electricitymagnetism-1- Chinese
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[00:00~02:03] I am Walter Lewin. My lectures will in general, not be a repeat of your book, but it will be complementary to the book. The book will support my lectures, the lectures will support the book. You will not see any tedious derivation in my lectures. for that we have the book. But I will stress the concepts, and I will make you see beyond the equations, beyond the concepts. I will show you whether you like it or not, that physics is beautiful and you may even start to like it. I suggest you do not slip it up, not even in one day. 802 is not easy. We have new concepts every week. And before you know, you maybe too far behind.
我是Walter Lewin,大致上,我上課的方式不是重複課本的內容,是配合著課本,這本書會輔助我的演講,我的演講也會輔助這本書.上課中不會有冗長的推導,因為我們有課本.然而我會強調觀念,使你體會甚於方程式及觀念本身.我將展現,不管你喜歡與否,物理是很美的,甚至你可能開始喜歡它.我建議你一天也不要忽略它.802(這們課)並不簡單,我們每週會有新的觀念.在你知道之前你可能已經落後太多.
Electricity and maganetism is all around us. We have electric lights, electric clocks. We have microphones, calculators, televisions, VCRs, radio, computers. Light itself is an electrical magnetism phenomenon, as radio waves are. The colors of the rainbow in the blue sky are there because of electricity, and I will teach you about that in this course. Cars, planes, trains, can only run because of electricity. Horses need electricity because muscle contractions require electricity. Your neuron system is driven by electricity. Atoms, molecules, all chemical reactions exist because of electricity. You could not see without electricity. Your heart will not beat without electricity. And you could not even think without electricity. Though I realized that even with electricity some of you may have a problem with that. [student’s laughing] The modern picture of the atom is a nucleus, which is very small compared to the size of the atom. The nucleus has protons which are positively charged and it has neutrons which have no charge. The mass of the proton is approximate the same as the mass of the neutron, is about six point seven times ten to the minus twenty-seventh (6.7*10-27) kilograms. Excuse me, it is 1.7, not 6.7 . The positive charges here is the nucleon with the neutrons and then we have electrons in a cloud around it. If the atom is neutral, the numbers of electrons, and the numbers of the protons is the same. If you take one electron off, you got a positive ion. If you add an electron, then you get a negative ion. The charge of the electron is the same as the charge of the proton. That is why the numbers are the same for neutral atoms. The mass of the electron is about eighteen hundred thirty times smaller than the mass of the proton. Therefore, it is is negligibly small in most cases, all the mass of an atom is in the nucleus. If I take six billion atoms lined up touching each other, right? I take six billion that’s about the number of people on earth. Then you will only have a length of sixty centimeters. This gives you an idea how small the atoms are. The nuclear has a size of about ten to the minus twelve centimeters (10-12 cm) and the atom itself is about ten thousand times larger, the cloud of the electrons, which is about ten to the minus eight centimeters (10-8). If you line six billion of those up, you only get this much.
電與磁環繞在我們周圍,我們有電燈,電子鐘,我們有麥克風,計算機,電視,錄放影機,收音機及電腦.光本身是一種電磁現象,無線電波也是.因為電的關係,藍天中七彩的彩虹會在那裡,我會在這們課中向大家解釋.汽車飛機火車可以使用是因為電力,馬也需要電力,因為肌肉收縮需要電力.你的神經系統也是由電力所驅動,原子分子以及所有的化學反應都是因為電力而存在.如果沒有電,你將無法「看」,如果沒有電,你的心臟將不會跳動,如果沒有電,你將無法思考,雖然我了解即使有電,你們之中仍有些人在那方面有困難.現代對於原子的概念為:原子核,大小跟原子比起來小很多,原子核中有質子,含正電荷,有中子,不帶電荷.質子的質量大約和中子差不多大約是六點七乘以十的負二十七次方公斤.抱歉,是一點七不是六點七.在這裡正電荷表示核子與中子,然後我們有一團雲狀的電子圍繞著它.如果這個原子是電中性的,則電子的數量和質子的數量一樣.如果你拿去了一個電子,這顆原子就會成為正離子,如果你加入了一個電子,這顆原子就會成為負離子,電子所帶的電量和質子所帶的電量相同,這就是為什麼中性原子的電子及質子的數目相同.電子的質量比質子小一千八百三時倍,因此在大部分的情況下,它的質量是可以被忽略的,原子所有的重量都是在原子核,如果我把六十億顆原子肩並肩排在一起,對吧!我取六十億是相當於全球人口的數目,而你只會得到六十公分的長度.這讓你知道原子有多麼的小.原子核的大小大約是十乘以十的負十二次方公分而原子大約是它的一千倍,電子雲大小大約是十的負八次方.如果你將六十億個它們疊加在一起來你只會得到這麼大.
04:14~07:14]
Already in 600 BC, it was known that if you rub amber that is going to attract pieces of dry leaves. And the Greek word for amber is elektron. That is why electricity got its name from. In the sixteen-century, there were more substances also known to do this. For instance, glass, and sulfur. And it is also known and written that when people were bored at parties, that the women will rub their amber jewelry and will touch frogs which then would start jumping of deperation, 'cause people considered it to be fun, not understanding what actually what’s happening to the amber, nor what’s happening to the frogs. In the 18 century, it was discovered that there were two types of electricity. One if you rub glass, and another if you rub rubber or amber for that matter. Let’s call one A and the other B. It was known that A repels A, and B repels B, but A attracts B. And it was Benjamin Franklin, without any knowledge of electrons and protons, who introduced the idea that all substances are penetrated with what he called electric fluids, electric fire, and he stated if you get too much of the fire, then you're positive charged; and you have the deficiency of that fire, then you're negative charged. He introduced the sign convention, and he decided if you rub glass, that is an excess of the fire and he called that therefore positive. You will see later in this course why these choices, he had 50% chances, is extremely unfortunate, but we have to live with it! So, if you take this fluid, according Benjamin Franklin, and bring it from one substance to the other, then the one gets the excess becomes positive charged, but automatically as a consequence that the one which you take the fluid becomes negatively charged. So that is the whole idea behind the conservation of charge. You cannot create charge if you create plus then you automatically create minus. Plus and plus repel each other, minus and minus repel each other, and plus and minus attract. And Benjamin Franklin who did the experiments also noticed that more the fire you have the stronger the forces; the closed these objects are to each other, the stronger the forces; and there are some substances that he noticed, which conduct this fluid, which conduct this fire, and they are called Conductors. 早在公元前600年，人們已知道磨擦琥珀會吸引枯葉，而希臘文中的琥珀(elektron)就是電(electricity)名字的由來。十六世紀時有更多的物質被發現有同樣的性質，如:玻璃、硫磺。根據記載，參加舞會的人感到無聊時，女人們會摩擦她們的琥珀珠寶去觸碰青蛙，使牠們不故一切地猛跳。人們覺得很有趣但並不知道琥珀與青蛙之間的關係。到了十八世紀，人們發現世上存在兩種電力。一種是摩擦玻璃產生的，另一種是由摩擦橡膠或琥珀產生的。我們稱一個為A另一個為B。我們知道A排斥A，B排斥B，但A吸引B。班傑明●福蘭克林在不知曉電子及質子的情況下猜測:所有的物質都被「electric fluid」或electric fire的東西所貫穿，他說:「如果你被過多的electric fire貫穿的話，你將產生正電荷；如果你缺乏electric fire的貫穿，將會產生負電荷。」福蘭克林也替符號命名，因摩擦玻璃而產生(也是因electric fire 作用產生)的電荷稱為「正電荷」。你將會在這門課學到為何這是個非常不幸的決定(他有50%的機會)，但我們還是
這樣承用了下來。根據福蘭克林的講法，你若將此流體(electric fluid)移轉到另一物質上，得到此流體的物質變成帶正電荷，自然而然地，失去流體的物質變成帶負電荷。這就是電荷守恆背後的意義。你不能創造電荷，如果你創造了正電荷，相對的你也創造了負電荷。正正相斥，負負相斥，正負相吸。福蘭克林做了實驗表示，得到越多的electric fire就可得到越多的力，兩個物質越接近，力也越大。福蘭克林表示有些物質可以導通electric fluid，也就是可以導通electric fire，稱為「導體」。 [07:15~09:17] If I have a glass rod as I have here and I rub it, then it gets this positive charge that we just discussed. So here is this rod and I rub it with some silk and it will get positively charged. What happened now to an object that I bring closed to this rud, and I will start off with taking a conductor. And the reason why I choose the conductor is that conductors have small fractions of their electrons, which are not bound to atoms, but which can freely move around in the conductor. That’s the characteristic for a conductor for metals. That’s not the case with the non-conductors. They're the all electrons are fixed to individual atoms. So here we have a certain fraction of the electrons that can wonder around. What is going to happen that the electrons want to be attracted by these positive charges, plus and minus attract each other. And so some of these electrons which can freely move, will move to this direction and so the plus stay behind. This process we call Induction. You get sort of a polarization, you get a charge division. It is a very small effect. Perhaps only one in ten to thirteen(th) electrons that were originally here will end up here. But that is all it takes. So, we got the polarization and we get a little bit more negative charge on the right side than we have on the left side. So what is going to happen is, since the attraction between these two (these two 在此指的是圖上兩個相互靠近的負極及正極) will be stronger than the repelling force between these two (these two在此指的是圖上兩邊相距較遠的的兩個正極電荷) because the distance is smaller, and Franklin had already noticed the shorter distance the stronger the force. What will happen is if this object (帶正極負極的布料) is free to move, it will move toward to this rod.
如果我有一個玻璃棒，就像我現在這裡有的，我摩擦它，他將帶正電，如同我們剛才討論的。這裡有支棒子，我用絲綢去摩擦它，它將帶正電荷。我將一物體靠近此棒子，我將先拿導體。我之所以要先拿導體是因為導體中有一部份電子並不被原子所束縛，它們可以自由自在的在導體中遊蕩，這就是導體的特色。也就不是「非導體」的特色，它的電子都緊緊地束縛於電子個別所屬的原子。所以這裡我們有一些電子可以自由的移動，它們很想被這些正電荷吸引，正負相吸。所以有些可以自由移動的電子會向這個方向移動，正電荷就會被留在後頭。這樣的過程我們稱「靜電感應」。你已經可以大約了解極化現象，你看到了一些分離的電荷。這是ㄧ個影響非常小的作用，大約只有1/10或1/13的電子原本在這裡，最後在這裡。但這樣就很足夠了。我們有了電荷分離，右邊的電子比左邊的電子來的多，這兩邊的吸引力比這兩邊的排斥力大，因為距離比較短，而福蘭克林已經表示物體之間距離愈短作用力就愈大。所以，如果這個物體可以自由移動的話它將移向這支棒子。
[09:18~12:35] This is the first thing I would like you to see. I have here a conductor as a balloon and I will rub this rod with silk. And as I approach to the balloon you will see that the balloon comes to the rod. I will then try to rub with that rod several times on that balloon. It will take a while perhaps because the rod itself is a very good non-conductor, it's not so easy to get charge exchange between the two.But if I do it long enough, I can certainly make that balloon positive. Then, they're both ( both 在此指rod 跟balloon 都被charge成帶正極的物體) positive and then they will repelling each other. First, the induction part, here by you will see the balloon comes to the glass rod. This experiment works best when it is dry in the winter. They don’t work well when it is humid, so it is a good time to teach 802 in winter. OK, there we go! This should be positive charged now and the balloon will come to the rod. See that, very clearly!! (Come on, baby!! ^^ Students laughing!! ) OK! So now I will try to get this balloon charge aittle, so it doesn’t change over with the electron that will go from the balloon to the glass, and the glass doesn’t, isn’t a conductor itself and it is not always easy to get charge exchanges. OK, let's see whether I had succeeded now in making the balloon positively charged as well as the glass rod. If that’s the case, then the balloon is not goingto like me, and the balloon now will be repelled. And you see that very clearly.To show you now there are indeed two different kinds of electricity, if I now rub with cat fur by tradition, we do that with cat fur, I don’t know why, by tradition we used the silk for the glass. So if we do this with cat fur now, then this becomes negatively charged then we are going to have two types of electricity. And since that balloon is positively charged, now the balloon will come to me. There it is!! So you have seen the first time now clearly, that there are two different kinds of electricity. The positive charge chosen by Franklin on the glass rod, and the negative charge on the rubber. So now, you may think, that if I approached a non-conducting balloon with a glass rod, and I have a non-conducting balloon here. You may think now the balloon will not come to the glass rod because there are no free electrons. So, these electrons cannot freely move, and so you don’t get this polarization, you don’t get this induction. That is not the case and this is actually quite subtle.
這就是我想要你看的第一件事，我這裡有一氣球導體(表面為金屬)，我用絲綢摩擦這根棒子，當棒子接近這顆氣球你看到氣球朝著棒子方向而來。我將試著用此棒子摩擦氣球幾下。這將需要一些時間， 因為棒子本身是個不良導體，要使兩物體的電性交換不容易。但如果我摩擦夠久，我一定可以使這氣球帶正電。然後，這兩個物體都帶正電它們將會互相排斥。但首先，由靜電感應，你看到氣球朝向玻璃棒。這個實驗在乾燥的冬天下做效果最好，若太潮溼將效果不彰。所以這堂802的課開在冬天很好。好，我們看。它應該已帶正電荷了，這氣球將向著棒子 而來。看到沒，非常明顯的。來寶貝，好。現在我試著使氣球帶一些電荷，避免棒子因傳出電子而改變電性，(教授摩擦玻璃棒)玻璃不是ㄧ個很好的導體所以我們總是很難將它帶上電荷。好，我們來看看我是否已成功地使氣球和玻璃棒一樣帶正電荷，如果是這樣，則氣球將不會喜歡我，而...看氣球被排斥了。你看得很清楚。為了使你信服世上確實存在兩種電荷，如果我使用貓毛磨擦，我不知道爲什麼我們用貓毛，根據傳統，我們用絲綢摩擦玻璃棒。所以我們如果用貓毛的話，我們將有兩種不同的電性。既然氣球帶正電，汽球現在會朝著我來。看它來了。所以你已經第一次非常明顯地看到了，世上有兩種不同的電性。在玻璃棒上的是正電荷由福蘭克林選擇的，及橡膠棒上的負電荷。現在，你可能想，如果我以玻璃棒接近非導體氣球，我這裡有個非導體汽球。你也許會想這汽球不會移向玻璃棒，因為氣球上沒有自由移動的電子。這些電子無法自由移動，沒有極化現象，也就沒有靜電感應。事實並不是這樣，這講起來很微妙。
[12:36~14:36]
You have to look now at the atom’s scale. If I take an atom that you have here, you have positive charge and you have the electron ishere in a cloud around the positive nucleus. If I bring a glass rod positively charge near by, then these electrons which are stuck tothe atoms, they cannot freely moved like in conductors, however will spend a little bit more ime on the side where the glass rod is, because they feel attracted by the glass rod , whereas the nuclei, if anything, want to go awayfrom the glass rod. So what you are going to see is that in a way if I started off with the spherical atom, let's suppose this is a spherical atom or a spherical molecule. Then what will happen is that you get sort of a shape like this, and the electrons spend a little bit more time here than they spend here. And that means I had actually polarized that atom. If the electrons spend more time on thisside of the atom than on this side, I have also created phenomenon of the induction and I therefore expect that this side becomes
more negative than that side. I can show you that in a nice way with a transparency. Whereby, I have plus and minus signs, and I have equal numbers of plus and minus signs. So they represent neutral atoms. There you see. (Oh~ Boy! It's a little dirty but maybe I can clean it a little! OK! ^^ So, Here we go! ) 你已經知道原子的尺度。如果有一個原子在這裡，這裡有正電荷，這裡有電子雲環繞著帶正電荷的原子核，如果我將帶正電的玻璃棒靠近，這些被原子核所束縛、無法如導體內自由自在移動的電子，會花多一點的時間在有玻璃棒的這端。因為它們感到被玻璃棒吸引，相對的，原子核很想要逃離那根玻璃棒。所以如果我假設這是ㄧ顆球狀的原子，你將看到它變成大約這樣的形狀，電子待在這裡的時間比這裡長一點。這表示我確實地做到了原子極化如果電子在這裡的時間花的比在這裡多，表示我已經製造出靜電感應的現象。也因此，我期待這邊的電性比這邊還負。我可以由幻燈片清楚地證明給你看。藉此，我有正號，負號，相同的數量。所以它們代表了中性的原子。阿!你看呼~這有點髒，或許我可以將它清乾淨一些。好，我們來看。
[14:37~17:50]
So, notice that there are equal amount of "+"s and "-"s. So think of plus and minus as one neutral atom. There is the representation.Now I am holding a glass rod on this side, which is positively charged. So each atom, the electron wants to go a little bit to this side, so the nucleus stays behind. And if each atom does that, this is what is going to happen. And now notice what you end up with, in the middle of the substance, plus and minus cancel each other out again. But on the right side, you have created a negatively charged layer, and on the left side, you have created a positively charged layer. So in a way you have again induction. So even in the no-conducting object, this side will go to negative, this side will go to positive, and therefore, if I approach anon-conducting balloon with a glass rod, I will also see the balloon come to me. So I can easily show you that it doesn’t make any difference whether I choose glass or I choose rubber. I can do it with both. Non-conducting balloon always have a potential problem. The potential problem is that, they can be charged by themselves just like the metal balloon can be charged by themselves. However, if I touched the metal balloon, then any charged is there will immediately flow me to the earth, we will understand that later,because this is a conductor. Remember, the electric fluid, is conducted by a metal, but not by a non-conductor. So, this is more difficult, even if I kiss it and touch it, it is not clear that I can take all the charge off. In fact, by doing that, I may make it worse.Let's hope it is not charged too much, and let's approach this glass rod and see whether I can convince you that indeed it (the balloon) is coming to the rod. Not because of the free electrons, but because of that process.(Oh~ Boy~~ ho!! ^^ ) And it should also do the same with rubber. (I hope… if it were negatively charged, it will go away!!) Oh! It does go away, so it is negatively charged. Did you see that? By touching it, I actually probably charged it and there is not much I can do about it! Very difficult to get charge off. I already have the suspicion when I approach it with the glass, it was too eager to come to the glass. Still negatively charged!! That is the way goes! It is not because of the demonstration fail but is because of the balloon is negatively charged and doesn’t want to give it up because it (this balloon) is a non-conductor.
注意到這裡有等量的「正」與「負」，想像這些正負號，如同在中性原子中。這就是它的表示。現在我握著玻璃棒在這端，它帶正電。每一顆原子中的電子都想要靠近這端一些，導致原子核留在後頭。每一顆原子都這麼做，最後你將看到物質中間，正負又再次相消。但你已在右邊製造出一層負電荷，再左邊製造出一層正電荷。所以你似乎又擁有了靜電感應的效果
。所以即使在非導體的物質上，這邊會呈現負電，這邊呈現正電。所以如果我用玻璃棒接近這個非導體的汽球，仍然會看到汽球朝著我來。因此我很容易地向你證明了，無論我選擇玻璃棒或是橡膠棒，我都可以得到相同的效果。非導體汽球永遠有電位差的問題。所謂電位差的問題就是:它們可以自己帶電，如同金屬汽球可以自行帶電。但是如果我碰觸這顆金屬汽球，任何在上面的電荷都會藉著我傳到地球，我們會在稍後理解是因為它是導體的緣故。記著，electric fluid是藉著金屬傳導，不是非導體。所以這問題變得很棘手因為即使我親它，碰它，我都不能確定我是否已清除它上面帶有的電荷。事實上，藉由這些動作，我反而有可能使情況更糟。希望它不要待太多的電荷。我們將玻璃棒接近，看看我是否能說服你汽球確實是會朝著棒子而來。並不是因為自由電子的關係，而是因為剛剛所討論的作用。喔!老天阿!喔!使用橡膠應該也會有相同的作用。我希望(它不帶電)...如果它是帶負電荷，它就會走開。喔!所以它是帶負電。你看到了嗎?藉由碰觸它，我可能反而使它帶上了電荷，而其實我也實在無計可施。非常難以將電荷去除。我剛剛早已懷疑它帶負電當我將玻璃棒接近汽球時，它太想急著靠近玻璃棒。仍然是帶著負電，它就是這樣。這不是代表這實驗失敗是因為汽球帶負電，而汽球並不打算放棄帶負電，因為它是個非導體。
[17:51~21:12]
Friction can cause electric charge. And that is exactly what happened when I touch this balloon and try to discharge it, through friction I may have charged it. If I take this party balloon that all of you may have seen and you just rub them on your shirt or on your trousers, they stick to my hands. They have charge on them, whether it is positive or negative I don’t know. I don’t even remember,it is not important. And so when I bring them to my hands, my hand is not a good conductor, but you get an induction. This phenomena that we just discussed then so the two attract each other. The positive and the negative side attract each other. You can stick them on the ceiling, you can stick them on the board, you can decorate your room that way. Very pretty, isn’t it? All that youcan do now because of 802. Now this heavy balloon maybe a little bit more difficult, also I am wearing cotton, if you wear nylon orpolyester it's much better, it's much easier to get … oh~ that’s good. That’s a nice one! I think we need a blue one! ^^ Here we go! So you see, friction, causes electricity; that is, of course, by the silk when we rub the glass and the catfur we rub the rubber,then we create charge on one. Of course, if you made the glass positively charged, your silk, will be automatically negatively charged. When you comb your hair, you may have noticed with dry weather that you can hear some cracking noise, cracking noise means sparks. You will learn all about sparks in this course though not today. But you can hear it if you are very quiet. As you do that, you charge the comb. I can hear the cracking. Interesting! So the comb is now charged, probably so am I, and there it comes. See! Not as good as the glass, but same idea. If you take your shirt off, and you make it dark in your dormitory, and you stand in frontof the mirror, an amazing experience (all student laughing … ^^ ), I will be happy to do it for you because that I told you I already wear the cotton and it doesn’t work with cotton so well. You really have to do with the nylon shirt. And when you take your nylon shirt off, not only do you hear the cracking, but you actually see the glow with the teeny tiny sparks. You actually like a light ball. This experiment that you cannot miss, and I will suggest you try that this weekend. Do it with a friend, that is even more fun!
摩擦可使物體帶電，我剛剛試著藉由碰觸汽球使它不帶電，但其實我也可能因摩擦使它帶電。如果我拿著這顆派對汽球就如同你們以前看過的，在衣服上或褲子上摩擦，汽球將粘在我手上。它們帶了電荷，無論是正電荷或負電荷，我根本不記得，並不重要。我將它們帶到手邊，我的手不是ㄧ個好的導體，有靜電感應。這個現象我們剛剛討論，所以兩個物體互相吸引。正電荷與負電荷互相吸引，你可以將它黏在天花板，黏在黑板，你可以這樣裝飾你的房間。很漂亮，不是嗎?因為802這堂課你可以這麼做。這個較重的汽球比較困難一些，也是因為我穿著純棉的衣服，如果你穿尼龍或是多元酯纖維的衣服會較好，會比較容易，喔!這樣很好。這是ㄧ顆好汽球。我想我們需要一顆藍色的。來。所以你看得到，摩擦，導致電荷產生。當然，那也是因為我們用絲綢摩擦玻璃棒，以貓毛摩擦橡膠，我們製造出電荷。以所當然，如果我們使玻璃棒帶正電，絲綢就會帶負電。當你梳著你的頭髮時，在乾燥的天氣下你或許會聽到小小爆裂聲。這聲音表示有星火。你將會學到星火，不過不是在今天。你可以聽到聲音如果這裡很安靜的話。當你梳頭髮時你正在使梳子帶電，我听到了。有趣。所以現在這支梳子帶電，也許我也是。好它來了。沒有像玻璃棒的效果，不過是ㄧ樣的概念。如果你站在黑暗宿舍裡的鏡子前，將上衣脫掉，這是個很棒的經驗!我會很高興體各位這麼做不過就像我告訴你們的我穿了棉衣服，而此現象將不那麼顯著。你真的必需自己穿著尼龍衣服這麼做。當你脫去尼龍上衣時，你不只聽見小小的爆裂聲，而且你會看到小小小小的星火。你就會像一個燈泡。你絕對不能錯過這個實驗，我建議你這個周末就試試看。和朋友一起做，這樣更有趣。
[21:13~25:45]
We all perhaps remember when you just walk around, do your normal things during the day, the rugs in rooms and you want to leave the room when you touch the door knob and you get a shock. The spark that flies over. It’s electricity. Even when you touch a person, you sometimes feel this shock. When you cook and you take Saran wrap (塑料薄膜) off these rolls, the damn stuff just doesn't want to come off because as you roll if off, there is a friction and it gets charged, and it often gets crumbled up, and it is very bad, very difficult to handle it. You've all experienced that! Also, cellophane around boxes with chocolate. The same thing happens, as you take it off, you charged it, whether you like it or not! I now want to do an experiment and I need a volunteer. I need a student who actually is wearing preferred not all cotton, but I think Simon you have a beautiful wonderful nylon parker. So if you are willing to sacrificed a little bit for the sake of the science and come over here and sit down here. Just relax, make sure your feet off to the ground, ok! So, what I am going to do now, Simon I am going to beat you with rag fur. (student laughing!) And as I beat you with the rag fur, you will get charged! And, since I don’t want you to be the only person who suffers on this experiment, I will also stand on an isolated stool, so if you become for instance positive charged, I don’t know whether it is positive or negative, I will get the other amount of charged. So we shared in the charge.And as I beat you, you will charged more and more, and I will charged more and more, and then we will have to convince the class that we are both charged. And we will do that in the way that will be hopefully rather convincing. I …. Ohm…. Let me just start
beating you a little bit (student laughing ^^ ) to make you feeling at home. We know each other, right ? OK! Now of course as I mention to you this experiment works well when it is dry, so if you are too wet won’t worked, but lets see if you sweat too much that it doesn’t work too well. So, are you ready? (student laughing loudly!! ) I have in my hand an nylon flash tube. And we don’t know yet whether the voltage is because we will learn that in this course. To get a good flash out you need about a fewthousand volts. So we will see when we make it dark shortly, and I will hold the flash tube, the flash I did on the one hand, and nylon discharge to, and Simon will touch it on the other side. If we succeed it, then you may see some light. So, Simon look at me first, don’t touch it yet because we are going to make all the way dark. You know where it is? It’s there. Ok, make it dark, Marcos.Touch it! Touch it! WOW~ (Student exclaim!) Good! Try it again, touch it again!! OK, thank you! Can we have some light?
(clapping!) Thank you very much! 我們都記得一天當中，你做事到處走動，地面上鋪著地毯，當你想離開房間，觸碰們把時會被電到。星火很快的消失。那就是電。 即使有時你觸碰別人，你也感覺被電到。你煮菜時想要將塑膠膜從滾捲中撕起來，這個該死的東西就是不起來。這之中有摩擦，所以它變得帶電。他後來就會捲成一團，這樣很糟，很難處理。你們都有類似的經驗。還有，包著巧克盒子的玻璃紙，同樣的情況發生，不管你是否喜歡，你已使它帶電。我現在想做一個實驗，我需要一個自願者。我需要一個穿著不是全棉衣服的學生，我想Simon你穿著一件非常漂亮美好的尼龍parker。如果你願意爲科學犧牲，請過來坐在這裡，。放鬆就好，確定你的腳不要碰到地面。好!我現在要做的就是，Simon我現在要用破布打你。當我用破布打你的同時，你也帶了電荷。為了使你不要成為這個實驗的唯一受害者，我也將站在這個獨立的凳子上，所以舉例來說如果你帶了正電荷，我不曉得是正或是負，我有將會得到另外那部份的電荷。所以我們共同擁有電荷。當我打你的同時，你會帶有愈來愈多的電荷，而我也帶有愈來愈多的電荷。我們將使班上的同學信服我們身上確實都帶了電荷。我們期望它是ㄧ個以令人信服方法做出的實驗。讓我再打你幾下，讓你覺得很自在。我們很熟識嘛!對吧!好。我之前曾經提到這樣的實驗要在乾燥的環境下進行效果最好，所以如果太潮溼，將會不成功，如果你流了很多汗，就不管用了。你準備好了嗎?我手上有一支尼龍做的火花棒。我們不知道電壓是什麼東西，我們將會在這堂課學到。爲了使得它發出火花，你必須有幾千伏特的電壓。待會兒等我們將燈光關掉，我將握著這支火花棒，而Simon將握著火花棒的另一端，如果我們成功，你將看到一些光。Simon你先看著我，先不要摸它，我們待會要使得教室全暗。你知道他在哪吧?它在這。好。關掉燈光
，Marcos。摸它，摸它。哇!很好。再摸一次。再摸一次。好。謝謝你。可以打開燈嗎?非常謝謝各位。
[25:46~29:47]
Equal charges repel each other! I showed that demonstration with the balloons. Here we have an instrument which called Van da Graaff. It is named after Prof. Van da Graaff who invented it, who was an MIT professor. And this instrument which I will not discuss in any detail though, but you will understand it latter on this course. I will tell you all about it later. This thing of this instrument has a super amber rod, and yet we don’t know what the voltage is, I mentioned already 20,000 volts between Simon and me. In this instrument you have to think in terms of several hundred thousand volts. So this instrument is not without danger, but of course that makes it more exciting to work with it! So, it is a super amber rod, and what I will do first now is to put some confetti on top and then we turn on the Van da Graaff, the confetti may at first go to the charge though, and it already on the top of it, and when it picks some of the charge, it will then spread out because it will repel each other. So lets go get some light there. We will make it better to see. Let me put some of this (confetti) on top. It is just some regular confetti, pieces of paper.All right, now all of I have to remember is how to start the Van da Graaff. (Machine running.) Most of the actions have already occurred. I will put a little bit more on! If he sparks, then don’t worry yet. (students laughing) Let's put some more on! Woops! Nothing left for the second class. Make it perhaps a little bit darker. Ahhh~ that’s too dark! Ok, try it once more, give it a zap.So look at the confetti on top, and I think it's quite convincing. Some of the confetti will stay there. Well, that's for reason that is not a good conductor, so it gets it first sucked in and if it doesn’t get charge of the Van de Graaff then it will not spread out. All right! So now let's try for the first time a little bit more quantitative.
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相同電性的電荷互相排斥，我已經用汽球示範給各位看過了。我們有一台Van da Graaff，是由麻省理工學院的Van da Graaff教授所發明我將在這堂課的後面再詳加解釋這台機器的工作原理。這台機器有一支超強的琥珀棒。各位還不知道電壓是什麼，不過我剛剛提到過Simon和我之間有兩千伏特的電壓，而這台機器你則必須以幾十萬伏特的電壓為單位來衡量，所以說這台機器是有危險性的，不過也因此和這台機器一起工作變得很刺激。它是ㄧ支超強琥珀棒，首先，我將碎紙片灑在上頭，然後打開機器。碎紙片會先和電荷吸在一起。它們已經在上頭了，當碎紙片也帶有電荷時就會散開，因為它們互相排斥。我們把燈光調亮一點。這樣看得比較清楚。我放上一些碎紙片。這只是平常的碎紙片，一小片一小片的紙。好的，現在我只需記得如何打開機器。大部分的反應已經在進行了，我再加點碎紙片下去。如果有電花產生，不用擔心。再加一點。喔喔。下一堂課會不夠用。也許我們再把燈光調暗一點。喔。太暗了。好，再是ㄧ次。把遙控器按下去。看看上頭的碎紙片，我想事實擺在眼前。有些碎花片仍然留在上面，那是因為碎花片不是ㄧ個好的導體，如果它們卡住了，且又沒有從機器上得到電荷，它們就不會散開。好，現在我們用試試以數量的角度來看。
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[29:48~32:06]
If I take two charges, and we use in general, we use for charge the symbol “q”. So here we have q1, and here we have q2. And let's say they are separated by a distance “r”. The unit vector in the direction from 1 to 2 are called that r-roof-12. The roof stands for unit vector. If these charges are equal, both minus or both plus, then they will repel each other. So, here, there is a force “F”, which I called F1,2, is a force due to number 1, and since action equals minus reaction,force here is F2,1, is equal in magnitude but 180o in opposite direction. Coulomb, France physicist, who did a lot of research on this in 19th, 18th century actually. Coulomb found the following relationship that the force is proportional to the product of the two charges. So, it is q1 times q2, times a constant which nowadays we call Coulomb's Constant K, divided by the distance between theses
charges squared; and this is in direction of the unit vector that goes 1 to 2. This is the force on number 2 due to 1. And notice that this equation is sign sensitive, because if q1 and q2 are both negative, the force will be in this direction (from number 1 to 2). If both are positive is also in this direction (from number 1 to 2) as I have it. However, if one is positive and one is negative, you get a minus direction so this force flips over, and that one (left side force F2,1) then also obviously flips over.
如果我有兩個電荷，通常以q來代表。我們有q1，這裡有q2，它們被距離r所分開。單位向量的方向由1到2，稱為「r，蓋子，1、2」，蓋子代表單位向量。如果這兩個電荷所帶的電量相同，都同為正或同為負，它們就會互相排斥。所以就會產生一個力F，我們稱「F1,2」是由q1作用在q2上的力，因為作用力等於反作用力，F2,1的大小和F1,2相同，方向相差180度
，就是剛好反向。法國的科學家庫倫在十九，不是十八世紀，做了一連串的研究，發現這兩個電荷之間的交互作用力的大小，和電荷的乘積成正比，也就是q1乘以q2再乘以一個我們現在稱為的庫倫常數K，最後再除以兩電荷之間的距離的平方。它的方向是由1到2，這是由1作用在2上的力。注意，這條式子的方向是很重要的。如果q1，q2都帶負電，就會是這個方向。如果都是帶正電，也會是這個方向。然而，如果一個帶正電，一個帶負電，你將得到負的方向，所以方向相反了過來，而這個也很明顯的方向會相反。
[32:07~40:02]
In the SI units, in this course, we will use for the unit of charge the coulomb named after this great man. One coulomb charge is a horrendous amount of charge, more than you'll ever see in your lifetime. We normally work with micro-coulombs, sometimes evenless than that! The charge of one proton, which is exactly the same as the charge of one electron, is approximately 1.6 times 10 to the minus nineteen coulomb (1.6*10-19). So one coulomb is something like 6 times 10 to the eighteen (6*1018) protons or electrons if the charge is negative. This constant K in SI unit is 9 times 10 to the ninth (K=9*109). And the unit you can find out because you know that this (F) is newtons, this(q1*q2) is coulomb squared, and this(r2) is square meters. So, the unit is Newton-square-meters divided by square-coulomb (Nm2/C2). But that's not so important. No one ever thinks of it that way. For historical reasons,which may at time be a pain in the neck for you, we write for K is 1 divided by 4 pi epsilon-zero. There is nothing magic about that!It’s just a historical reason. So 1 divide 4 epsilon-zero is 9 times 10 to the ninth. (1/(4 πε 0) = 9*109). That’s all that matters.
This epsilon-zero has a name, it's called “permittivity of free space” (ε0 = 8.854*10-12 (Farad/meter)). But you can forget about that.It is not important the name. Notice that there is a clear parallel with gravity. Newton's law of gravity that the force which in that case is always attracting, gravity never repels, is the product of two masses, and then you have here gravitational constant and again you have the distance square. So there is an enormous parallel between the two. It is a great beauty that electricity acts in the way is very parallel to the way that gravity works. If I added a third charge, for instancehere q3, and if now I want to know what the forces are on q2, then I use the superposition principle which we used many times in 801 class. And we say ok the net force on number-2 (q2), is the force due to number-1 (q1), plus the force from number-3 (q3).If number-3, if this is positive and this is positive, and this is negative, then this force will be in this direction F3,2, and then the net force on number-2 will be the vectorial sum of these two (指來自q1和q3的力).Is it obvious that the superposition principle works? Not at all! It’s not at all obvious. Do we believe in it? Yes, we do! Why do we believe it? Because it's consistent with all the experiments that we have done.
But the superposition principle, which is very powerful, is really not a matter of course. But it works. We can always use it and we will! If you compare 801 with 802, thereby comparing electricity with gravity, you will see that electric forces are way more powerful than gravitational forces. And the way I can best show you that is by taking two protons, which are distances d apart. Here is a proton, and here is a proton, and they are separate by a distance d. They repel each other, and the force by which they repel each other, is of course extremely easy to calculate. We know Coulomb’s Law, that law is called after Coulomb. And so the force, the electric force with which repel each other, this is now just the magnitude of the force, is the charge the proton, which is 1.6 times 10 to the negative nineteen (1.6*10-19) but I have to square that! I have to multiply by Coulomb’s Constant which is 9 times 10 to the ninth (9*109), and I divide it by d square (d2). That’s the electric force. If I want to know the gravitational force, which is the force with which they attract each other. These (electric force) are repelling force. I just want the magnitude here, then I have to take the mass of the proton, which is 1.7 times 10 to the minus twenty-seven (1.7*10-27), and I have to square that. Remember m1 times m2 times the gravitational constant, the gravitational constant in SI unit, is 6.7 times 10 to the minus 11 (6.7*10-11), and I divide that by d2. If now I compare the electric force with the gravitational force, so I divide itone by the other. Notice that d cancels. They both have d2 downstairs. So you will easily be able to show that this ratio is roughly
10 to the 36th (1036). So the electric force is thirty-six orders of magnitude more potent than the gravitational attraction. This teaches you some respect perhaps for 802. If these were the only forces that acted on the protons, and you bring them in the nucleus, which has the size of the 10 to the minus 12(10-12) centimeters. Then the acceleration that the proton will experience is the
electric force divided by the mass of the proton. F equals m*a! Basics of 801. And if you take this electric force, when you make d 10 to the minus 12 (10-12) centimeters, which is 10 to the minus fourteen(10-14) meters, and you calculate this ratio and you will find that it is twenty-six order of magnitude higher than the gravitational acceleration on earth. Twenty-six order of magnitude higher.
So you wonder what the hell holds the nucleus together if there is a such tremendous force on these protons. Well, what is holding them together are the nuclear forces which we do not fully understand, but thank goodness the nuclear forces are not part of 802. So I will leave that alone for now.
以SI(國際單位制)單位來看，我們理所當然以庫倫作為計算電荷的單位來紀念這位偉大的人。一庫倫的電荷是多的很恐怖的電量，比你一生看到的電量都還多。我們通常用千分之庫倫來計算，有時甚至使用更小的尺度。質子所帶的電量和電子帶的電量相同，大約都是一點六乘以十的負十九次方(1.0 × 10-19)庫倫。所以一庫倫所帶的電量就是六乘以十的十八次方(6*1018)個質子，或電子。SI制中，常數K是九乘以十的九次方(9*109)。而常數的單位你可以從:力的單位是牛頓，電荷的單位是庫倫平方，距離平方的單位是公尺平方。所以就是牛頓乘以公尺平方再除以庫倫平方。不過這不重要，根本沒有人去在意他。因為一些歷史因素，我們有時把K寫成一除以四乘pi乘以epsilon-zero。這沒什麼特別的，只是一些歷史的原因而已。
一除以四乘以epsilon零等於九乘以十的九次方，知道這樣就夠了。epsilon-zero(ε0)有個名字叫「真空超導率」，不過你可以把它忘掉。這不是什麼重要的名字。注意到這裡有和重力非常相似的地方。牛頓的萬有引力，永遠是吸引力，從來不為排斥力，也是質量的乘積，這裡也有個萬有引力常數G，也有距離的平方。這是兩個對稱性很強的式子，電力與萬有引力的式子對稱得非常美妙!舉例來說，如果我加了第三顆電荷，而我想知道作用在q2上的力，我們這時使用「疊加原理」，這個原理我們已經在這堂課上使用很多次了。作用在q2上的淨力是由1號電荷產生的力加上3號電荷產生的力。如果三號電荷為正電荷，這是帶正電，這是帶正電，這個帶負電。結果這個力的方向會是F3,2的方向，二號電荷上的淨力將會是這兩個向量的加總。疊加原理很明顯是正確的嗎?不不!一點也不明顯。但我們相信它的存在嗎?是的，我們相信。?什麼我們相信呢?因為它和我們所做的所有實驗都相符合。疊加原理非常的有用，但它不是我們這堂課的教材。不過他確實成立。我們可以一直用它，現在就可以用。我們拿801與802這兩門課來比較，也就是比較電力與萬有引力，你會發現電力遠遠比萬有引力來的強大。一個最好讓你了解的方法便是拿兩顆質子，分離d的距離。它們互相排斥，這個排斥力很容易算，
我們知道以庫倫命名的庫倫定律，所以這個排斥力的大小就是ㄧ點六乘以十的負十九次方(1.6*10-19)，我必須將它平方!再乘以庫倫常數也就是九乘以十的十九次方(9*109)，再除以d平方。這就是電力。如果我想知道萬有引力，也就是它們倆之間的吸引力，這個(電力)是排斥力。這裡我只想要知道力的大小，我必須知道質子的質量是ㄧ點七乘以十的負二十七次方(1.7*10-12)，將它平方。記得，是m1乘以m2乘以萬有引力常數。SI制中的萬有引力常數是六點七乘以十的負十一次方(6.7*10-11)，再將它除以d平方。現在我將這電力及萬有引力
拿來比較，將它們相除。注意到d被消掉，它們都有d平方在樓下(分母)。因此你很清楚知道比例大約是十的三十六個次方倍。所以電力比萬有引力大了三十六次方倍。(大約是十億十億十億個十億倍)，這或許使你對802產生敬意，如果這是世界上唯一作用在質子上的兩個力，你將它們放進大小為十的負十二次方公分(10-12cm)的核子中。則質子所體驗到的加速度是電力除以
質子的質量。F=ma，801這堂課的基礎。若你將電力放進d為十的負十二次方公分(10-12 cm )也就是十的負十四次方公尺(10-14m)的長度裡，計算比例，你會發現電力的加速度比地球上的加速度大十的二十六次方倍(1026)。二十六的次方倍。你開始懷疑，在這麼大的斥力(質子產生的)下，到底是什麼將原子核結合在一起?原來是我們不太了解的「核力」，但幸好核力不在802的範圍內，所以我們可以先不去管它。 [40:03~47:48]
So, what’s hold our world together? Well, on the nuclear scale, 10-12 centimeters, very important are the nuclear forces. On the atomic scale,up to thousands of kilometers is really electric forces that hold our world together. But on a much larger scale, planets, stars, and galaxies, it is the gravity that holds our world together. And now you may say ah that is very inconsistent with what you just told us because didn’t you just tell us the d cancels, if you compare the gravity with the electricity. Yes! However, most objects are neutral or very close to neutral. And so if you take the earth, it is very unlikely even that the earth as a whole will have a charge of more than 10 coulomb. That probably is already an exaggeration. So if I take the earth and I take the moon, and I put on both a charge of 10 coulomb. Here is the earth and here is the moon, and I could say just arbitrary 10 coulomb here, and let us put on here either –10 coulomb so they will attract each other. But given the distance so much nothing, the force is negligibly small. But, of course, the force of the gravity, which is proportional to their masses wins. And in this particular case, you take the earth and the moon, the gravitational force wins over the electric force by 25 orders of magnitude. So, even though our immediate surroundings, are dominated by electric forces, including your own body for that matter, the behavior of the universe on the large scaleis dictated by gravity. We will use various instruments to measure charge in a quantitative way. And one of these instruments that you will see, we will use it often the lectures that are to come, is called the electroscope. It is a very simple instrument. In general, it is just a conducting rod. It could be aluminum, metal.And at the end, are two pieces of tinsels, two pieces of aluminum foil, and often there is a nice knob here, and if I touch this with a charge object, then because this can conduct electricity, this can conduct the fire, as found by Benjamin Franklin. If I touch this object which is positively charged, then this object will become positively charged. If I charged it with an object which is negatively charged, it will become negatively charged. And you see now here these two very light pieces of aluminum foil will repel each other. And so you will see that this shows a certain angle, and the more charge there is and the larger that angle. So it gives a way doing some quantitative measurement. There are other electrical scopes which are not too different, just one central rod and there would have only one leave hanging there. That’s why you charge that one of then this leave will go up and if you charge more, it will go up even further. I don’t have electroscope now here, but what I want you to see that if I charge myself up, and I holding my hand this Christmas tree tinsels that in the way if I get enough charge only. And these tinsels will spread out. So the idea that immediately follows from the fact that you get certain amount of charge, whether it is negative charged form me or whether I am positively charged that didn’t make any difference. These tinsels will spread out. Of course, the best way I can do that is by charge myself with the Van de Graaff. And as I said earlier, the experiments of this nature are not entirely without risks. And so there is always the possibility that of course I don’t survive this demonstration. But don’t worry, because in that case there will be someone else who will lecture 8.02 except he is not likely to show this demonstration again. So you might want to take a close look because this maybe the only time you will ever see it. So, I will give you some nice light on the Van de Graaff, and it's always a scary moment for me. Slip nice about the Van de Graaff, Now am I going to turn it on or Marco you have the courage to turn it on? You will turn it on? OK, hold it,
Marco. This is too close for comforts. Are you ready? Are you nervous? (Dr. look at the student and said: ) See you! So look at the tinsels and try not to look at me please. Go ahead! I am now a living electroscope. If the weather is cooperating today, and if I have a long hair, you will even see my hair will start to act like an electroscope. We can try that, too. Or we can show it. (laughter and applause) Is it working? (yes! Student response) Ok, well this weekend make sure you take this nylon shirt off in front of the mirror and enjoy the experiment at home. Don’t try this ever. See you Friday. (Applause)
我們不禁要問，到底什麼東西維持著這個世界?以核子的尺度來看(大約是十的負十二次方公分)來看。最重要的力就是核力了。以原子到幾千公里的尺度來看，是電力組合了這個世界。但若以更大的尺度來看，如星球、星星、星系，則是由萬有引力將世界支撐起來。現在你可能感到疑惑，這不是和我剛剛說的矛盾嗎?因為你明明就說比較萬有引力及電力時，距離d會被消掉。沒錯!然而，大部分的物質都是電中性，或是非常接近電中性，所以以地球為例子來看，整體而言，它不會帶有超過十庫倫的電荷。這數據或許已經挺誇張的了。當我拿一顆地球，一顆月球，分別使它們帶十庫倫的電荷，這裡是地球，這裡是月球，大約有10庫倫的電荷放在地球、月球上。它們會互相吸引但由於距離實在太遙遠(38萬公里)，這個力幾乎可以忽略。當然，這時正比於質量乘積的萬有引力勝出。在這個特別的例子中，有地球有月球，萬有引力勝過電力二十五次方倍(1025)。所以，即使我們切身所處的環境，包括你的身體，是由電力所主宰，大範圍的如太空這樣的尺度則是由萬有引力所統治。我們日後會用利用一些儀器測量電荷，其中有一種你將常常在上課中遇到，是驗電器。這是個非常簡易的儀器。大致上來說，它就只是ㄧ個可導電的棒子，可以是鋁，金屬等。最後我要講的是，這裡有兩片薄金屬，兩片鋁金屬片。通常這裡有個圓開關。如果我用一個帶電物體觸碰金屬片，因為金屬片可以導電，也就是可以導通由福蘭克林發現的electric fire。如果我以帶正電的物體觸碰金屬片，則金屬片就會帶正電。以帶負電的物體觸碰金屬片，它就會帶負電。。結果你就會看到這兩片極輕的鋁片互相排斥，產生一個角度。帶愈多電，角度愈大。以此我們可以做一些數量的計算。還有一些原理大致相同的驗電器，只有一個中心棒子，僅一片薄金屬，如果你使金屬片帶電，這金屬片會向上。如果你充更多電，它將更往上。我現在手邊沒有驗電器，但我想讓你瞧瞧，如果我把自己充電，手中握著聖誕節金屬箔紙的裝飾。無論我帶的是正電或負電，假如我帶的電量夠多時，這些箔紙將會散開，所以這個概念很快的閃過，如果你得到足夠的電量，不管它是正或是負，那並不重要，這些鋁箔紙片將會散開。
一個最好使自己帶電的最好的方法就是使用Van de Graaff，不過正如我告訴你們的，這台機器並非絕對安全。所以總是有可能我無法經由這次實驗存活下來。不過別擔心，如果是這樣的話，一定會有人來教授這堂802，不過他可能不會再示範這個實驗給你看。所以你可要仔細的看好，這也許是你一生中唯一看到的機會了。我將會把燈光調好照設到Van de Graaff，我總是在這時感到很害怕現在我要打開機器，其實, 用這些細紙條跟Van de Graaff電磁場產生器做實驗會有很好的效果，或者是，Marco你有勇氣打開它吧!你會將它打開嗎?等等, Marco, 這個腳踏的小凳子太接近了, 這不太安全，你準備好了嗎?你緊張嗎?我們永遠都不再見面啦!好，試著看著這金屬做的流蘇不要看我，謝謝。可以動手了，我已經是ㄧ個活生生的驗電器，如果今天天氣合作的話，而且我也留長頭髮的話，你會看到我的頭髮如驗電器一般，我們可以試試看。可以證明看看。它成功了嗎?是的!好，這個周末記得要站在鏡子前面脫去尼龍上衣，好好的在家享受這個實驗。絕對不要試這個。下星期五見!
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Last Modified 2/14/07 5:12 PM
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