文獻(xiàn)</b></p><p>　　[1] Ma Wenwei, physical [M].Beijing: Higher education press.2008.</p><p>　　[2] Chen Yincong, new centur

54、y physics, [M].Shanghai, East China normal University press, 2006.</p><p>　　[3] Shi Chuanzhu, Discussion of Gauss theorem, [J] .Qujing normal university. Press, 2002, 3.</p><p>　　[4] "Findi

55、ngs and Recommendations to Enhance Reliability From the Summer of 1999", Final Report, Power Outage Study Team, U. S. Department of Energy, March 2000, p S-2</p><p>　　[5] IntelliTEAM Overview of Operati