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ECE802 – Lec11 Note: the red color words or question marks are the words that I cannot recognized!![00:00~10:01] So far, we have already discussed in this course is electricity. Calm down! But this course is about electricity and magnetism. Today, we are going to talk about magnetism. In the 15th century BC, the Greeks already knew that there are some rocks that attract bit of iron. And they are very plentiful in the district of Magnetsia. And so that where the name magnet and magnetism come from. The rock contains iron oxide which we will call an magnetite. In 1100 AD, the Chinese used these needles of magnetite to make compasses. And in the 13th century, it was discovered that magnetite has two places of maximum attractions, which we called poles. So if you take one piece of magnetite, it always has two poles. Lets call one pole A and the other B. A and A repel each other, B and B repel each other, but A and B attract each other. There is a huge difference between electricity and magnetism which electricity it also has two polarities. You are free to choose a plus or a minus pole. With magnetism, you don’t have that choice. The poles always come in pairs. Isolated magnetic pole do not exist or as a physicist will say magnetic monopoles do not exist as far as we know. If anyone find the magnetic monopole, and don’t think that people are not looking, that were certainly be worth for a Nobel Prize. In principle, they could exist, but as far as we know, they don’t exist. They have never been seen. Electric monopole do exist. If you have a plus charge that is an electric monopole, you have a minus charge, electric charge, that is an electric monopole. If you have a plus and minus of equal strength that is an electric dipole. When ever you have a magnet, you always have a magnetic dipole. That is no such thing as a magnetic monopole. In the 16th century, Gilber discovered that the Earth is real a giant magnet and he experimented with a compass and he effectively the first person to map out the magnetic field of the Earth. And if you take one of those magnetite needles, and the needle is pointing in this direction which is the direction of the northern Canada. Then, by convention we called this side of needle plus……oh! Not plus! North, and we called this side of needle South. Since A repels A, and B repels B, but A and B attract each other. In north Canada is the magnetic south pole of the Earth, not the magnetic north pole. That is the details now of course. So this is the way that we defined the direction, north and south of these magnetite needles. A crucial discovery was made it in 18th 19th by the daily physics Urchithat. And he discovered that the magnetic needle will response to a current in a wire. And this link magnetism was electricity. And this is the arguing perhaps the most important experiment ever done. 1st step concluded that the current in the wire produces the magnetic field. And that magnetic needle moves in response that the magnetic field which is produced by the wire. And this magnificence discovery caused an explosion of an activitie at 19th century. Notably by Amp here by Farad and by Henry. And it colligate into the brilliant work of the scholastic theoretician Maxwell. Maxwell composes a universal field theory which connected electricity with magnetism. And that is the heart of this course. Maxwell’s equations. You will see them all field all four by the end of this course. If I have a current, a wire. Lets say the wire is perpendicular to the blackboard, and the current goes into the blackboard. I put a cross in there. If the current comes out the blackboard, I put the dot there. And there is a historical reason for that. You have always talked about vector in 18.01 or in other course. But you have never seen the vector. And I am going to show you the vector. This is the vector. And this is when it comes to you. That’s why you see the dot. And this is what it goes away from you, that is why you see a cross. So, this current when it is going into the blackboard, I can put this magnetite needles in the facility and they were then do this. And when I put it here, it will go like this. And they follow the tangent of a circle. And this is the way that we define magnetic field and in the direction of the magnetic field namely that the magnetic field. So which we always write the symbol B, magnetic field, is now in the clockwise direction. By convention, current goes into the blackboard. And if you ever forget that, used what we called the right hand corkscrew rule (right hand cork service rule). If you take a corkscrew, and you turn it clockwise, the corkscrew could go into the board. That connects the B with the current. If you take a corkscrew and you rotate it counterclockwise then the corkscrew rule will come to you, comes out of the cork. And that is how you find the magnetic field going around current wires. It is just a convention. I want to show you how an magnetic needle response to a current. I have here a wire to which I am going to run fabulous amount of the current. Something like 300A here. And you are going to see that wire there. Let me get my lights right. See how I want to go. This is the way I want it to go. OK! Get optimum light there. When I draw a current………here you see the magnetite, we called it compass now nowadays and it is line up with the direction of the magnetic field of the Earth. We are going to run 300A through here and it will change the direction. It wil change the direction, which is going to be a magnetic field around the wire like this. So we will go like this. The current that I run is so high that things began to smell that smoke with the in second. The battery is not going to like when I draw a such high current. I can therefore do it only for few seconds. So this compass will swing in this direction and it starts to isolate. I can’t keep the current so long that it stops the isolation. So I will stop it by hand and convince you that is really the equilibrium position. So, if you ready for that……… so we got it now connection. Watch it! 3…2…1…0… there it goes! Now I stop it, the current is still going. That is the equilibrium position. And I will stop the current. And now I will reverse the current in the opposite direction. Now you will see that it swins backward. Under the 80 degree difference of direction. 3…2…1…0…there it goes! I will stop it few seconds. That is the equilibrium position. And I will let it go. So you have seen that ……indeed the magnetic needle responded to the magnetic field that was produce by the wire. That was the greatest discover by Urchithat. He discovered this demonstration all by himself. It may not be very spectacular for you, but historically it is abnormal important. I will argue……perhaps the most important demonstration, the most important research ever done in physics. Because it connects the electricity with magnetism. It was the foundation of the creation of the whole concept of a field theory. H equals minus reaction. And that means that if a wire that runs a current has a force on the magnet. Then of course, the magnet must also observe of the force on the wire. And I am going to demonstrate that to you, too. But now, I have much more important magnet for which I will use this one. And the magnet will not move. It is so heavy so that it can’t move. So now you will only see the wire move. And the basic idea is as then as follows.[10:02~20:42] Here is the magnet. This is the north pole of the magnet and this is the south pole. I don’t remember which is which to be effect to you. So the magnetic field runs like that also. And I have here a current wire, a wire that once there has a current through to it. The wire is perpendicular to the blackboard. If……when I turn the current on……if the current is comes out of the blackboard. Now I have 50% chance because I really don’t remember whether this is North or this is South. But lets assume that this is the configuration that the current is coming out of the blackboard. Then you will see this wire experience the force up. It is experimental affect that the force ^ F on the wire is always in the direction of ^ I cross ^ B. These are unit vectors. And since ^ I is coming out of the blackboard, if I cross ^ I with ^ B, I get a force in this direction. And so if I reverse now the current. If the current goes like this, then of course, the wire wants to go down. Now I will show you both. But I don’t know which one will come first because I didn’t mark the poles. ……ah……oh…... So you see it now …… slightly different from the way I draw it. I drawn you the magnetic field looking this way. But it is of course much nice if you can see it this way. So you see the wire. And there is the magnet. And now I am going to run few hundreds amps through that wire. And then, either will jump up or will jump down and then I will reverse the current. And that the opposite thing will happen. OK! We ready for this? 3…2…1…0…! Notice that was a distinct force down. The force was so high that even pull down the supports. So now I can predict if I reverse the current from this experiment, that now the wire will jump up. There we go! I know now exactly because I switch this way. So now I will switch this way and the wire will jump up. That’s the first draw when you seen. 3…2…1…0...! Very clear saw it come up! OK! Take this down. All right. If I have a wire to which I run a current. Lets say I run a current I1. This is a wire. It will produce a magnetic field, right hand corkscrew, right here that the magnetic field will be in the blackboard. I called it B1. Right here, it will be out of blackboard. But that is irrelevant right now. But it is out of the blackboard. Here is into the blackboard. And here I have another wire. I am going to run a current I2. There will be a force now on this wire in the direction ^ I cross ^ B. Take your hand, ^ I cross ^ B, that force is up. So this wire will experience the force up. But of course, if this wire has experienced force up, since H equals the minus reaction, this wire will experience a force down. So it will go toward to each other. They will be attracted by each other. You can use an independent way to confirm that the force here is down. This is the force. For real will be enough to say action H is equals the minus reaction due to third law. But if you want to put in here, the magnetic field, B2, which is the result of this current, which is of course, out of the blackboard. Remember the right hand corkscrew, then you will see that this force now here must be in the direction I1 cross with B2. And that is down. That is exactly what I predicted. So the two wires will go toward to each other. However, if I leave everything the same but I reverse the direction of I2……so now the two currents are opposite in the direction, then the force will flip it over. And so now the two wires will repel each other. And I will demonstrate that to you. I have those two wires here and you will see them there on the screen. I will explain what you are looking at in some detail. The two wires run vertically. This is one wire and this is the other wire. And when I run the current in the same direction, then they will attract each other. You will see that shortly. 3…2…1…0…! See they are going toward to each other. I will do it again. Now! If, I run the current in opposite direction, they will repel each other. Now I will run them opposite direction. They repel each other. Now I will do it again. 3…2…1…0…they repel to each other. The reason why I show you this demonstration is different one. What I want you to appreciate that if I have this conducting plate of aluminum. It is a conductor. And I put that in between the two wires, and I repeat the experiment that exactly the same thing will happen. And that tells you that the magnetic fields are really very different from electric fields, because the electric fields will be heavily effective by a conducting sheet like this. Magnetic fields are not. So what I am going to do now is I am going to put this plate in between. And then, I am going to again force the current in the opposite direction and so you will see the wires repel each other as if the plate were not there. 3…2…1…0…There you go! So, magnetic fields are the very interesting story to tell. However, electricity and magnetism are connected. How do we to find the strength of the magnetic field? With the electricity, we define the strength of the electric field in the following way. We measure the force, electric force à Fel, or the charge on the electric charge q, and then the electric force is the charge times the electric field (à E). 17.44 That determines the strength of the electric field. Would it be nice if we could now say ……OK! The magnetic force (à FB) is the magnetic charge qB times the à B field. So that will then define the magnitude of the à B field. It will be nice, but as long as we haven’t found the magnetic monopole, we can’t do it. If you come a magnetic monopole tomorrow, then I can do this. But we have no magnetic monopoles. And so it cannot be down this way. How is the magnetic field then defined? Well, that is defined in the following way. I take an electric charge and the electric charge is q. And if that electric charge move with velocity à v, and there is a magnetic field where the electric charge is moving. Then there is an experimental affect that the force à F is always perpendicular to à v. If you want to call that à FB is the magnetic indication. That is fine. So there is a magnetic field. The charge is moving with this velocity à v. And there is a force on that charge which is always perpendicular to à v. The magnitude of that force à FB is proportional to the speed of the particle (υ). And it is also proportional to the charge (q) itself. If I double the charge, then the force doubles. If I double the speed, then the force doubles. And so the way that we define now, magnetic field strength à FB is this way, the force (à FB) that I give it the B to remain you, the magnetic; q is the electric charge, à v is the velocity of electric charge, the cross product with à B. And you see that the forces is always perpendicular to à v. And that is linearly proportional with the speed (à v) that is linearly proportional with the charge q. And this is often called the Rouland Force after the Dutch physicist. This equation is completely sign sensitive. If you charge from a positive charge to an negative charge, then the force flips over, 180 degrees. You change the direction of à v, the force flips over. Change the direction of à B, force flips over. So it’s completely sign sensitive equation. The unit for magnetic field strength follows from this equation. This (à FB) is Newtons; q is coulomb; and à v is meters per second. So this will be the unit for magnetic field strength but no one who will ever say that. In SI unit, this will be SI unit. We called that 1 T (Tesla), for which we write one capital T.[20:43~30:56] The tesla is an extremely strong magnetic field. The magnetic field of this magnet is only 2/10 of the Tesla. And that is a very strong magnet. We often used therefore an unit which is the Gauss (G) which is not a SI unit, but you see it often in book. And 1 Gauss (1G) is 10–4 T. The Earth magnetic field is roughly half the Gauss. And so this magnet is about 2kG. But in SI unit, is Tesla. If you look at the television or the screen of your computer, you have a fluorescent screen and the television there are electro-guns that rest scan through the fluorescent screen. On the television screen you have 525 lines and the electro-guns scan that in 1/30 of the second. And the intention changes of these electrons beans create images. So if you look at the tube from the side, then there are electrons, one moment in time they may move like this, another moment they may be here in the rest of the scan. So it is clear if you bring a strong magnet in the facility of your television screen that you will distort the image because you are now affecting the motion of this current of these electrons. And that is a very famous artist name Namupike, who uses this for his art. And almost every major museum in this world has a work by Namupike, which distorted images using magnets and using television screen. I don’t want competes with a Numupike but I do want to show this to you. I have there television set and I have a very strong magnet and I will try to distort that image and give you the best light that we know how to and I suggest we try to find a program that we hate. So here is my magnet………oh…Man, this is extremely strong magnet. And lets turn on the television. And lets see what we can get first. Oh! I turn it off in stead of on! (TV program sounds……………I don’t think………) neither do I!………Oa! I hate commercials. Lets go for commercial. Oa~ I hate commercials. Now watch it closely. Here comes my magnet. There is the image. Did you see that? Don’t do this to your own computer because once you have done this, it may not looks the same. But these electrons now………can you see it?………Did you see the distortion? Can you see the distortion? You are so quite. OK! So you have seen that ……so you have seen that we can with a magnet and a moving charge that we can change the direction of the moving charges, force on the moving charges. If you have an electric field as well as a magnetic field, then of course, you have also an electric force. And so the total force à Ftot on a moving charge particle will then be q times the electric field vector à E, plus à vcross à B. And this of course, we have seen it before. An electric field can do work on a charge. Remember q*∆v can be positive, can be negative, but it can’t do work. It can change the connective energy of the charge. Magnetic field can never do work on the moving charge. And the reason is that the force is always perpendicular to the velocity à v. And so the force is always perpendicular to the motion. You can change the direction of the motion, but you cannot change the connective energy. So that is the fundamental difference between the electric force and the magnetic force. So now I want to calculate with you the force on a current that runs the wire I through it. And we have a magnetic field, à B. So we are going to be slowly……we are going to be more and more quantitative. This by the way is often also called the law and force. Just a combination of the two. That one certainly is. So let us start with a wire and the wire that runs a current through. Here is the wire. And the current is I. And lets say at this point here we have a magnetic field à B. And the magnetic field can be difference along the wire in principle. Here, I have a plus charge +dq, and this charge is running through the wire with a draft velocity Vd. Lets first think about what happen if the current is zero. If the current is zero at room temperature, these free electrons in this wire have huge speed, 3 million meters per second. Way large then the drift velocity. But, they are in all chaotic directions. Random motions. It is a thermo motions. And so on each individual charge, there will be a force but the average out to be zero. It is not until I run a current that each charge is going to work through with a very slow drift of velocity. And now of course therefore, is not zero. So lets have this charge, dq, that is moves in this direction. And so that gives me a current. And let this angle be θ between them. θ is going to be important because it is a cross product between velocity Vd and à B. That means the sign of thisθ comes in later. You will say……… I hope you will say …… well, listen man, this is ridiculous, positive charges don’t move through wires. It is the electrons that move through wires. They are responsible for the current. And the electrons have the negative charge and they go in this direction. You are right! Perfectly fine! However, an negative charge going in this direction. It is mathematically exactly the same as the positive charge going in that direction. In both cases we do agree that the current is in this direction. So I have preferred for mathematical reason to take a +dq charge going in this direction rather then taking a –dq charge that goes with this drift velocity in that direction. So there is no difference at all in the outcome that you will see. So on this charge, there is a force, à dFB. This is a magnetic force. And that is the charge dq, that equation, times à vd cross à B . Well, à vd was that drift velocity, and here is the magnetic field at this location. The current through the wire, everywhere on the wire must be dq/dt because that is the definition of the current, how many coulombs per second. Current is always dq/dt. So I can also write this as I*dt times à vd cross à B . But I remember 801 class, that à vd times dt, that is a speed times a time, is a distances. And I called that distances à dl. It is a distance along the wire. I will put the distance in here now because I don’t want to collapse my drawing. So this charge in time, dt, moves over that distances. That is the vector in 801 class. So I can write down for this product. I can write down the à dl. So I can also write down that à dFB equals I times à dl cross à B. Last Modified 1/22/06 10:28 PM |
