electricitymagnetism-2- Chinese

Translator:	abhouse24@yahoo.com.tw
Date finished:

Brief Bio:

(0:05)  Today, I am going to work with you on a new concept, and that is a concept of what we called Electric Field.  We'll spend a whole lecture on Electric Field.  If I have a charge, I just choose Q, capital Q and plus (+· ), at a particular location, and another location, I have another charge little q, I think that might test charge ( · ).  And there is a separation betweenthe two, just r.  The unit vector from capital Q to the little q is this vector ( r vector).  So now I know that the two charges if they were positive, if the little q is positive, they would repel each other; they would, if little q were negative, they would attract each other.  And that is force, the F (F vector), and last time we introduced Coulomb's Law, that force is equal tolittle q times capital Q, times Coulomb's constant divided by r squares in direction of r roof

(Equation).  The two have same sign to this direction, or the opposite sign if it's in the other direction.

(1:38)  And now I introduce the idea of electric field which we symbolize with capital E (E vector).  The capital E (E vector), at that location P, where have my test charge little q at that location p is simply the force that the test charge experience divided by that test charge, so I eliminate the test charge.  So I have something looked quite similar, but it doesn't have the little q in it any more, and it is also a vector (Equation).  And by convention, we choose the force, such that if this is a positive test charge, then we say the E field is away from Q if Q is positive; if Q is negative, the force is in the other direction, and therefore E is in the other direction.  So we adopted the convention that the E field is always in the direction that force is on a positive test charge.  Which we've gained now is that you have taken out the little q, in another words, the force here, depends on little q, electric field is not.  So the electric field is a representation for what happened around the charge plus Q, it could be a very complicated configuration and electric field tells you something about that charge configuration.  The unit for electric field, you can see it's Newton divided by coulomb [N/C], in SI unit, and normally we won't indicate the unit, we just leave that as it is.

我現在向大家介紹一個場的概念，以大寫E來表示。E，代表測試電荷q在它所處的位置上所感受到的力。也就是消去測試電荷q。我現在得到了一個和力公式很像的東西，仍然是一個向量，一個有方向的東西，但是不再有小q在裡面了。力的正負方向可由: 如果測試電荷為正，大Q也為正，電場的方向是由大Q發散出去。假設大Q為負，電場就是相反方向。如此，我們承襲了傳統的寫法，電場的方向，永遠是以測試電荷帶正電時決定的方向為方向。我們學到現在，就是把小q提出來。力的方向取決於小q。電場，卻不受測試電荷小q的影響。電場E，代表著電荷大Q週遭發生的事情，它可能非常的複雜，電場E就是告訴你這個電荷的組成。你可以看到，電場的單位是牛頓除以庫倫，SI單位。通常我們不會特別的註明，我們就先暫時不理它。

(3:28)  Now we have graphical presentations for the electric field.  Electric field is a vector,so you expect arrows.  And I have here the example of a charge +3, so by convention, the arrows are pointing away from the charge in the same direction that the positive test charge would experience the force,and you know that, very close to charge, the arrows are larger, then farther away, that sort of represent, or trying to represent the influence of r square relationship.  Of course it cannot be very quantitative.  But the basic idea is it of course, it's spherically symmetric, this is point charge, the basic idea is, you see the field vectors and direction of the arrows tell you which the direction, the force would be if it's positive charge, and the length of the vector gives you idea of the magnitude.  And here I have another charge of minus 1 (-1), doesn't matter whether the minus 1 (-1) coulomb, or minus micro coulomb, just is a relative representation.  You see now the E field vectors, I reverse in direction to pointing forward, the minus charge by convention, and you go further out, they are smaller.  And you have to go all the way to infinitive, of course, for the field to become zero because one of our square fields falls off, and you have to be infinitive far away for you to not experience the principle any effect from the charge. 

現在讓我們來看電場的圖形表示，電場是個向量，理應看到箭頭。我這裡有一個帶有三個正電的電荷，根據以往的寫法，箭頭由電荷為中心向外指，測試電荷就會感受到這電場產生的力。你可以看到，愈接近電荷，箭頭愈長，愈遠的話，就是你看到的愈短了，它試著表示距離的平方的影響力。當然它並不是太精準。這是個點電荷，是球對稱。最基本的概念是，當你看到場向量，箭頭的方向告訴你，放了一個+1C的測試電荷所感受到的力的方向，箭頭的長度告訴你力的大小。我這裡有另一個帶有-1C的電荷，它是-1C或是-1mC不重要，只是個相對的表示法。根據傳統，我把箭頭畫相反方向，指向電荷。你走遠一點，箭頭就小一點。你走到無限遠處，電場就變成零，因為有與距離平方成反比的緣故。你必須要走到無限遠才可以感受到電場為零，否則你仍會感受到電荷本身的效應。

(5:18)  What do we do now when we have more than one charge?  Well, if we have several charges, here we have Q1 ·, and here we have Q2 ·, and here we have Q3 ·, and here we have Q of i, we have i charges.  And now we want to know what the electric field at point p.  So it's independent of the test charge that I put here, you can think if you want to, as the force per unit charge, you divided out the charge.  So now I can say what is the E field due to Q1 alone, that would be, if Q1 were positive, and this might be a representation for E1.  If Q2 were negative, this might be representation of E2, pointing to negative charge, and if this one (Q3) were negative, then I would have here the contribution E3, and so on, and now we use the superposition principle as we did last time which Coulomb's law, that the net electric field at point p is a vector, is E1 influence of charge Q1, plus the vector E2, plus E3 and so on.  And if you have i charges, this is sum of all i charges of individual E vectors.  Is it obvious that the superposition principle works?  No.  Does it work?  Yes.  How do we know it works?  Because it's consistent with all our experimental results, so we take this superimposition principle for granted.  And that is acceptable.  But it's not obvious. 

現在如果我們有多於一個電荷，該怎麼辦呢?假設我們有許多電荷，我們有Q1有Q2有Q3有Qi，也就是說有i個Q。我們想知道在點p這個地方的電場。電場與測試電荷無關。你可以這樣想，電場是每單位電荷感受到的力，把力除以測試電荷。我現在可以寫出Q1產生的電場E1，如果Q1是正的，這是E1的表示法。如果Q2是負的，這就是Q2的表示法，方向指向負電荷。如果這個是帶負電，它將貢獻電場E3，等等。現在我們使用疊加原理，就像我們上次在庫倫定律中使用到的。點p這的電場是個向量，由Q1貢獻的電場E1加上E2,E3…。如果你有i個電荷，這將會是它們所貢獻的電場向量的加總。疊加原理很明顯的是正確的嗎?不!那它是正確的嗎?是的!那麼它為什麼可以被接受的呢?因為它和所有的實驗都符合，所以我們視疊家原理為理所當然。它是可以被接受的，不過並不是顯而易見的。

(7:28)  If you tell me what the Electric field at this point is, which is vectorial sum of the individual vectors.  Then I can always tell you what the force will be, if I bring a charge at that location.  I take all the charge I have in my pocket, and I take it out of my pocket, and I put it out there in the location, and the charge of that point might be little q, then the force on that charge is always q times E, doesn't matter whether the q is positive, then it will be the same direction as E, if it's negative, it will be the opposite direction of E.  If q is large the force will be large, if q is small the force will be small.  So once you know the E field would be the result of the very complicated charge configurations, the real secret behind the concept over E field is that if you bring any charge at that location, and you know what force X at that point on that charge.

電場是向量的加總，如果你告訴我這點的電場是多少，我一定可以告訴你一個被帶到這裡來的電荷所受的電力是多少。我把我口袋中所有的電荷都拿出來，把它們放在這個地方，電荷是小q，那電力就會是小q乘以電場E，如果電荷為正，電力的方向就會與電場的方向相同，為負，就與電場的方向相反。如果q帶的電荷很多，電力就會很大，如果電荷很少，電力就會很小。電場背後的意義就是:一但你知道了構造非常複雜的電荷所場生的電場，當你把一顆電荷放在適當的位置，你就已經知道電荷所感受到的電力了。

(8:33)  If we try to be a little bit more quantitative, suppose I have here a charge +3, and here I have a charge -1.  Here is -1, and I want to know what the field configurations as a result of these two charges.  So you can go to any particular point, you get the E vector which is going away from the +3, you get one that goes to -1, and you have 2 vectors and add the two.  If you very close to -1, it's very clear because influence of r square relationship, that the -1 is probably going to win.  Let's, in our mind, take a plus charge now. And we put the plus charge now very close to -1, say we put it here; even thought +3 is trying to push it out, clearly -1 is most likely to win.  So it will probably be a force on my test charge in this direction (s), the net results of the vectors of the two.  Suppose I take the same test charge and I put it here, very far away, much far away than this separation.  What do you think now is the direction of the force of my plus charge?  Very far away!  Excuse me?  (Student answered.)  Why do you think it's to the left?  You think -1 wins?  (Student answered.) Do you really think -1 is through +3, because +3 is pushing it out?  And the -1 is trying to lure it because the test charge is positive.  (Student answered.)  Imaging all this way in Mass. Avenue, you think that this thing matters?  Who think the force is in this direction?  Who think it's in the direction (to the left)?  Very good, you help him, really.  The force is obvious in that direction because if you very far away, the field will be the same.  If you just have +3 and -1 somewhere here, which is +2.  So if you far away from the configuration like this, even if you are here, or if you are there, or away there, clearly the field is likely a +2 charge, and so force is one over r square, so therefore if you are far away and force is in this direction (a).  Now look what's very interesting. Here if you close to -1, it's in this direction (s).  Here if you are very far away, maybe I should be all the way here, it's in that direction (a).  So, that means there must be somewhere here a point where the E field is zero.  Because if the force is here in this direction (s), it ultimately turns over in that direction (a), there must be somewhere a point where E is zero, and that is part of your assignment.  I want you to find that point for a particular charge configuration.

現在我們試著數量化一點，假設我有一個+3電荷，一個-1電荷。這個是-1電荷。我現在想要知道，由這兩個電荷組成的電場。你可以到任何一點，就會得到+3電荷場生的電場正以電荷為中心向外散射，另外一電場是指向-1電荷，你有兩個向量，並將它們加起來。如果你很接近-1電荷，很明顯的，因為與距離成平方反比的關係，-1電荷會勝出。我們是著想像出一個+1測試電荷，把它放在離-1電荷很近的地方，這裡好了。即使+3電荷試著想把它推開，但很顯然的，-1電荷還是會贏。所以我的測試電荷，所受的力應該是這個方向，是兩個向量相加的結果。假設我拿了相同的測試電荷放在這裡，很遠很遠，比這個距離遠很多。你覺得現在這個情況下，我的測試電荷所受的電力是什麼方向?記住是很遠很遠喔!你講什麼?為什麼你覺得會是向左?你覺得-1電荷贏了嗎?

你真的認為-1勝過+3因為+3電荷試著推遠它嗎?而-1電荷試著誘惑它，因為測試電荷是帶正電?想像測試電荷已經到了麻州街了，你還認為你說的會發生嗎?還有誰認為電力是這個方向?有人認為電力是這個方向嗎?很好，你們幫了他。電力很明顯的是這個方向因為如果你已經在很遠的地方了，電場都長的一樣了。如果你就只有+3電荷-1電荷在這裡某個地方，相加起來是+2。所以如果你離這個組成很遠，你在這裡，或是那裡，甚至是那裡，這個電場就會像是+2電荷所產生的電場。電力是與距離平方成反比的，如果你離電荷很遠，電力是這個方向，一件很有趣的是發生了。假設你很靠近-1電荷，方向朝這。在很遠的地方，或許我應該站遠一點，電場的方向是朝這個方向。所以，這意味著空間中一定有一點電場為零。因為電力原本是朝這個方向，最後轉向另一個方向，表示這兩邊中一定有一點電場為零。這是你們其中的一項作業，我希望你們在某一電荷組成中，找出那一點。

 (11:46)  So let's now go to some graphical representation of a situation, which is actually +3, -1.  Try to improve on the light situation.  And let's see how these electric vectors, how they show up in the facility of these two charges.  So here you see the +3 and -1, relative unit, and let's take a look at this in some detail.  First of all, the length of arrows again indicates the strength, gives you the feeling of strength, not very quantitative of course. So let's first look at the +3, which is very powerful.  You see these arrows all go away from +3, and when you go closer to +3, they are stronger which is a representation of influence of r square field.  If you're very close to the -1, the arrows are pointing into the -1, because of one over r square, the -1 wins, so you see there clearly go in to the direction of -1.  But if you're in between the +3 to the -1 in this line, always the E field will be pointing from the plus (+) to the minus (-).  Because the plus is pushing out and the minus is sucking in so the two support each other. But now if you go very far away from this charge configuration, anywhere, but very far away, much farther than the distance between these two charges, so somewhere there, somewhere there, or somewhere there, or here, noticed that the arrows are always pointing away.  The reason is the +3 and -1 is as good as +2 if you are very, very far away.  But of course if you're very close in, then the field configuration can be very, very complicated.  But you see very clearly that these arrows are all pointing outwards.  None of them come back to -1, none of them point to the -1 direction, and that is because +3 is more powerful.  And then there is here this point, and only one point where by electric field is zero, if you put a positive test charge here, the minus will attract it, the plus will repel it, and therefore it comes to a point where the two cancel each other exactly.