1 00:00:00 --> 00:00:00,564 2 00:00:00,564 --> 00:00:05,081 So far, we have only discussed in this course, 3 00:00:05,081 --> 00:00:07,29 electricity. Calm down. 4 00:00:07,29 --> 00:00:12,309 But this course is about electricity and magnetism. 5 00:00:12,309 --> 00:00:16,324 Today, I'm going to talk about magnetism. 6 00:00:16,324 --> 00:00:21,745 In the fifth century B. ., the Greeks already knew that 7 00:00:21,745 --> 00:00:26,363 there are some rocks that attract bits of iron. 8 00:00:26,363 --> 00:00:31,082 And they are very plentiful in the 9 00:00:31,082 --> 00:00:35,26 district of Magnesia, and so that's where the name 10 00:00:35,26 --> 00:00:38,245 "magnet" and "magnetism" comes from. 11 00:00:38,245 --> 00:00:42,339 The rocks contain iron oxide, which we will call, 12 00:00:42,339 --> 00:00:45,238 uh, magnetite. In eleven hundred A. 13 00:00:45,238 --> 00:00:49,758 ., the Chinese used these needles of magnetite to make 14 00:00:49,758 --> 00:00:55,131 compasses, and in the thirteenth century, it was discovered that 15 00:00:55,131 --> 00:00:59,225 magnetites have two places of maximum attraction, 16 00:00:59,225 --> 00:01:03,233 which we call poles. So if you take one piece of 17 00:01:03,233 --> 00:01:07,429 magnetite, it always has two poles. 18 00:01:07,429 --> 00:01:10,426 Let's call one pole A, and the other B. 19 00:01:10,426 --> 00:01:14,37 A and A repel each other, B and B repel each other, 20 00:01:14,37 --> 00:01:18,866 but A and B attract each other. There is a huge difference 21 00:01:18,866 --> 00:01:21,469 between electricity and magnetism. 22 00:01:21,469 --> 00:01:25,097 With electricity, you also have two polarities, 23 00:01:25,097 --> 00:01:28,962 but you are free to choose a plus or a minus pole. 24 00:01:28,962 --> 00:01:32,275 With magnetism, you don't have that choice. 25 00:01:32,275 --> 00:01:35,036 The poles will always come in pairs. 26 00:01:35,036 --> 00:01:39,454 Isolated magnetic poles do not exist -- or, 27 00:01:39,454 --> 00:01:42,573 as a physicist would say, magnetic monopoles do not 28 00:01:42,573 --> 00:01:45,753 exist, as far as we know. If anyone finds a magnetic 29 00:01:45,753 --> 00:01:49,62 monopole -- and don't think that people are not looking -- that 30 00:01:49,62 --> 00:01:51,99 would certainly be worth a Nobel Prize. 31 00:01:51,99 --> 00:01:53,861 In principle, they could exist, 32 00:01:53,861 --> 00:01:56,293 but as far as we know, they don't exist, 33 00:01:56,293 --> 00:01:59,66 they have never been seen. Electric monopoles do exist. 34 00:01:59,66 --> 00:02:03,091 If you have a plus charge, that's an electric monopole. 35 00:02:03,091 --> 00:02:05,585 You have a minus charge, electric charge, 36 00:02:05,585 --> 00:02:11,372 that is an electric monopole. If you have a plus and a minus 37 00:02:11,372 --> 00:02:14,813 of equal strength, that is an electric dipole. 38 00:02:14,813 --> 00:02:18,866 Whenever you have a magnet, you always have a magnetic 39 00:02:18,866 --> 00:02:21,466 dipole. There is no such thing as a 40 00:02:21,466 --> 00:02:24,754 magnetic monopole. In the sixteenth century, 41 00:02:24,754 --> 00:02:29,19 Gilbert discovered that the Earth is really a giant magnet, 42 00:02:29,19 --> 00:02:32,707 and he experimented with compasses, and he was, 43 00:02:32,707 --> 00:02:35,766 effectively, the first per- person to map 44 00:02:35,766 --> 00:02:40,508 out the elec- the magnetic field of the Earth. 45 00:02:40,508 --> 00:02:44,6 And if you take one of those magnetite needles, 46 00:02:44,6 --> 00:02:48,514 and the needle is pointing in this direction, 47 00:02:48,514 --> 00:02:52,162 which is the direction of Northern Canada, 48 00:02:52,162 --> 00:02:56,699 then, by convention, we call this side of the needle 49 00:02:56,699 --> 00:03:01,859 plus -- uh, not plus -- north, and we call this side of the 50 00:03:01,859 --> 00:03:04,528 needle south. Since A repels A, 51 00:03:04,528 --> 00:03:08,62 and B repels B, but A and B attract each other, 52 00:03:08,62 --> 00:03:14,788 in north Canada is the magnetic South Pole of the Earth, 53 00:03:14,788 --> 00:03:18,594 not the magnetic North Pole. That's a detail, 54 00:03:18,594 --> 00:03:22,14 now, of course. So this is the way that we 55 00:03:22,14 --> 00:03:25,34 define the direction, north and south, 56 00:03:25,34 --> 00:03:30,27 of these magnetite needles. A crucial discover was made in 57 00:03:30,27 --> 00:03:34,508 eighteen nineteen by the Danish physicist Oersted. 58 00:03:34,508 --> 00:03:39,093 And he discovered that a magnetic needle responds to a 59 00:03:39,093 --> 00:03:44,542 current in a wire. And this linked magnetism with 60 00:03:44,542 --> 00:03:47,188 electricity. And this is arguably, 61 00:03:47,188 --> 00:03:51,038 perhaps, the most important experiment ever done. 62 00:03:51,038 --> 00:03:55,53 Oersted concluded that the current in the wire produces a 63 00:03:55,53 --> 00:03:58,979 magnetic field, and that the magnetic needle 64 00:03:58,979 --> 00:04:03,551 moves in response to that magnetic field which is produced 65 00:04:03,551 --> 00:04:06,92 by the wire. And this magnificent discovery 66 00:04:06,92 --> 00:04:11,652 caused an explosion of activity in the nineteenth century -- 67 00:04:11,652 --> 00:04:15,582 notably by Ampere, by Faraday, and by Henry -- and 68 00:04:15,582 --> 00:04:20,555 it culminated into the brilliant work of the 69 00:04:20,555 --> 00:04:25,518 Scottish theoretician Maxwell. Maxwell composed a Universal 70 00:04:25,518 --> 00:04:29,283 Field Theory, which connects electricity with 71 00:04:29,283 --> 00:04:32,449 magnetism. And that is at the heart of 72 00:04:32,449 --> 00:04:35,187 this course. Maxwell's equations. 73 00:04:35,187 --> 00:04:38,524 You will see them, all fear -- all four, 74 00:04:38,524 --> 00:04:42,46 by the end of this course. If I have a current, 75 00:04:42,46 --> 00:04:48,963 a wire, let's say the wire is perpendicular to the blackboard, 76 00:04:48,963 --> 00:04:53,005 and the current goes into the blackboard, I put a cross in 77 00:04:53,005 --> 00:04:55,629 there. If the current comes out of the 78 00:04:55,629 --> 00:04:59,529 blackboard, I put a dot there. And there is a historical 79 00:04:59,529 --> 00:05:02,507 reason for that. You're always talked about 80 00:05:02,507 --> 00:05:05,982 vectors, in eighteen oh one, and in other courses, 81 00:05:05,982 --> 00:05:10,095 but you're never seen a vector. And I'm going to show you a 82 00:05:10,095 --> 00:05:11,797 vector. This is a vector. 83 00:05:11,797 --> 00:05:14,138 And this is where it comes to you. 84 00:05:14,138 --> 00:05:18,109 That's when you see a dot. And this is where it goes away 85 00:05:18,109 --> 00:05:23,161 from you. That's when you see a cross. 86 00:05:23,161 --> 00:05:27,541 So this current, when it's going into the 87 00:05:27,541 --> 00:05:33,126 blackboard, I can put these magnetite needles in its 88 00:05:33,126 --> 00:05:37,069 vicinity, and they will then do this. 89 00:05:37,069 --> 00:05:41,887 And when I put it here, it will go like this. 90 00:05:41,887 --> 00:05:48,348 And they follow the tangents of a circle, and this it eh way 91 00:05:48,348 --> 00:05:52,822 that we define magnetic fields, 92 00:05:52,822 --> 00:05:56,787 and the direction of the magnetic field, 93 00:05:56,787 --> 00:06:03,192 namely, that the magnetic field -- for which we always write the 94 00:06:03,192 --> 00:06:09,495 symbol B, magnetic fields -- is now in the clockwise direction. 95 00:06:09,495 --> 00:06:13,053 By convention, current goes into the 96 00:06:13,053 --> 00:06:17,119 blackboard. And, if you ever forget that, 97 00:06:17,119 --> 00:06:23,117 use what we call the right-hand corkscrew rule. 98 00:06:23,117 --> 00:06:27,374 If you take a corkscrew, and you turn it clockwise, 99 00:06:27,374 --> 00:06:30,013 the corkscrew goes in the board. 100 00:06:30,013 --> 00:06:33,077 That connects the B with the current. 101 00:06:33,077 --> 00:06:38,015 IF you take a corkscrew and you rotate it counterclockwise, 102 00:06:38,015 --> 00:06:43,037 then the corkscrew would come to you, comes out of the cork. 103 00:06:43,037 --> 00:06:47,634 And that's how you find the magnetic field going around 104 00:06:47,634 --> 00:06:50,783 current wires. It's just a convention. 105 00:06:50,783 --> 00:06:54,87 I want to show you how a magnetic 106 00:06:54,87 --> 00:06:59,468 needle responds to a current. I have here a wire through 107 00:06:59,468 --> 00:07:03,732 which I'm going to run a fabulous amount of current, 108 00:07:03,732 --> 00:07:08,749 something like three hundred amperes, and you're going to see 109 00:07:08,749 --> 00:07:13,013 that wire there -- I'm going to get my lights right, 110 00:07:13,013 --> 00:07:17,36 see how I want it to go, this is the way I want it to 111 00:07:17,36 --> 00:07:22,544 go, get you optimum light there. When I draw a current -- here, 112 00:07:22,544 --> 00:07:28,194 you see the the magnetite, the -- we call it a compass, 113 00:07:28,194 --> 00:07:31,942 nowadays -- and it's lined up in the direction of the magnetic 114 00:07:31,942 --> 00:07:34,645 fields of the Earth. We're going to run three 115 00:07:34,645 --> 00:07:37,779 hundred amperes through here, and it will change the 116 00:07:37,779 --> 00:07:41,342 direction, it will change the direction which is -- there's 117 00:07:41,342 --> 00:07:44,046 going to be a magnetic field around the wire, 118 00:07:44,046 --> 00:07:46,135 like this. So it will go like this. 119 00:07:46,135 --> 00:07:49,76 The current that I run is so high that things begin to smell 120 00:07:49,76 --> 00:07:52,955 and smoke within seconds. The battery is not going to 121 00:07:52,955 --> 00:07:55,351 like it when I draw such a high current. 122 00:07:55,351 --> 00:07:58,668 I can, therefore, only do it for a 123 00:07:58,668 --> 00:08:01,843 few seconds. So this compass will swing in 124 00:08:01,843 --> 00:08:05,094 this direction, and it starts to oscillate, 125 00:08:05,094 --> 00:08:08,888 I can't keep the current so long that it stops the 126 00:08:08,888 --> 00:08:11,83 oscillation. So I will stop it by hand, 127 00:08:11,83 --> 00:08:16,475 and convince you that that's really the equilibrium position. 128 00:08:16,475 --> 00:08:19,959 So if you're ready for that -- so we get, now, 129 00:08:19,959 --> 00:08:23,21 connection, watch it three, two, one, zero. 130 00:08:23,21 --> 00:08:26,694 There it goes. Now I'll stop it -- the current 131 00:08:26,694 --> 00:08:30,945 is still going. You see, that's the -- that is 132 00:08:30,945 --> 00:08:34,078 the equilibrium position. And I will stop the current. 133 00:08:34,078 --> 00:08:37,034 And now I will reverse the current, in the opposite 134 00:08:37,034 --> 00:08:40,108 direction, now you will see that it swings backwards. 135 00:08:40,108 --> 00:08:42,827 It -- hundred and eighty degrees in a different 136 00:08:42,827 --> 00:08:44,364 direction. Three, two, one, 137 00:08:44,364 --> 00:08:45,487 zero. There it goes, 138 00:08:45,487 --> 00:08:47,674 I will stop it, [sniffs], few seconds, 139 00:08:47,674 --> 00:08:50,689 that's the equilibrium position, and I'll let it go. 140 00:08:50,689 --> 00:08:53,467 So you've seen that, indeed, the magnetic needle 141 00:08:53,467 --> 00:08:57,073 responded to the magnetic field that was produced by the wire, 142 00:08:57,073 --> 00:09:02,423 this was the great discovery by Oersted, the discovery -- this 143 00:09:02,423 --> 00:09:04,491 demonstration, all by itself, 144 00:09:04,491 --> 00:09:08,48 may not be very spectacular for you, but, historically, 145 00:09:08,48 --> 00:09:11,656 it is of enormous importance. I would argue, 146 00:09:11,656 --> 00:09:14,685 perhaps, the most important demonstration, 147 00:09:14,685 --> 00:09:18,231 the most important research ever done in physics, 148 00:09:18,231 --> 00:09:21,629 because it connects electricity with magnetism. 149 00:09:21,629 --> 00:09:26,061 It was the foundation of the creation of the whole concept of 150 00:09:26,061 --> 00:09:29,09 a field theory. Actually, [unintelligible] 151 00:09:29,09 --> 00:09:33,321 reaction, and that means that if a wire 152 00:09:33,321 --> 00:09:37,1 that runs a current has a force on a magnet, then, 153 00:09:37,1 --> 00:09:41,496 of course, the magnet must also exert a force on the wire. 154 00:09:41,496 --> 00:09:44,966 And I'm going to demonstrate that to you, too, 155 00:09:44,966 --> 00:09:48,128 but now, I have a much more potent magnet, 156 00:09:48,128 --> 00:09:52,678 fro which I will use this one, and the magnet will not move, 157 00:09:52,678 --> 00:09:57,229 it's so heavy that it can't move -- so now you will only see 158 00:09:57,229 --> 00:10:02,318 the wire move. And the basic idea is then as 159 00:10:02,318 --> 0. follows, here is that magnet. 160 0. --> 00:10:04,875 Oh, I turned it off instead of 161 00:10:04,875 --> 00:10:09,817 This is the north pole of the magnet, and this is the south 162 00:10:09,817 --> 00:10:14,93 pole -- I don't remember which is which, to be frank with you 163 00:10:14,93 --> 00:10:19,106 -- so the magnetic field would run, then, like so, 164 00:10:19,106 --> 00:10:21,833 and I have, here, a current wire, 165 00:10:21,833 --> 00:10:26,178 a wire that runs a current through it -- the wire is 166 00:10:26,178 --> 00:10:33,336 perpendicular to the blackboard. If, when I turn the current on, 167 00:10:33,336 --> 00:10:37,995 if the current is coming out of the blackboard -- and I have 168 00:10:37,995 --> 00:10:42,101 fifty percent chance, because I really don't remember 169 00:10:42,101 --> 00:10:46,997 whether this is north or south -- but let's assume that this is 170 00:10:46,997 --> 00:10:50,787 the configuration, that the current is coming out 171 00:10:50,787 --> 00:10:54,34 of the blackboard, then you will see this wire 172 00:10:54,34 --> 00:10:58,288 experience a force up. It is an experimental effect 173 00:10:58,288 --> 00:11:02,868 that the force on the wire is always in the direction of I 174 00:11:02,868 --> 00:11:07,131 cross B. These are unit vectors. 175 00:11:07,131 --> 00:11:10,855 And since I is coming out of the blackboard, 176 00:11:10,855 --> 00:11:14,406 if I cross I with B, I get a force in this 177 00:11:14,406 --> 00:11:17,004 direction. And so if I reverse, 178 00:11:17,004 --> 00:11:21,94 now, the current -- if the current goes like this -- then, 179 00:11:21,94 --> 00:11:25,058 of course, the wire wants to go down. 180 00:11:25,058 --> 00:11:29,908 And I will show you both. But I don't know which one will 181 00:11:29,908 --> 00:11:33,631 come first, because I didn't mark the poles. 182 00:11:33,631 --> 00:11:35,796 Ahh -- uhh. So you see it, 183 00:11:35,796 --> 00:11:40,559 now, slightly different from the way I 184 00:11:40,559 --> 00:11:43,585 have drawn it. I've drawn you the magnet 185 00:11:43,585 --> 00:11:46,455 looking this way, but it's, of course, 186 00:11:46,455 --> 00:11:49,326 much nicer fro you to see it this way. 187 00:11:49,326 --> 00:11:52,739 So you see the wire, and there is the magnet, 188 00:11:52,739 --> 00:11:57,238 and now I'm going to run a few hundred amperes through that 189 00:11:57,238 --> 00:12:01,815 wire, and then it either will jump up, or it will jump down, 190 00:12:01,815 --> 00:12:06,237 and then I will reverse the current, and then the opposite 191 00:12:06,237 --> 00:12:07,866 thing will happen. OK. 192 00:12:07,866 --> 00:12:10,504 We ready for this? Three, two, one, 193 00:12:10,504 --> 00:12:14,578 zero. Notice, there was a distinct 194 00:12:14,578 --> 00:12:19,082 force down, the force was so high that it even pulled down 195 00:12:19,082 --> 00:12:22,48 the supports. So now I can predict that if I 196 00:12:22,48 --> 00:12:27,063 reverse the current from this experiment, that now the wire 197 00:12:27,063 --> 00:12:30,066 will jump up. Here we go -- I know now, 198 00:12:30,066 --> 00:12:34,807 exactly, because I switched it this way, so now I will switch 199 00:12:34,807 --> 00:12:37,81 it this way, and the wire will jump up. 200 00:12:37,81 --> 00:12:40,339 That's the first drawing you see. 201 00:12:40,339 --> 00:12:41,998 Three, two, one, zero. 202 00:12:41,998 --> 00:12:46,537 Very clear. You saw it come out. 203 00:12:46,537 --> 00:12:49,346 OK. Let me take this down. 204 00:12:49,346 --> 00:12:52,716 All right. If I have a a wire, 205 00:12:52,716 --> 00:12:59,346 through which I run a current -- let's say I run a current I 206 00:12:59,346 --> 00:13:05,862 one through this wire -- it will produce a magnetic field, 207 00:13:05,862 --> 00:13:11,705 right-hand corkscrew, right here, that magnetic field 208 00:13:11,705 --> 00:13:19,949 will be in the blackboard -- I'll call it B one -- right 209 00:13:19,949 --> 00:13:23,132 here, it will be out of the blackboard. 210 00:13:23,132 --> 00:13:25,729 But that's irrelevant right now. 211 00:13:25,729 --> 00:13:28,326 But it is out of the blackboard. 212 00:13:28,326 --> 00:13:33,268 Here, it's in the blackboard. And here, I have another wire, 213 00:13:33,268 --> 00:13:35,949 I'm going to run a current I two. 214 00:13:35,949 --> 00:13:39,216 There will be a force now, on this wire, 215 00:13:39,216 --> 00:13:42,818 in the direction I cross B. Take your hands, 216 00:13:42,818 --> 00:13:45,666 I cross B [krrk], that force is up. 217 00:13:45,666 --> 00:13:50,524 So this wire will experience a force up. 218 00:13:50,524 --> 00:13:53,764 But of course, if this wire experiences a 219 00:13:53,764 --> 00:13:57,327 force up, since action equals minus reaction, 220 00:13:57,327 --> 00:14:00,405 this wire will experience a force down. 221 00:14:00,405 --> 00:14:03,158 So they will go towards each other. 222 00:14:03,158 --> 00:14:06,074 They will be attracted by each other. 223 00:14:06,074 --> 00:14:10,852 You can in an independent way confirm that the force here is 224 00:14:10,852 --> 00:14:13,12 down. That this is the force. 225 00:14:13,12 --> 00:14:17,331 For me, it would be enough to say action equals minus 226 00:14:17,331 --> 00:14:23,035 reaction, Newton's Third Law. But if you want to put in here, 227 00:14:23,035 --> 00:14:26,354 the magnetic field B two, which is the result of this 228 00:14:26,354 --> 00:14:28,843 current, which is, of course, out of the 229 00:14:28,843 --> 00:14:32,29 blackboard -- remember the right-hand corkscrew rule -- 230 00:14:32,29 --> 00:14:35,098 then you will see that this force, now, here, 231 00:14:35,098 --> 00:14:38,481 must be in the direction of I one, crossed with B two. 232 00:14:38,481 --> 00:14:40,97 And that's down, which is exactly what I 233 00:14:40,97 --> 00:14:43,14 predicted. So the two wires will go 234 00:14:43,14 --> 00:14:46,267 towards each other. However, if I leave everything 235 00:14:46,267 --> 00:14:50,033 the same, but I reverse the direction of I two -- so now the 236 00:14:50,033 --> 00:14:53,927 two currents are in opposite direction -- 237 00:14:53,927 --> 00:15:00,642 then the forces will flip over, and so now the two wires repel 238 00:15:00,642 --> 00:15:05,155 each other. And I will demonstrate that to 239 00:15:05,155 --> 00:15:08,678 you. I have those two wires here, 240 00:15:08,678 --> 00:15:13,192 and you will see them there on the screen. 241 00:15:13,192 --> 00:15:18,916 I will explain what you're looking at in some detail. 242 00:15:18,916 --> 00:15:24,2 The two wires run vertically -- this is one wire, 243 00:15:24,2 --> 00:15:30,848 and this is the other wire -- and when I run a 244 00:15:30,848 --> 00:15:37,622 current in the same direction, then they will attract each 245 00:15:37,622 --> 00:15:41,9 other. And you will see that shortly. 246 00:15:41,9 --> 00:15:44,396 Three, two, one, zero. 247 00:15:44,396 --> 00:15:48,08 See? They go towards each other. 248 00:15:48,08 --> 00:15:50,813 I will do it again, now. 249 00:15:50,813 --> 00:15:57,469 If I run the current in opposite directions, 250 00:15:57,469 --> 00:16:01,774 they will repel each other. Now I run them in opposite 251 00:16:01,774 --> 00:16:04,455 directions. They repel each other. 252 00:16:04,455 --> 00:16:07,136 I'll do it again, three, two, one, 253 00:16:07,136 --> 00:16:09,33 zero. They repel each other. 254 00:16:09,33 --> 00:16:13,392 The reason why I showed you this demonstration is a 255 00:16:13,392 --> 00:16:16,885 different one. What I want you to appreciate 256 00:16:16,885 --> 00:16:21,597 that if I have this conducting plate of aluminum -- it's a 257 00:16:21,597 --> 00:16:27,121 conductor -- and I put that in between the two 258 00:16:27,121 --> 00:16:30,421 wires, and I repeat the experiment, that exactly the 259 00:16:30,421 --> 00:16:33,397 same thing will happen. And that tells you that 260 00:16:33,397 --> 00:16:37,473 magnetic fields are really very difference from electric fields, 261 00:16:37,473 --> 00:16:40,902 because electric fields would be heavily affected by a 262 00:16:40,902 --> 00:16:44,201 conducting sheet like this. Magnetic fields are not. 263 00:16:44,201 --> 00:16:48,083 So what I'm going to do now is I'm going to put this plate in 264 00:16:48,083 --> 00:16:51,641 between, and then I'm going to again put the currents in 265 00:16:51,641 --> 00:16:54,746 opposite directions, and so we will see the wires 266 00:16:54,746 --> 00:16:57,787 repel each other as if the plate were not there. 267 00:16:57,787 --> 00:17:00,682 Three, two, one, zero. 268 00:17:00,682 --> 00:17:06,101 There you go. So magnetic fields have a very 269 00:17:06,101 --> 00:17:12,403 interesting story to tell. However, electricity and 270 00:17:12,403 --> 00:17:19,083 magnetism are connected. How do we define the strength 271 00:17:19,083 --> 00:17:23,747 of a magnetic field? With electricity, 272 00:17:23,747 --> 00:17:31,183 we defined the strengths of electric fields in the following 273 00:17:31,183 --> 00:17:35,28 way -- we measured the force, 274 00:17:35,28 --> 00:17:37,856 the electric force, on a charge, 275 00:17:37,856 --> 00:17:42,178 on an electric charge, and then the electric force is 276 00:17:42,178 --> 00:17:45,087 the charge times the electric field. 277 00:17:45,087 --> 00:17:49,243 That determines the strength of the electric field. 278 00:17:49,243 --> 00:17:52,9 Wouldn't it be nice if we could now say, "OK, 279 00:17:52,9 --> 00:17:57,055 the magnetic force is a magnetic charge times the B 280 00:17:57,055 --> 00:17:59,964 field. So that would then define the 281 00:17:59,964 --> 00:18:03,621 magnitude of the B field. That would be nice. 282 00:18:03,621 --> 00:18:08,297 But as long as we haven't found a magnetic 283 00:18:08,297 --> 00:18:12,181 monopole, we can't do it. If you come with a magnetic 284 00:18:12,181 --> 00:18:14,57 monopole tomorrow, I can do this. 285 00:18:14,57 --> 00:18:18,529 But we have no magnetic monopoles, and so it cannot be 286 00:18:18,529 --> 00:18:21,516 done this way. How is magnetic field then 287 00:18:21,516 --> 00:18:24,055 defined? Well, it is defined in the 288 00:18:24,055 --> 00:18:27,043 following way. I take an electric charge, 289 00:18:27,043 --> 00:18:31,225 and the electric charge is Q. And if that electric charge 290 00:18:31,225 --> 00:18:35,183 moves with a velocity V, and there is a magnetic field 291 00:18:35,183 --> 00:18:40,038 where the electric charge is moving, then it is 292 00:18:40,038 --> 00:18:44,467 an experimental fact that the force is always perpendicular 293 00:18:44,467 --> 00:18:46,869 to V. If you want to call that B, 294 00:18:46,869 --> 00:18:49,797 with a magnetic indication, that's fine. 295 00:18:49,797 --> 00:18:54,226 So there is a magnetic field, the charge is moving with this 296 00:18:54,226 --> 00:18:58,73 velocity, and there is a force on that charge which is always 297 00:18:58,73 --> 00:19:02,408 perpendicular to V. The magnitude of that force is 298 00:19:02,408 --> 00:19:06,612 proportional to the speed of the particle, and it is also 299 00:19:06,612 --> 00:19:09,09 proportional to the charge itself. 300 00:19:09,09 --> 00:19:13,294 If I double the charge, then the 301 00:19:13,294 --> 00:19:16,588 force doubles. If I double the speed, 302 00:19:16,588 --> 00:19:21,438 then the force doubles. And so the way that we define, 303 00:19:21,438 --> 00:19:25,19 now, magnetic field strength, is this way. 304 00:19:25,19 --> 00:19:30,314 The force -- and I give it a B to remind you -- magnetic, 305 00:19:30,314 --> 00:19:35,165 is Q, is the electric charge, V is the velocity of the 306 00:19:35,165 --> 00:19:38,916 electric charge, the cross-product with B. 307 00:19:38,916 --> 00:19:43,401 And you see that the force is always 308 00:19:43,401 --> 00:19:46,465 perpendicular to V, and that it is linearly 309 00:19:46,465 --> 00:19:50,696 proportional with the speed, and linearly proportional with 310 00:19:50,696 --> 00:19:53,688 the charge Q. And this is often called the 311 00:19:53,688 --> 00:19:56,46 Lorenz force after the Dutch physicist. 312 00:19:56,46 --> 00:19:59,525 This equation is completely sign-sensitive. 313 00:19:59,525 --> 00:20:03,683 If you change from a positive charge to a negative charge, 314 00:20:03,683 --> 00:20:07,404 then the force flips over, a hundred eighty degrees. 315 00:20:07,404 --> 00:20:10,833 You change the direction of V, force flips over. 316 00:20:10,833 --> 00:20:15,334 Change the direction of B, force flips over. 317 00:20:15,334 --> 00:20:18,863 So it's a completely sign-sensitive equation. 318 00:20:18,863 --> 00:20:23,114 The unit for magnetic field strength follows from this 319 00:20:23,114 --> 00:20:26,402 equation, this is Newton's, Q is Coulombs, 320 00:20:26,402 --> 00:20:30,894 and V is meters per second. So this would be the unit for 321 00:20:30,894 --> 00:20:35,305 magnetic field strength, but no one would ever say that. 322 00:20:35,305 --> 00:20:40,358 In SI units -- this would be SI units -- we call that one Tesla, 323 00:20:40,358 --> 00:20:44,127 for which we write one capital T. 324 00:20:44,127 --> 00:20:47,905 A Tesla is an extremely strong magnetic field. 325 00:20:47,905 --> 00:20:52,605 The magnetic field of this magnet is only two-tenths of a 326 00:20:52,605 --> 00:20:55,123 Tesla. And that's a very strong 327 00:20:55,123 --> 00:20:56,802 magnet. We often use, 328 00:20:56,802 --> 00:20:59,908 therefore, a unit, which is the gauss, 329 00:20:59,908 --> 00:21:04,272 which is not an SI unit, but you will see it often in 330 00:21:04,272 --> 00:21:08,805 books, and one t- gauss is ten to the minus four Tesla. 331 00:21:08,805 --> 00:21:13,002 The Earth's magnetic field is roughly half a gauss. 332 00:21:13,002 --> 00:21:18,107 And so this magnet is about two kilogauss. 333 00:21:18,107 --> 00:21:23,918 But the SI unit is Tesla. If you look at a television, 334 00:21:23,918 --> 00:21:29,621 or the screen of your computer, you have a fluorescent 335 00:21:29,621 --> 00:21:35,863 screen -- and in a television, there are electron guns that 336 00:21:35,863 --> 00:21:41,566 raster scan this fluorescent screen -- on a television 337 00:21:41,566 --> 00:21:49,853 screen, you have five hundred and twenty five lines, 338 00:21:49,853 --> 00:21:54,086 and the electron guns scan that it one-thirtieth of a second. 339 00:21:54,086 --> 00:21:57,966 And the intensity changes of these electron beams create 340 00:21:57,966 --> 00:22:00,648 images. So if you look at the tube from 341 00:22:00,648 --> 00:22:04,599 the side, then there are electrons -- one moment in time, 342 00:22:04,599 --> 00:22:07,35 they may move like this, another moment, 343 00:22:07,35 --> 00:22:10,526 they may be here, in the raster scan -- and so 344 00:22:10,526 --> 00:22:14,9 it's clear that if you bring a strong magnet in the vicinity of 345 00:22:14,9 --> 00:22:18,287 your television screen, that you will distort the 346 00:22:18,287 --> 00:22:22,606 image, because you are now affecting 347 00:22:22,606 --> 00:22:27,07 the motion of these currents, of these electrons. 348 00:22:27,07 --> 00:22:32,277 And there is a very famous artist, Nam June Paik who used 349 00:22:32,277 --> 00:22:36,555 this for his art, and almost every major museum 350 00:22:36,555 --> 00:22:42,413 in this world has a work by Nam June Paik, with distorted images 351 00:22:42,413 --> 00:22:46,319 using magnets and using television screens. 352 00:22:46,319 --> 00:22:51,433 I don't want to compete with Nam June Paik, 353 00:22:51,433 --> 00:22:55,714 but I do want to show this to you. 354 00:22:55,714 --> 00:22:59,476 I have there, television sets, 355 00:22:59,476 --> 00:23:05,832 and I have a very strong magnet, and I will try to 356 00:23:05,832 --> 00:23:14,003 distort that image and give you the best lights that we know how 357 00:23:14,003 --> 00:23:18,284 to. And I suggest we try to find a 358 00:23:18,284 --> 00:23:24,51 program that we hate. So here is my magnet -- oh, 359 00:23:24,51 --> 00:23:29,828 man -- this is an extremely strong magnet, 360 00:23:29,828 --> 00:23:36,055 and let's turn on the television, 361 00:23:36,055 --> 00:23:46,808 and let's see what we can get first. 362 00:23:46,808 --> 0. 363 0. --> 00:23:56,333 Oh, I turned it off instead of 364 00:23:56,333 --> 00:24:08,316 on. Ah, I hate commercials. 365 00:24:08,316 --> 00:24:23,538 Now, watch it closely. Here comes my magnet, 366 00:24:23,538 --> 00:24:40,531 there's the image. [background] You see that? 367 00:24:40,531 --> 00:24:44,772 that [background] so you've seen that we can, 368 00:24:44,772 --> 00:24:50,169 with a magnet and a moving charge, that we can change the 369 00:24:50,169 --> 00:24:55,856 direction of the moving charge. Force on the moving charges. 370 00:24:55,856 --> 00:25:01,349 If you have an electric field as well as a magnetic field, 371 00:25:01,349 --> 00:25:05,397 then, of course, you have also the electric 372 00:25:05,397 --> 00:25:08,578 force. And so the total force on a 373 00:25:08,578 --> 00:25:13,589 moving charged particle would then be Q 374 00:25:13,589 --> 00:25:17,54 times the electric field vector, plus V cross B. 375 00:25:17,54 --> 00:25:20,735 And this, of course, we've seen before. 376 00:25:20,735 --> 00:25:24,181 An electric field can do work on a charge. 377 00:25:24,181 --> 00:25:27,208 Remember, Q delta V. Can be positive, 378 00:25:27,208 --> 00:25:30,15 can be negative, but it can do work. 379 00:25:30,15 --> 00:25:34,017 It can change the kinetic energy of the charge. 380 00:25:34,017 --> 00:25:38,388 Magnetic fields can never do work on a moving charge. 381 00:25:38,388 --> 00:25:43,264 And the reason is that the force is always perpendicular to 382 00:25:43,264 --> 00:25:45,831 the velocity V. 383 00:25:45,831 --> 00:25:49,533 And so if the force is always perpendicular to the motion, 384 00:25:49,533 --> 00:25:53,625 you can change the direction of the motion, but you can't change 385 00:25:53,625 --> 00:25:56,353 the kinetic energy. So that's a fundamental 386 00:25:56,353 --> 00:26:00,25 difference between the electric force and the magnetic force. 387 00:26:00,25 --> 00:26:03,563 So now I want to calculate, with you, the force on a 388 00:26:03,563 --> 00:26:06,875 current that runs a wire I through it, and we have a 389 00:26:06,875 --> 00:26:09,928 magnetic field B. So we're going to be slowly -- 390 00:26:09,928 --> 00:26:12,785 we're going to be more and more quantitative. 391 00:26:12,785 --> 00:26:18,057 This, by the way, is often -- also called the 392 00:26:18,057 --> 00:26:22,832 Lorenz force, just a combination of the two. 393 00:26:22,832 --> 00:26:28,274 That one certainly is. So let is start with a -- a 394 00:26:28,274 --> 00:26:33,271 wire, and a wire that runs a current through, 395 00:26:33,271 --> 00:26:37,491 here is the wire, and the current is I. 396 00:26:37,491 --> 00:26:41,156 And let's say, at this point here, 397 00:26:41,156 --> 00:26:49,817 we have a magnetic field B. And the magnetic field could be 398 00:26:49,817 --> 00:26:53,67 difference along the wire, in principle. 399 00:26:53,67 --> 00:26:58,609 Here, I have a charge, plus D Q, and this charge is 400 00:26:58,609 --> 00:27:03,548 running through the wire with a drift velocity V D. 401 00:27:03,548 --> 00:27:09,376 Let's first think about what happens if the current is zero. 402 00:27:09,376 --> 00:27:13,623 If the current is zero, at room temperature, 403 00:27:13,623 --> 00:27:18,562 the free electrons in these wires have huge speeds. 404 00:27:18,562 --> 00:27:23,578 Three million meters per second. 405 00:27:23,578 --> 00:27:26,349 Way larger than the drift velocity. 406 00:27:26,349 --> 00:27:29,446 But they are in all chaotic directions. 407 00:27:29,446 --> 00:27:32,381 Random motion, it's a thermal motion. 408 00:27:32,381 --> 00:27:36,863 And so on each individual charge, there will be a force. 409 00:27:36,863 --> 00:27:39,39 But they average out to be zero. 410 00:27:39,39 --> 00:27:44,362 It's not until I run a current that these charges are going to 411 00:27:44,362 --> 00:27:47,948 walk through with a very slow drift velocity, 412 00:27:47,948 --> 00:27:51,616 and now, of course, the net force is not zero. 413 00:27:51,616 --> 00:27:57,892 So let's have this charge D Q that moves in this direction, 414 00:27:57,892 --> 00:28:02,106 and so that gives me a current. And let this angle be theta 415 00:28:02,106 --> 00:28:04,721 between them. Say, that's going to be 416 00:28:04,721 --> 00:28:08,718 important, because it's a cross-product between velocity 417 00:28:08,718 --> 00:28:11,115 and B. That means the sine of this 418 00:28:11,115 --> 00:28:14,894 theta comes in later. You will say -- I hope you will 419 00:28:14,894 --> 00:28:18,018 say, "Well, listen, man, this is ridiculous. 420 00:28:18,018 --> 00:28:21,288 Uh, positive charges don't move through wires. 421 00:28:21,288 --> 00:28:24,412 It is the electrons that move through wires. 422 00:28:24,412 --> 00:28:28,197 They are responsible for the current. 423 00:28:28,197 --> 00:28:31,808 And electrons have a negative charge, and they go in this 424 00:28:31,808 --> 00:28:33,291 direction. You're right. 425 00:28:33,291 --> 00:28:35,935 Perfectly fine. However, a negative charge 426 00:28:35,935 --> 00:28:39,61 going in this direction is mathematically exactly the same 427 00:28:39,61 --> 00:28:42,448 as a positive charge going in that direction. 428 00:28:42,448 --> 00:28:45,349 In both cases, do we agree that the current is 429 00:28:45,349 --> 00:28:47,799 in this direction. So I have preferred, 430 00:28:47,799 --> 00:28:51,41 for mathematical reasons, to take a plus D Q charge going 431 00:28:51,41 --> 00:28:55,215 in this direction rather than taking a minus D Q charge that 432 00:28:55,215 --> 00:28:59,722 goes with the drift velocity in that 433 00:28:59,722 --> 00:29:03,94 direction. But there is no difference at 434 00:29:03,94 --> 00:29:07,834 all in the outcome that you will see. 435 00:29:07,834 --> 00:29:11,62 So on this charge, there is a force, 436 00:29:11,62 --> 00:29:16,055 D F -- that's this -- this magnetic force, 437 00:29:16,055 --> 00:29:20,49 and that is the charge D Q, that equation, 438 00:29:20,49 --> 00:29:24,6 times V cross B. Well, V was that drift 439 00:29:24,6 --> 00:29:30,689 velocity, and here is the magnetic field, 440 00:29:30,689 --> 00:29:36,033 at this location. The current through the wire, 441 00:29:36,033 --> 00:29:40,563 everywhere on the wire, must be D Q D T. 442 00:29:40,563 --> 00:29:47,301 Because that's the definition of current, how many Coulombs 443 00:29:47,301 --> 00:29:51,6 per second. Current is always D Q D T. 444 00:29:51,6 --> 00:29:58,803 So I can also write this as I D T times V D cross B. 445 00:29:58,803 --> 00:30:03,41 But I remember eight oh one, that V D times D T, 446 00:30:03,41 --> 00:30:07,332 that is speed times a time is a distance. 447 00:30:07,332 --> 00:30:13,214 And I call that distance D L. It's a distance along the wire. 448 00:30:13,214 --> 00:30:18,803 I will put a distance in here now, because I don't want to 449 00:30:18,803 --> 00:30:23,018 clutter up my -- my drawing. So this charge, 450 00:30:23,018 --> 00:30:26,646 in time D T, moves over that distance, 451 00:30:26,646 --> 00:30:29,734 that's a vector. 452 00:30:29,734 --> 00:30:35,761 Eight oh one. So I can write down for this 453 00:30:35,761 --> 00:30:44,729 product, I can write down D L. So I can also write down that D 454 00:30:44,729 --> 00:30:49,581 F of B equals I times D L cross B. 455 00:30:49,581 --> 00:30:57,226 What is this telling you? This is the force of a wire 456 00:30:57,226 --> 00:31:03,913 over a small segment of the wire which has length D 457 00:31:03,913 --> 00:31:08,086 L, I is the current through the wire, and B is the local 458 00:31:08,086 --> 00:31:12,411 magnetic field at that location D L, that's what it means. 459 00:31:12,411 --> 00:31:16,356 And if you want to know the entire force on the wire, 460 00:31:16,356 --> 00:31:19,999 you have to do the integral along the whole wire. 461 00:31:19,999 --> 00:31:24,172 And so you have to do an integral along the entire wire, 462 00:31:24,172 --> 00:31:28,193 and at every portion D L, you have to determine what B 463 00:31:28,193 --> 00:31:30,469 is, and you get, then, a force, 464 00:31:30,469 --> 00:31:35,271 which is a vector, and you have to add 465 00:31:35,271 --> 00:31:40,821 those vectors vectorially. Could be a pain in the neck, 466 00:31:40,821 --> 00:31:46,269 but that's the basic idea. So now, I want to calculate 467 00:31:46,269 --> 00:31:52,23 what the force was on this wire, roughly, when we ran three 468 00:31:52,23 --> 0. hundred amperes through there. 469 0. --> 00:31:55,416 Oh, I turned it off instead of 470 00:31:55,416 --> 00:32:02,92 And I make a geometry so simple that we can execute that 471 00:32:02,92 --> 00:32:05,282 integral. This was the wire, 472 00:32:05,282 --> 00:32:10,183 and we had a current running through here which was three 473 00:32:10,183 --> 00:32:12,284 hundred amperes, roughly. 474 00:32:12,284 --> 00:32:17,097 And we have a magnetic field, which was right in the gap 475 00:32:17,097 --> 00:32:22,086 there, that magnetic field B, and that was two-tenths of a 476 00:32:22,086 --> 00:32:23,836 Tesla. Two kilogauss. 477 00:32:23,836 --> 00:32:27,949 And that magnetic field was only operating here. 478 00:32:27,949 --> 00:32:32,063 It wasn't operating there. And I 479 00:32:32,063 --> 00:32:37,015 make the assumption -- which is a simplifying assumption -- that 480 00:32:37,015 --> 00:32:41,732 that magnetic field was constant over the portion of the wire 481 00:32:41,732 --> 00:32:44,563 which was, say, only ten centimeters. 482 00:32:44,563 --> 00:32:49,122 And so I assume here that I have a length which is oh point 483 00:32:49,122 --> 00:32:53,289 one meters, and that in during -- in this range here, 484 00:32:53,289 --> 00:32:57,77 the magnetic field is constant. I just want to get a rough 485 00:32:57,77 --> 00:33:02,016 number for the force on that wire. 486 00:33:02,016 --> 00:33:05,409 So now I can integrate that equation very easily, 487 00:33:05,409 --> 00:33:09,792 because I have assumed that the magnetic field is perpendicular 488 00:33:09,792 --> 00:33:14,175 to the direction D L -- because D L is now in this direction -- 489 00:33:14,175 --> 00:33:18,276 so the sine of theta is one, so I don't have to worry about 490 00:33:18,276 --> 00:33:22,659 that -- and so I simply get that the force on this section F -- 491 00:33:22,659 --> 00:33:26,123 of this section L, that force -- call it F of B if 492 00:33:26,123 --> 00:33:29,799 you want to -- is the current I, which we have there, 493 00:33:29,799 --> 00:33:32,698 we get the length L, which is this length, 494 00:33:32,698 --> 00:33:36,312 multiplied by the magnetic field. 495 00:33:36,312 --> 00:33:41,675 There is no sine I anywhere because the angels are ninety 496 00:33:41,675 --> 00:33:45,218 degrees. And so I find that that force 497 00:33:45,218 --> 00:33:50,389 is three hundred times oh point one times oh point two, 498 00:33:50,389 --> 00:33:55,847 so it is thirty times point two, that is about six Newton. 499 00:33:55,847 --> 00:34:00,348 Six Newton is more that the weight of one pound. 500 00:34:00,348 --> 00:34:05,998 And so it is not so surprising that when I turn this current 501 00:34:05,998 --> 00:34:08,722 on, that something, 502 00:34:08,722 --> 00:34:12,086 all of a sudden, that something all of a sudden 503 00:34:12,086 --> 00:34:16,254 pulls that wire down with a weight that is equivalent of a 504 00:34:16,254 --> 00:34:19,983 little more than a pound, almost a pound and a half, 505 00:34:19,983 --> 00:34:22,762 actually. And so it's not so surprising 506 00:34:22,762 --> 00:34:27,003 that these supports fell over. So you see that you can turn 507 00:34:27,003 --> 00:34:30,439 this quantitatively, provided that you make some 508 00:34:30,439 --> 00:34:34,754 simplifying assumptions about the uniformity of the magnetic 509 00:34:34,754 --> 00:34:38,922 field, and about where the magnetic field 510 00:34:38,922 --> 00:34:43,414 is present. Now, I want to talk about the 511 00:34:43,414 --> 00:34:47,008 great eight oh two motor contest. 512 00:34:47,008 --> 00:34:52,961 We are about to start on this great eight oh two motor 513 00:34:52,961 --> 00:34:59,7 contest, you got an envelope today, and I'm going to start to 514 00:34:59,7 --> 00:35:03,631 tell you, slowly, about the physics. 515 00:35:03,631 --> 00:35:08,797 The goal is, ultimately, to build a 516 00:35:08,797 --> 00:35:11,62 motor. If I have a current loop -- 517 00:35:11,62 --> 00:35:15,469 here is a current loop. Current comes in at A, 518 00:35:15,469 --> 00:35:19,318 and I'll try to make it -- make you look at it 519 00:35:19,318 --> 00:35:22,824 three-dimensionally, which is not so easy. 520 00:35:22,824 --> 00:35:26,075 This is -- current goes out here, at D. 521 00:35:26,075 --> 00:35:30,095 This is a current loop. Current go through here, 522 00:35:30,095 --> 00:35:32,832 go through here, go through here, 523 00:35:32,832 --> 00:35:36,766 and we turn here. And we have a magnetic field, 524 00:35:36,766 --> 00:35:42,496 we will assume that the magnetic field is constant 525 00:35:42,496 --> 00:35:47,869 throughout, in this direction. There is a force right here on 526 00:35:47,869 --> 00:35:51,182 this wire, in the direction I cross B. 527 00:35:51,182 --> 00:35:54,674 That force is up. There is a force here, 528 00:35:54,674 --> 00:35:57,629 on this wire, which is, of course, 529 00:35:57,629 --> 00:36:00,673 down. Magnetic field is in the same 530 00:36:00,673 --> 00:36:05,24 direction, the current is in the opposite direction, 531 00:36:05,24 --> 00:36:09,627 so the force is down. If this wire has a length A, 532 00:36:09,627 --> 00:36:14,193 this wire has a length A, that force 533 00:36:14,193 --> 00:36:18,352 -- the magnitude of that force is the current through the wire 534 00:36:18,352 --> 00:36:21,488 times the length of the wire times the B field. 535 00:36:21,488 --> 00:36:24,419 We just derived that. There's that integral, 536 00:36:24,419 --> 00:36:27,76 we just assume that the magnetic field is constant 537 00:36:27,76 --> 00:36:30,964 everywhere here, there, at ninety-degree angles, 538 00:36:30,964 --> 00:36:34,509 so the sine of theta is one, and so that's the force. 539 00:36:34,509 --> 00:36:37,849 What is the force here and what is the force here? 540 00:36:37,849 --> 00:36:41,053 Well, it's zero. Zero here, and it is zero here. 541 00:36:41,053 --> 00:36:43,78 Why is that? Because the cross-product is 542 00:36:43,78 --> 00:36:47,461 zero. No matter how you look at it, 543 00:36:47,461 --> 00:36:50,794 you can say D L and B are either in the same direction or 544 00:36:50,794 --> 00:36:53,71 in opposite directions. You can also say the drift 545 00:36:53,71 --> 00:36:57,46 velocity and B are either in the same or the opposite direct- it 546 00:36:57,46 --> 00:37:00,138 is all the same thing. There is no force here, 547 00:37:00,138 --> 00:37:03,471 and there is no force here. Because that equation that we 548 00:37:03,471 --> 00:37:06,387 had that gives us the magnetic force becomes zero. 549 00:37:06,387 --> 00:37:10,017 The sine of that angle is zero. So what's going to happen with 550 00:37:10,017 --> 00:37:12,517 this thing? Well, there is a torque on this 551 00:37:12,517 --> 00:37:14,243 system. There is no net force, 552 00:37:14,243 --> 00:37:18,17 because this force up is the same as this force 553 00:37:18,17 --> 00:37:21,71 down, but there is a torque which wants to rotate in 554 00:37:21,71 --> 00:37:25,319 counterclockwise direction. And the magnitude of that 555 00:37:25,319 --> 00:37:28,927 torque is, of course, this force -- you remember from 556 00:37:28,927 --> 00:37:32,744 eight oh one -- times the perpendicular distance between 557 00:37:32,744 --> 00:37:35,867 these two forces, and so the magnitude of that 558 00:37:35,867 --> 00:37:39,476 torque is I times A B times B at this moment in time, 559 00:37:39,476 --> 00:37:41,835 when the forces are this far apart. 560 00:37:41,835 --> 00:37:45,375 Now, this is going to rotate, and so as they rotate, 561 00:37:45,375 --> 00:37:50,667 these forces come closer, and so the torque will become 562 00:37:50,667 --> 00:37:53,126 less. Still, it wants to rotate 563 00:37:53,126 --> 00:37:56,405 counterclockwise. And there comes a time, 564 00:37:56,405 --> 00:38:00,094 ninety degrees later, that the torque is zero. 565 00:38:00,094 --> 00:38:03,946 And I will try to make you see that, again, in a 566 00:38:03,946 --> 00:38:07,717 three-dimensional way, it's not so easy for me. 567 00:38:07,717 --> 00:38:10,422 Now, this is D, this has become D, 568 00:38:10,422 --> 00:38:15,176 a current always leaves at D. I'll try to make you see this 569 00:38:15,176 --> 00:38:19,773 three-dimensionally. It goes like this, 570 00:38:19,773 --> 00:38:23,704 current comes in here, at A, so we get this, 571 00:38:23,704 --> 00:38:27,27 and we get this. It doesn't look so bad. 572 00:38:27,27 --> 00:38:32,481 And the magnetic field B has not changed, uniform B in the 573 00:38:32,481 --> 00:38:36,321 same direction. So the current now comes in 574 00:38:36,321 --> 00:38:41,897 through A, it has not changed, the only thing is that the loop 575 00:38:41,897 --> 00:38:46,743 has rotated ninety degrees. If, now I ask you what the 576 00:38:46,743 --> 00:38:51,862 forces are, you have to go I cross 577 00:38:51,862 --> 00:38:52,953 B. I cross B. 578 00:38:52,953 --> 00:38:57,585 If you do I cross B here, I cross B, you get a force 579 00:38:57,585 --> 00:39:02,218 which is towards you. Here, you get forces which are 580 00:39:02,218 --> 00:39:06,487 in the blackboard. Here you get forces which are 581 00:39:06,487 --> 00:39:10,302 up, and here you get forces which are down. 582 00:39:10,302 --> 00:39:15,298 At home, you will have some time to use your right hand, 583 00:39:15,298 --> 00:39:18,75 and do the I cross B, and you will see, 584 00:39:18,75 --> 00:39:23,708 then, that, indeed, all these forces are in the 585 00:39:23,708 --> 00:39:26,685 direction that I put them. So now, there is, 586 00:39:26,685 --> 00:39:28,97 again, no net force on the system. 587 00:39:28,97 --> 00:39:31,394 There was no net force here, either. 588 00:39:31,394 --> 00:39:33,748 But now, there is no torque either. 589 00:39:33,748 --> 00:39:36,102 So now, the torque has become zero. 590 00:39:36,102 --> 00:39:39,426 If we rotate it a little further, it is possible, 591 00:39:39,426 --> 00:39:42,818 then we start this motor, starts to rotate counter 592 00:39:42,818 --> 00:39:46,557 clockwise, comes to this position, torque goes to zero, 593 00:39:46,557 --> 00:39:50,435 but it has enough inertia so it rotates a little further. 594 00:39:50,435 --> 00:39:54,036 And now the torque will reverse. 595 00:39:54,036 --> 00:39:57,233 And this is something that I leave you alone with, 596 00:39:57,233 --> 00:40:01,149 I don't want to make another drawing and convince you that it 597 00:40:01,149 --> 00:40:03,107 reverses. But it's easy to see, 598 00:40:03,107 --> 00:40:06,631 because, take this thing, and just flip it over hundred 599 00:40:06,631 --> 00:40:09,242 eighty degrees. The magnetic field hasn't 600 00:40:09,242 --> 00:40:12,897 changed, but the currents in these two sides have changed 601 00:40:12,897 --> 00:40:15,703 direction now, because whatever is D is here 602 00:40:15,703 --> 00:40:18,379 and A is here. And so the torque reverses, 603 00:40:18,379 --> 00:40:21,903 and so it goes like this, [wssshhht], and then [wsshht] 604 00:40:21,903 --> 00:40:26,974 it comes back. And that's not much of a motor. 605 00:40:26,974 --> 00:40:30,645 Current meters are very frequently used, 606 00:40:30,645 --> 00:40:35,069 they are in your cars, many more than you think, 607 00:40:35,069 --> 00:40:39,398 your, um, your fuel gauge and your temperature, 608 00:40:39,398 --> 00:40:43,163 of the cooling water, are current meters. 609 00:40:43,163 --> 00:40:46,552 And a current meter works as follows. 610 00:40:46,552 --> 00:40:50,411 We attach to this loop a needle, a handle, 611 00:40:50,411 --> 00:40:55,117 and we calibrate it here. And you can read how many 612 00:40:55,117 --> 00:40:59,438 amperes are going through this meter. 613 00:40:59,438 --> 00:41:01,742 It wants to go counterclockwise. 614 00:41:01,742 --> 00:41:05,46 Here, we attach a spring, and the spring produces a 615 00:41:05,46 --> 00:41:08,88 counter-torque, and so the needle will start to 616 00:41:08,88 --> 00:41:13,192 deflect, but come to a halt. But if you double the current, 617 00:41:13,192 --> 00:41:16,761 it will go further. That's the way that a current 618 00:41:16,761 --> 00:41:19,958 meter works. And your fuel gauge in your car 619 00:41:19,958 --> 00:41:23,452 is a current meter, except that the level of the 620 00:41:23,452 --> 00:41:27,764 fuel is somehow converted into an electric 621 00:41:27,764 --> 00:41:30,86 signal, and then it's sent to a current meter, 622 00:41:30,86 --> 00:41:34,437 and that's what you're reading. And it is, of course, 623 00:41:34,437 --> 00:41:37,532 calibrated in terms of how much fuel you have. 624 00:41:37,532 --> 00:41:41,659 And your temperature gauge is calibrated in terms of degrees, 625 00:41:41,659 --> 00:41:43,861 whatever, Fahrenheit or whatever. 626 00:41:43,861 --> 00:41:47,644 So these current meters are very common, even when we're 627 00:41:47,644 --> 00:41:51,633 dealing with something that has nothing to do with current. 628 00:41:51,633 --> 00:41:54,454 How do you build, now, a motor that works? 629 00:41:54,454 --> 00:41:58,394 How do you get over this torque reversal? 630 00:41:58,394 --> 00:42:02,437 Well, it's not only the torque reversal that is a problem, 631 00:42:02,437 --> 00:42:06,41 but there is also the problem that if you could keep this 632 00:42:06,41 --> 00:42:09,176 going around, that these two wires would 633 00:42:09,176 --> 00:42:11,446 intertwine, and they would break. 634 00:42:11,446 --> 00:42:15,631 You roll it around a hundred times, you can see what happens 635 00:42:15,631 --> 00:42:19,249 at A and D, it will break. So you have to think of a 636 00:42:19,249 --> 00:42:23,221 design whereby you have slipping contacts -- we call them 637 00:42:23,221 --> 00:42:24,853 brushes. Suppose I have, 638 00:42:24,853 --> 00:42:27,903 here, a conductor which is connected with A, 639 00:42:27,903 --> 00:42:31,964 physically soldered to the wire at A. 640 00:42:31,964 --> 00:42:35,426 And here, I have a conductor which is D. 641 00:42:35,426 --> 00:42:38,533 So the -- the loop is where you are. 642 00:42:38,533 --> 00:42:42,261 Soldered wires coming out the loop is here. 643 00:42:42,261 --> 00:42:47,143 But now the battery -- plus side of the battery is here, 644 00:42:47,143 --> 00:42:50,782 and the minus side of the battery of here, 645 00:42:50,782 --> 00:42:54,599 and this is a slipping contact. In practice, 646 00:42:54,599 --> 00:42:59,126 we call them brushes. So that immediately takes care 647 00:42:59,126 --> 00:43:04,007 of the problem, that the wires wind up. 648 00:43:04,007 --> 00:43:07,983 But there is something else which is very clever about this 649 00:43:07,983 --> 00:43:10,45 design. If the gap between A and D is 650 00:43:10,45 --> 00:43:13,261 an insulator, then, what's going to happen 651 00:43:13,261 --> 00:43:16,002 when this rotates hundred eighty degrees? 652 00:43:16,002 --> 00:43:20,184 A, which now is on the positive side of the battery -- this is 653 00:43:20,184 --> 00:43:21,829 negative, of course, heh? 654 00:43:21,829 --> 00:43:25,05 -- A is now on the positive side of the battery, 655 00:43:25,05 --> 00:43:28,203 if you -- if you rotate hundred eighty degrees, 656 00:43:28,203 --> 00:43:31,287 A will be on the negative side of the battery. 657 00:43:31,287 --> 00:43:33,961 So now every rotation, the current will, 658 00:43:33,961 --> 00:43:37,638 all by itself, change direction. 659 00:43:37,638 --> 00:43:41,923 And we call that a commutator. And so now, what's going to 660 00:43:41,923 --> 00:43:45,607 happen is, now the torque reversal will not occur. 661 00:43:45,607 --> 00:43:49,741 If, at the right moment, the current switches direction, 662 00:43:49,741 --> 00:43:54,252 the torque will always want to rotate the loop in exactly the 663 00:43:54,252 --> 00:43:57,184 same direction. That's the idea behind a 664 00:43:57,184 --> 00:44:00,116 commutator. The great eight oh two motor 665 00:44:00,116 --> 00:44:02,297 contest. You have an envelope, 666 00:44:02,297 --> 00:44:06,056 when you open it up -- don't do it 667 00:44:06,056 --> 00:44:09,946 now -- you will find in there a copper wire, two meters 668 00:44:09,946 --> 00:44:12,396 insulated copper wire, two magnets, 669 00:44:12,396 --> 00:44:14,558 two paper clips, and some wood. 670 00:44:14,558 --> 00:44:19,025 And the idea is that you try to build a motor that runs as fast 671 00:44:19,025 --> 00:44:22,123 as possible. For every hundred RPM -- an RPM 672 00:44:22,123 --> 00:44:26,446 is a rotation per minute -- for every hundred -- hundred RPM, 673 00:44:26,446 --> 00:44:30,913 I'll give you one credit point, with a maximum of twenty credit 674 00:44:30,913 --> 00:44:33,435 points. So if your motor runs t- two 675 00:44:33,435 --> 00:44:38,335 thousand RPM or more, you get twenty credit points. 676 00:44:38,335 --> 00:44:41,539 That is equivalent to two homework assignments. 677 00:44:41,539 --> 00:44:45,37 And these credit points count over and above your course 678 00:44:45,37 --> 00:44:47,598 grade. You have my word for that. 679 00:44:47,598 --> 00:44:51,708 I'll give you a final course grade, the way that you've seen 680 00:44:51,708 --> 00:44:54,564 in the ground rules, in the first handout, 681 00:44:54,564 --> 00:44:57,907 and we add your motor contest, what you deserved. 682 00:44:57,907 --> 00:45:00,693 For every hundred RPM, you get one point, 683 00:45:00,693 --> 00:45:03,34 plus, with a maximum of, uh, of twenty. 684 00:45:03,34 --> 00:45:07,589 And we're going to test these motors on these second of April, 685 00:45:07,589 --> 00:45:12,744 an I gave you a handout in which I give you some hints, 686 00:45:12,744 --> 00:45:15,451 some ideas. There is one idea that I gave 687 00:45:15,451 --> 00:45:18,97 you which you may ignore, and that is to overcome the 688 00:45:18,97 --> 00:45:21,881 torque reversal, you can build a commutator. 689 00:45:21,881 --> 00:45:24,453 But that's, uh, that's really not easy. 690 00:45:24,453 --> 00:45:27,431 Not only is it not easy, but when you built a 691 00:45:27,431 --> 00:45:30,747 commutator, your system may get a lot of friction, 692 00:45:30,747 --> 00:45:33,116 and you may lose more than you gain. 693 00:45:33,116 --> 00:45:36,703 There is an alternative solution, which I mentioned in 694 00:45:36,703 --> 00:45:40,494 my handout that you picked up today, and that is that you 695 00:45:40,494 --> 00:45:44,826 design your motor in such a way that when the 696 00:45:44,826 --> 00:45:47,797 reversal, when the torque reversal occurs, 697 00:45:47,797 --> 00:45:50,769 that there is no current running any more. 698 00:45:50,769 --> 00:45:54,973 And when it is half a rotation further, the torque is there 699 00:45:54,973 --> 00:45:57,365 again, the current is there again. 700 00:45:57,365 --> 00:46:00,409 So for half the time, you stop the current, 701 00:46:00,409 --> 00:46:04,685 you will see that's very easy, I give you some hints how you 702 00:46:04,685 --> 00:46:07,077 do that. So you have to weigh that 703 00:46:07,077 --> 00:46:10,556 against the possibility of building a commutator. 704 00:46:10,556 --> 00:46:13,963 The bottom line is, the maximum is twenty credit 705 00:46:13,963 --> 00:46:17,876 points. That's an equivalent of two 706 00:46:17,876 --> 00:46:21,808 homework assignments. You get it over and above your 707 00:46:21,808 --> 00:46:24,353 course grade. And it's also great, 708 00:46:24,353 --> 00:46:27,282 fun, believe me. What more do you want? 709 00:46:27,282 --> 00:46:30,289 To do physics, get credit, and have fun. 710 00:46:30,289 --> 00:46:34,529 That's what I do every day, that's the great thing about 711 00:46:34,529 --> 00:46:37,151 physics. We have five minutes left, 712 00:46:37,151 --> 00:46:41,545 and in those five minutes, I'm going to demonstrate to you 713 00:46:41,545 --> 00:46:44,552 a motor. What you see there is a current 714 00:46:44,552 --> 00:46:49,332 loop -- I'll try to make you see it three-dimensionally -- this 715 00:46:49,332 --> 00:46:54,896 is the current loop, and we're going to run a 716 00:46:54,896 --> 00:46:59,052 current in this direction, and we, here, 717 00:46:59,052 --> 00:47:01,929 have a magnet, north, south, 718 00:47:01,929 --> 00:47:05,658 magnetic field is in this direction. 719 00:47:05,658 --> 00:47:08,535 And we, here, have a magnet, 720 00:47:08,535 --> 00:47:13,117 north, south, magnetic field is also in this 721 00:47:13,117 --> 00:47:16,954 direction. I'm going to run a current 722 00:47:16,954 --> 00:47:21,322 through here, and if the current is in the 723 00:47:21,322 --> 00:47:25,772 blackboard, I cross B -- I is in, 724 00:47:25,772 --> 00:47:29,216 cross B, force is up. This side wants to go up. 725 00:47:29,216 --> 00:47:33,634 If this side wants to go up, since the magnetic field is the 726 00:47:33,634 --> 00:47:37,078 same direction here, but the current is hundred 727 00:47:37,078 --> 00:47:41,196 eighty degrees in opposite direction, this force will be 728 00:47:41,196 --> 00:47:43,891 down. And so there's a torque on this 729 00:47:43,891 --> 00:47:45,988 motor. And you will see that. 730 00:47:45,988 --> 00:47:50,255 You will see that go like this. However, when it's hundred 731 00:47:50,255 --> 00:47:54,598 eighty degrees and it swings here, by, it wants to go back, 732 00:47:54,598 --> 00:47:58,272 because of the torque reversal. 733 00:47:58,272 --> 00:48:01,901 That's the first thing that I want to show you. 734 00:48:01,901 --> 00:48:05,767 And I think I don't need any changes in the light. 735 00:48:05,767 --> 00:48:09,79 So here, we have this loop, and here we have the two 736 00:48:09,79 --> 00:48:13,34 magnets -- the magnetic field is, by no means, 737 00:48:13,34 --> 00:48:16,654 uniform, by the way, it's very strong here, 738 00:48:16,654 --> 00:48:21,072 and it's very strong there. And now I have to power that. 739 00:48:21,072 --> 00:48:23,596 Hmm, there we go. I can't -- yes, 740 00:48:23,596 --> 00:48:28,96 I think I know that this one will come up this side, 741 00:48:28,96 --> 00:48:32,626 I'm fairly sure that I have the directions right. 742 00:48:32,626 --> 00:48:35,986 Let's first take a look at it. There it goes. 743 00:48:35,986 --> 00:48:38,811 So when it's here, notice, it goes up. 744 00:48:38,811 --> 00:48:42,705 But now, if I power it here again, wants to go back. 745 00:48:42,705 --> 00:48:46,829 So here, wants to go up, and here, it wants to go back. 746 00:48:46,829 --> 00:48:50,8 So we've got to do something. And that something is a 747 00:48:50,8 --> 00:48:53,778 commutator. So if we can somehow reverse 748 00:48:53,778 --> 00:48:59,429 the current when it's here, then it wants to go down again. 749 00:48:59,429 --> 00:49:01,927 I'll show you that. So now it's here. 750 00:49:01,927 --> 00:49:05,328 And I'll drive the current in the other direction. 751 00:49:05,328 --> 00:49:07,688 You ready for that? Did you notice? 752 00:49:07,688 --> 00:49:11,02 It now wants to go down. Now it wants to go down. 753 00:49:11,02 --> 00:49:14,421 But when it's here, I have to reverse the current, 754 00:49:14,421 --> 00:49:17,822 it wants to go up. And if I do that with my hands, 755 00:49:17,822 --> 00:49:20,737 I can see whether I can keep this rotating. 756 00:49:20,737 --> 00:49:24,138 It may take me a while, but I'll do my best I can. 757 00:49:24,138 --> 00:49:26,151 There it goes. Switch, switch, 758 00:49:26,151 --> 00:49:29,621 switch, switch, switch, switch, 759 00:49:29,621 --> 00:49:31,164 switch, switch, switch. 760 00:49:31,164 --> 00:49:32,916 Yes, got it, yes I got it. 761 00:49:32,916 --> 00:49:36,071 I'm a commutator! This motor is going at least 762 00:49:36,071 --> 00:49:40,067 sixty RPM, that's one credit point for me for this course. 763 00:49:40,067 --> 49:45 Thank you.