1 00:00:00 --> 00:00:00,03 2 00:00:00,03 --> 00:00:05,53 Yesterday we had two hundred and twenty-five motors, 3 00:00:05,53 --> 00:00:11,678 and six of those motors went faster than two thousand RPM, 4 00:00:11,678 --> 00:00:15,561 which is a reasonable accomplishment. 5 00:00:15,561 --> 00:00:20,091 And the elite is here. These are the elite, 6 00:00:20,091 --> 00:00:23,326 the six highest. The winner is, 7 00:00:23,326 --> 00:00:27,964 um, Yungun Lee, I talked to her on the phone 8 00:00:27,964 --> 00:00:32,035 last night. If all goes well, 9 00:00:32,035 --> 00:00:34,216 she is here. Are you here? 10 00:00:34,216 --> 00:00:36,658 Where are you? There you are. 11 00:00:36,658 --> 00:00:41,803 Why don't you come up so that I can con- congratulate you in 12 00:00:41,803 --> 00:00:44,158 person. I thought about the, 13 00:00:44,158 --> 00:00:48,257 the prize for a while, and I decided to give you 14 00:00:48,257 --> 00:00:52,094 something that is not particularly high tech, 15 00:00:52,094 --> 00:00:55,67 but come up here, give me a European kiss, 16 00:00:55,67 --> 00:00:59,246 and another one -- in Europe, we go three. 17 00:00:59,246 --> 00:01:03,178 OK. Um, the prize that I have for 18 00:01:03,178 --> 00:01:07,378 you is a thermometer which goes back to the days of Galileo 19 00:01:07,378 --> 00:01:10,782 Galilei -- come here. Uh, it was designed in the 20 00:01:10,782 --> 00:01:13,823 early part of the, um, seventeenth century. 21 00:01:13,823 --> 00:01:16,938 Uh, it doesn't, uh, require any knowledge of 22 00:01:16,938 --> 00:01:19,545 eight oh two to explain how it works. 23 00:01:19,545 --> 00:01:22,007 If anything, you need eight oh one. 24 00:01:22,007 --> 00:01:26,425 It's not a digital thermometer. But it's accurate to about one 25 00:01:26,425 --> 00:01:29,249 degree centigrade, and if you come here, 26 00:01:29,249 --> 00:01:32,798 you can tell, you look at these 27 00:01:32,798 --> 00:01:35,832 floaters, and the highest floater indicates the 28 00:01:35,832 --> 00:01:38,471 temperature. It's now seventy-two degrees 29 00:01:38,471 --> 00:01:40,846 here. And I suggest that you brush up 30 00:01:40,846 --> 00:01:44,673 on your knowledge of eight oh one so that perhaps next week 31 00:01:44,673 --> 00:01:46,916 you can explain to me how it works. 32 00:01:46,916 --> 00:01:49,159 [laughter]. And of course tell your 33 00:01:49,159 --> 00:01:52,655 grandchildren about it. You may want to leave it here. 34 00:01:52,655 --> 00:01:55,822 It's very fragile. Uh, there is also some package 35 00:01:55,822 --> 00:01:58,593 material here, so that you can take it home 36 00:01:58,593 --> 00:02:01,76 without breaking it. So congratulations once more 37 00:02:01,76 --> 00:02:05,93 [applause] and of course -- [applause]. 38 00:02:05,93 --> 00:02:09,363 Terrific. And you will join us for dinner 39 00:02:09,363 --> 00:02:13,998 on the thirteenth of April with the other five winners. 40 00:02:13,998 --> 00:02:18,29 Thank you very much. There are two other people who 41 00:02:18,29 --> 00:02:21,551 are very special who I want to mention. 42 00:02:21,551 --> 00:02:25,499 And one is a person who is not enrolled in, uh, 43 00:02:25,499 --> 00:02:28,847 eight oh two, but he did extremely well, 44 00:02:28,847 --> 00:02:34,083 and he was very generous. He was not competing. 45 00:02:34,083 --> 00:02:37,359 His name is Daniel Wendel. His motor went forty-nine 46 00:02:37,359 --> 00:02:39,8 hundred RPM. And then there was Tim Lo. 47 00:02:39,8 --> 00:02:43,333 Is Tim Lo in the audience? I hope he's going to be there 48 00:02:43,333 --> 00:02:46,16 at eleven o'clock. Tim made a motor -- when I 49 00:02:46,16 --> 00:02:48,087 looked at it, I said to myself, 50 00:02:48,087 --> 00:02:50,528 it'll never run, but it's so beautiful. 51 00:02:50,528 --> 00:02:53,676 It was so artistic that we introduced a new prize, 52 00:02:53,676 --> 00:02:56,438 a second prize, for the most artistic motor, 53 00:02:56,438 --> 00:02:59,586 and Tim Lo definitely is the one, by far the best, 54 00:02:59,586 --> 00:03:02,477 the most beautiful, the most terrific artistic 55 00:03:02,477 --> 00:03:06,43 design. And so for him I bought a book 56 00:03:06,43 --> 00:03:10,883 on modern art -- what else can it be for someone who built such 57 00:03:10,883 --> 00:03:14,403 a beautiful motor? It is here for those of you who 58 00:03:14,403 --> 00:03:18,138 want to see it later. It's very hard to display it on 59 00:03:18,138 --> 00:03:20,652 television because it's so delicate. 60 00:03:20,652 --> 00:03:24,889 It's like a birdcage that he built instead of having just -- 61 00:03:24,889 --> 00:03:28,265 looks like that it's a birdcage. It's very nice. 62 00:03:28,265 --> 00:03:32,503 The winning motor I have here, and I'm going to show you the 63 00:03:32,503 --> 00:03:35,52 winning motor, and I also want to teach you 64 00:03:35,52 --> 00:03:39,714 some, some physics by demonstrating 65 00:03:39,714 --> 00:03:44,625 the winning motor to you in a way that you may never have 66 00:03:44,625 --> 00:03:48,132 thought of. So this is the winning motor. 67 00:03:48,132 --> 00:03:53,043 And when we start this motor, the ohmic resistance of the 68 00:03:53,043 --> 00:03:58,304 current loop is extremely low. So the moment that you connect 69 00:03:58,304 --> 00:04:03,127 it with your power supply, a very high current will run. 70 00:04:03,127 --> 00:04:08,3 But the moment that the motor starts to rotate, 71 00:04:08,3 --> 00:04:12,427 you have a continuous magnetic flux change in these loops, 72 00:04:12,427 --> 00:04:15,251 and so now the system will fight itself, 73 00:04:15,251 --> 00:04:19,378 and it will immediately kill the current, which is another 74 00:04:19,378 --> 00:04:21,767 striking example of Faraday's Law. 75 00:04:21,767 --> 00:04:25,894 I will show you the current of this motor when I block the 76 00:04:25,894 --> 00:04:29,876 rotor so that it cannot rotate. It's about one point six 77 00:04:29,876 --> 00:04:32,41 amperes. And you will see the moment 78 00:04:32,41 --> 00:04:36,392 that I run the motor that that current plunges by a huge 79 00:04:36,392 --> 00:04:38,998 amount. Striking example of Faraday's 80 00:04:38,998 --> 00:04:41,532 Law. So I now have to first show you 81 00:04:41,532 --> 00:04:45,216 this current, so here you see the 82 00:04:45,216 --> 00:04:48,562 one and a half volts, and on the right side you see 83 00:04:48,562 --> 00:04:51,44 the current. There is no current flowing now 84 00:04:51,44 --> 00:04:54,786 because the loop is hanging in such a way that the, 85 00:04:54,786 --> 00:04:57,53 that it makes no contact with the battery. 86 00:04:57,53 --> 00:05:00,608 And I'm going to try to make it -- there it is. 87 00:05:00,608 --> 00:05:03,888 Do you see the one point six amperes on the right? 88 00:05:03,888 --> 00:05:07,903 The current is so high that due to the internal resistance of 89 00:05:07,903 --> 00:05:10,714 the power supply, the voltage also plunges. 90 00:05:10,714 --> 00:05:14,394 But you saw the one point six, right? 91 00:05:14,394 --> 00:05:18,872 Now I'm going to run the motor. See, the motor is running now, 92 00:05:18,872 --> 00:05:21,808 and now look at the current. Current now, 93 00:05:21,808 --> 00:05:24,67 forty milliamperes, thirty milliamperes, 94 00:05:24,67 --> 00:05:28,047 fifty milliamperes. It's forty times lower than 95 00:05:28,047 --> 00:05:31,716 when I blocked the rotor. And so this is one of the 96 00:05:31,716 --> 00:05:36,047 reasons why when you have a, a motor, whichever motor it is, 97 00:05:36,047 --> 00:05:40,084 it could be just a drill, you try not to block it all of 98 00:05:40,084 --> 00:05:43,46 a sudden, because an enormous current will run, 99 00:05:43,46 --> 00:05:48,17 and it can actually damage the motors. 100 00:05:48,17 --> 00:05:55,175 So you see here how the current goes down by a factor of forty 101 00:05:55,175 --> 00:05:59,998 between running and not running. All right. 102 00:05:59,998 --> 00:06:06,429 Electric fields can induce electric dipoles in materials, 103 00:06:06,429 --> 00:06:11,826 and in case that the, the molecules or the atoms 104 00:06:11,826 --> 00:06:17,798 themselves are permanent electric dipoles, 105 00:06:17,798 --> 00:06:21,631 an external electric field will make an attempt to align them. 106 00:06:21,631 --> 00:06:25,402 We've discussed that in great detail before when we discussed 107 00:06:25,402 --> 00:06:27,728 dielectrics. And the degree of success 108 00:06:27,728 --> 00:06:31,499 depends entirely on how strong the external electric field is 109 00:06:31,499 --> 00:06:34,579 and on the temperature. If the temperature is low, 110 00:06:34,579 --> 00:06:38,287 you have very little thermal agitation, then it is easier to 111 00:06:38,287 --> 00:06:41,241 align those dipoles. We have a similar situation 112 00:06:41,241 --> 00:06:44,446 with magnetic fields. If I have an external magnetic 113 00:06:44,446 --> 00:06:47,651 field, this can induce in material 114 00:06:47,651 --> 00:06:51,073 magnetic dipoles. And it, uh, induces magnetic 115 00:06:51,073 --> 00:06:55,406 dipoles at the atomic scale. Now in case that the atoms or 116 00:06:55,406 --> 00:06:59,663 the molecules themselves have a permanent magnetic dipole 117 00:06:59,663 --> 00:07:04,3 moment, then this external field will make an attempt to align 118 00:07:04,3 --> 00:07:07,265 these dipoles, and the degree of success 119 00:07:07,265 --> 00:07:10,686 depends on the strength of the external field, 120 00:07:10,686 --> 00:07:14,867 and again on the temperature. The lower the temperature, 121 00:07:14,867 --> 00:07:20,526 the easier it is to align them. So the material modifies the 122 00:07:20,526 --> 00:07:23,227 external field. This external field, 123 00:07:23,227 --> 00:07:26,546 today I will often call it the vacuum field. 124 00:07:26,546 --> 00:07:30,097 So when you bring material into a vacuum field, 125 00:07:30,097 --> 00:07:33,725 the field changes. The field inside is different 126 00:07:33,725 --> 00:07:37,276 from the external field, from the vacuum field. 127 00:07:37,276 --> 00:07:41,675 I first want to remind you of our definition of a magnetic 128 00:07:41,675 --> 00:07:44,995 dipole moment. It's actually very simple how 129 00:07:44,995 --> 00:07:49,086 it is defined. If I have a current -- 130 00:07:49,086 --> 00:07:53,189 a loop could be a rectangle, it doesn't have to be a circle 131 00:07:53,189 --> 00:07:56,726 -- and if the current is running in this direction, 132 00:07:56,726 --> 00:08:00,122 seen from below clockwise, and if this area is A, 133 00:08:00,122 --> 00:08:04,509 then the magnetic dipole moment is simply the current times the 134 00:08:04,509 --> 00:08:06,985 area A. But we define A according to 135 00:08:06,985 --> 00:08:10,169 the, the vector A, according to the right-hand 136 00:08:10,169 --> 00:08:13,423 corkscrew rule. If I come from below clockwise, 137 00:08:13,423 --> 00:08:17,102 then the vector A is perpendicular to the surface and 138 00:08:17,102 --> 00:08:20,71 is then pointing upwards. And so the magnetic dipole 139 00:08:20,71 --> 00:08:25,881 moment, for which we normally write mu, 140 00:08:25,881 --> 00:08:31,9 is then also pointing upwards. And so this is a vector A, 141 00:08:31,9 --> 00:08:38,133 which is this normal according to the right-hand corkscrew. 142 00:08:38,133 --> 00:08:44,796 And if I have N of these loops, then the magnetic dipole moment 143 00:08:44,796 --> 00:08:50,17 will be N times larger. Then they will support each 144 00:08:50,17 --> 00:08:54,684 other if they're all in the same direction. 145 00:08:54,684 --> 00:08:59,52 I first want to discuss with you diamagnetism. 146 00:08:59,52 --> 00:09:03,477 Diamagnetism. All materials, 147 00:09:03,477 --> 00:09:07,245 when you expose them to an external magnetic field, 148 00:09:07,245 --> 00:09:10,713 will to some degree oppose that external field. 149 00:09:10,713 --> 00:09:13,878 And they will generate, on an atomic scale, 150 00:09:13,878 --> 00:09:17,119 an EMF which is opposing the external field. 151 00:09:17,119 --> 00:09:19,531 Now you will say, yes, of course, 152 00:09:19,531 --> 00:09:20,813 Lenz's Law. Wrong. 153 00:09:20,813 --> 00:09:23,526 It has nothing to do with Lenz's Law. 154 00:09:23,526 --> 00:09:27,823 It has nothing to do with the free electrons in conductors 155 00:09:27,823 --> 00:09:31,817 which produce an eddy current when there is a changing 156 00:09:31,817 --> 00:09:35,918 magnetic field. I'm not talking about a 157 00:09:35,918 --> 00:09:39,289 changing magnetic field, I'm talking about a permanent 158 00:09:39,289 --> 00:09:41,959 magnetic field. So when I apply a permanent 159 00:09:41,959 --> 00:09:43,994 magnetic field, in all materials, 160 00:09:43,994 --> 00:09:47,556 a magnetic dipole moment is induced to oppose that field. 161 00:09:47,556 --> 00:09:51,371 And there is no way that we can understand that with eight oh 162 00:09:51,371 --> 00:09:53,533 two. It can only be understood with 163 00:09:53,533 --> 00:09:56,649 quantum mechanics. So we'll make no attempts to do 164 00:09:56,649 --> 00:10:00,02 that, but we will accept it. And so the magnetic field 165 00:10:00,02 --> 00:10:03,517 inside the material is always a little bit smaller than, 166 00:10:03,517 --> 00:10:08,993 than the external field, because the dipoles will oppose 167 00:10:08,993 --> 00:10:12,448 the external field. Now I will talk about 168 00:10:12,448 --> 00:10:14,867 paramagnetism. Paramagnetism. 169 00:10:14,867 --> 00:10:19,186 There are many substances whereby the atoms and the 170 00:10:19,186 --> 00:10:23,505 molecules themselves have a magnetic dipole moment. 171 00:10:23,505 --> 00:10:28,86 So the atoms themselves or the molecules, you can think of them 172 00:10:28,86 --> 00:10:33,525 as being little magnets. If you have no external field, 173 00:10:33,525 --> 00:10:37,758 no vacuum field, then these dipoles 174 00:10:37,758 --> 00:10:41,217 are completely chaotically oriented, and so the net el- 175 00:10:41,217 --> 00:10:44,293 magnetic field is zero. So they are not permanent 176 00:10:44,293 --> 00:10:46,727 magnets. But the moment that you expose 177 00:10:46,727 --> 00:10:50,507 them to an external magnetic field, this magnetic field will 178 00:10:50,507 --> 00:10:53,262 try to align them. And the degree of success 179 00:10:53,262 --> 00:10:57,106 depends on the strength of that field and on the temperature. 180 00:10:57,106 --> 00:10:59,861 The lower the temperature, the easier it is. 181 00:10:59,861 --> 00:11:03,577 And so if you had a magnetic field, say, like so -- this is 182 00:11:03,577 --> 00:11:06,204 your B field, this is your vacuum field -- 183 00:11:06,204 --> 00:11:09,023 and you bring in there paramagnetic material, 184 00:11:09,023 --> 00:11:13,979 then there is the tendency for the north pole to go a 185 00:11:13,979 --> 00:11:18,243 little bit in this direction. And so these atomic magnets, 186 00:11:18,243 --> 00:11:22,73 then, would on average try to get the north pole a little bit 187 00:11:22,73 --> 00:11:26,321 in this direction. Or, if I speak the language of 188 00:11:26,321 --> 00:11:30,36 magnetic dipole moments, then the magnetic dipole would 189 00:11:30,36 --> 00:11:33,351 try to go a little bit in this direction. 190 00:11:33,351 --> 00:11:37,016 If you remove the external field of a paramagnetic 191 00:11:37,016 --> 00:11:40,906 material, immediately there is complete, total chaos, 192 00:11:40,906 --> 00:11:45,095 so there is no permanent magnetism left. 193 00:11:45,095 --> 00:11:49,488 If you bring paramagnetic material in a non-uniform 194 00:11:49,488 --> 00:11:53,354 magnetic field, it will be pulled towards the 195 00:11:53,354 --> 00:11:57,747 strong side of the field. And this is very easy to, 196 00:11:57,747 --> 00:12:02,228 to see how that works. Suppose I have a magnet here, 197 00:12:02,228 --> 00:12:07,676 and let this be the north pole of the magnet and this the south 198 00:12:07,676 --> 00:12:10,575 pole. And so the magnetic field is 199 00:12:10,575 --> 00:12:15,144 sort of like so. Notice right here it's 200 00:12:15,144 --> 00:12:18,512 very non-uniform. And I bring some paramagnetic 201 00:12:18,512 --> 00:12:21,806 material in there. Let's say -- think of it as 202 00:12:21,806 --> 00:12:24,588 just one atom there. It's not to scale, 203 00:12:24,588 --> 00:12:28,175 what I'm going to draw. And here is that one atom, 204 00:12:28,175 --> 00:12:30,884 and this one atom now is paramagnetic, 205 00:12:30,884 --> 00:12:33,373 has its own magnetic dipole moment. 206 00:12:33,373 --> 00:12:37,473 And this magnetic dipole moment, now, would like to align 207 00:12:37,473 --> 00:12:40,255 in this direction to support the field. 208 00:12:40,255 --> 00:12:45,086 The field is trying to push it in that direction. 209 00:12:45,086 --> 00:12:47,847 Let's suppose it is in this direction. 210 00:12:47,847 --> 00:12:51,875 So if we look from above, the current then in this atom 211 00:12:51,875 --> 00:12:55,456 or in this molecule is running in this direction. 212 00:12:55,456 --> 00:12:57,395 Seen from above, clockwise. 213 00:12:57,395 --> 00:13:01,275 So that would be ideal alignment of this atom or this 214 00:13:01,275 --> 00:13:05,527 molecule in that external field. This current loop will be 215 00:13:05,527 --> 00:13:08,958 attracted -- it wants to go towards the magnet. 216 00:13:08,958 --> 00:13:13,136 Let's look at this point here. That point, the current is 217 00:13:13,136 --> 00:13:18,019 going in the blackboard. So here is that current I. 218 00:13:18,019 --> 00:13:22,3 And the magnetic field is like so, the external magnetic field 219 00:13:22,3 --> 00:13:24,967 is like so. So in what direction is the 220 00:13:24,967 --> 00:13:28,055 Lorentz force? It's always in the direction I 221 00:13:28,055 --> 00:13:29,599 cross B. And I cross B, 222 00:13:29,599 --> 00:13:33,669 I cross B is in this direction. That's the direction of the 223 00:13:33,669 --> 00:13:35,634 Lorentz force. So right here, 224 00:13:35,634 --> 00:13:38,862 there is a force on the loop in this direction. 225 00:13:38,862 --> 00:13:42,722 So therefore right here, there is a force on the loop in 226 00:13:42,722 --> 00:13:46,511 this direction, on the current loop. 227 00:13:46,511 --> 00:13:50,089 And so everywhere around this loop, there is a force that is 228 00:13:50,089 --> 00:13:52,999 pointing like this, and so there clearly is a net 229 00:13:52,999 --> 00:13:55,363 force up. And so this matter wants to go 230 00:13:55,363 --> 00:13:58,334 towards the magnet. Another way of looking at this 231 00:13:58,334 --> 00:14:01,85 is that this current loop is all by itself a little magnet, 232 00:14:01,85 --> 00:14:05,367 whereby the south pole is here and the north pole is there, 233 00:14:05,367 --> 00:14:08,944 because this is the direction of the magnetic dipole moment. 234 00:14:08,944 --> 00:14:11,49 And the north pole attracts the south pole. 235 00:14:11,49 --> 00:14:13,612 That's another way of looking at it. 236 00:14:13,612 --> 00:14:17,735 That's the reason why magnets attract each other, 237 00:14:17,735 --> 00:14:20,378 why north and south pole attract each other, 238 00:14:20,378 --> 00:14:23,206 and why north and north poles repel each other. 239 00:14:23,206 --> 00:14:26,341 That's exactly the reason. It is the current that is 240 00:14:26,341 --> 00:14:30,091 flowing, it is the Lorentz force that causes the attraction or 241 00:14:30,091 --> 00:14:32,98 the repelling force. So paramagnetic material is 242 00:14:32,98 --> 00:14:36,238 attracted by a magnet. Essential is that this field is 243 00:14:36,238 --> 00:14:38,513 non-uniform. And diamagnetic material, 244 00:14:38,513 --> 00:14:41,955 of course, will be repelled, will be pushed away from the 245 00:14:41,955 --> 00:14:44,537 strong field, because in paramagnetic -- in 246 00:14:44,537 --> 00:14:47,734 diamagnetic material, this current will be running in 247 00:14:47,734 --> 00:14:52,888 the opposite direction, because it opposes the external 248 00:14:52,888 --> 00:14:55,97 field whereas paramagnetism supports it. 249 00:14:55,97 --> 00:15:00,079 We have a third form, and the third form of magnetism 250 00:15:00,079 --> 00:15:03,398 -- it's actually the most interesting -- is 251 00:15:03,398 --> 00:15:06,954 ferromagnetism. In the case of ferromagnetism, 252 00:15:06,954 --> 00:15:11,695 we again have that the atoms have themselves permanent dipole 253 00:15:11,695 --> 00:15:14,54 moments. But now, for very mysterious 254 00:15:14,54 --> 00:15:18,333 reasons which can only be understood with quantum 255 00:15:18,333 --> 00:15:22,995 mechanics, there are domains which have the 256 00:15:22,995 --> 00:15:26,404 dimensions of about a tenth of a millimeter, 257 00:15:26,404 --> 00:15:30,684 maybe three tenths of a millimeter, whereby the dipoles 258 00:15:30,684 --> 00:15:34,331 are hundred percent aligned. And these dipoles, 259 00:15:34,331 --> 00:15:38,215 domains, which are in one direction, are uniformly 260 00:15:38,215 --> 00:15:42,099 distributed throughout the ferromagnetic material, 261 00:15:42,099 --> 00:15:45,745 and so there may not be any net magnetic field. 262 00:15:45,745 --> 00:15:50,501 If I have here -- if I try to make a sketch of those domains, 263 00:15:50,501 --> 00:15:55,155 something like this, then perhaps here all these 264 00:15:55,155 --> 00:15:58,705 dipoles would all be hundred percent aligned in this 265 00:15:58,705 --> 00:16:02,673 direction, but for instance here, they will all be aligned 266 00:16:02,673 --> 00:16:05,527 in this direction. And the number of atoms 267 00:16:05,527 --> 00:16:09,635 involved in such a domain is typically ten to the seventeen, 268 00:16:09,635 --> 00:16:12,349 maybe up to ten to the twenty-one atoms. 269 00:16:12,349 --> 00:16:16,317 So if now I apply an external field, these domains will be 270 00:16:16,317 --> 00:16:19,868 forced to go in the direction of the magnetic field, 271 00:16:19,868 --> 00:16:23,905 and of course the degree of success depends on the strength 272 00:16:23,905 --> 00:16:26,699 of the external field, 273 00:16:26,699 --> 00:16:30,83 the strength of the vacuum field, and on the temperature. 274 00:16:30,83 --> 00:16:34,003 The lower the temperature, the better it is, 275 00:16:34,003 --> 00:16:37,248 because then there is less thermal agitation, 276 00:16:37,248 --> 00:16:41,675 which of course adds a certain rando- randomness to the whole 277 00:16:41,675 --> 00:16:44,257 process. So when I apply an external 278 00:16:44,257 --> 00:16:47,208 field, these domains as a whole can flip. 279 00:16:47,208 --> 00:16:51,339 Inside the ferromagnetic material, the magnetic field can 280 00:16:51,339 --> 00:16:55,322 be thousands of times stronger than it 281 00:16:55,322 --> 00:16:58,639 is in the vacuum field. And we will see some examples 282 00:16:58,639 --> 00:17:01,19 of that today. If you remove the external 283 00:17:01,19 --> 00:17:03,422 field, in the case of paramagnetism, 284 00:17:03,422 --> 00:17:06,229 you have again complete chaos of the dipoles. 285 00:17:06,229 --> 00:17:09,481 That's not necessarily the case with ferromagnetism. 286 00:17:09,481 --> 00:17:13,244 Some of those domains may stay aligned in the direction that 287 00:17:13,244 --> 00:17:15,476 the external field was forcing them. 288 00:17:15,476 --> 00:17:18,538 If you very carefully remove that external field, 289 00:17:18,538 --> 00:17:21,982 undoubtedly some domains will flip back, because of the 290 00:17:21,982 --> 00:17:24,916 temperature, there is always thermal agitation. 291 00:17:24,916 --> 00:17:29,544 Some may remain oriented, and therefore the material, 292 00:17:29,544 --> 00:17:32,933 once it has been exposed to an external magnetic field, 293 00:17:32,933 --> 00:17:35,192 may have become permanently magnetic. 294 00:17:35,192 --> 00:17:39,02 And the only way you can remove that permanent magnetism could 295 00:17:39,02 --> 00:17:42,471 be to bang on it with a hammer, and then of course these 296 00:17:42,471 --> 00:17:45,797 domains will then get very nervous, and then they will 297 00:17:45,797 --> 00:17:48,621 randomize themselves. Or you can heat them up, 298 00:17:48,621 --> 00:17:52,198 and then you can also undo the orientation of the domains. 299 00:17:52,198 --> 00:17:55,713 The domains themselves will remain, but then they average 300 00:17:55,713 --> 00:17:59,855 out not to produce any permanent magnetic field. 301 00:17:59,855 --> 00:18:03,627 So for the same reason that paramagnetism is pulled towards 302 00:18:03,627 --> 00:18:06,163 the strong field, in case that we have a 303 00:18:06,163 --> 00:18:09,806 non-uniform magnetic field, ferromagnetism of course will 304 00:18:09,806 --> 00:18:12,342 also be pulled towards the strong field, 305 00:18:12,342 --> 00:18:14,684 except in the case of ferromagnetism, 306 00:18:14,684 --> 00:18:18,131 the forces with which ferromagnetic material is pulled 307 00:18:18,131 --> 00:18:21,057 towards the magnet, way larger than in case of 308 00:18:21,057 --> 00:18:24,309 paramagnetic material. If I take a paperclip -- you 309 00:18:24,309 --> 00:18:27,626 can do that at home, you can hang a paperclip on the 310 00:18:27,626 --> 00:18:32,642 south pole of your magnet or the north pole of your magnet -- 311 00:18:32,642 --> 00:18:35,373 you all have gotten magnets in your motor kit, 312 00:18:35,373 --> 00:18:38,103 so you can try that at home. Take a paperclip, 313 00:18:38,103 --> 00:18:41,197 hang it on the magnets. Doesn't matter on which side 314 00:18:41,197 --> 00:18:44,352 you hang it, because ferromagnetic material is always 315 00:18:44,352 --> 00:18:47,871 pulled towards the strong field. If you hang a few of those 316 00:18:47,871 --> 00:18:51,755 paperclips on there and you very carefully and slowly remove them 317 00:18:51,755 --> 00:18:55,456 -- don't hit them with a hammer yet -- you may actually notice 318 00:18:55,456 --> 00:18:59,157 that after you remove them that the paperclips themselves have 319 00:18:59,157 --> 00:19:01,826 become magnetic. You can actually try to hang 320 00:19:01,826 --> 00:19:05,08 them on each other, make a little 321 00:19:05,08 --> 00:19:07,278 chain. But drop them on the floor a 322 00:19:07,278 --> 00:19:10,574 few times and that magendas- magnetism will go away. 323 00:19:10,574 --> 00:19:14,451 So what you have witnessed then is that some of those domains 324 00:19:14,451 --> 00:19:17,23 remained aligned due to your external field. 325 00:19:17,23 --> 00:19:20,268 With paramagnetism, there is no way that you can 326 00:19:20,268 --> 00:19:24,339 hang paramagnetic material under most circumstances on a magnet. 327 00:19:24,339 --> 00:19:27,7 There is one exception. I will show you the exception 328 00:19:27,7 --> 00:19:30,156 later today. And the reason is that the 329 00:19:30,156 --> 00:19:34,034 forces involved with paramagnetic material 330 00:19:34,034 --> 00:19:37,351 in general are only a few percent of the weight of the 331 00:19:37,351 --> 00:19:39,918 material itself. So if you take a piece of 332 00:19:39,918 --> 00:19:43,612 aluminum and you have a magnet, aluminum will not stick to a 333 00:19:43,612 --> 00:19:45,114 magnet. There is a force. 334 00:19:45,114 --> 00:19:48,933 Aluminum will be attracted by the magnet, but the force is way 335 00:19:48,933 --> 00:19:52,814 smaller than the weight of the aluminum, so it won't be able to 336 00:19:52,814 --> 00:19:56,758 pick it up, unlike ferromagnetic material, which you can pick up 337 00:19:56,758 --> 00:19:59,513 with a magnet. So what I could demonstrate to 338 00:19:59,513 --> 00:20:02,518 you, for one thing, I could take a bar magnet and 339 00:20:02,518 --> 00:20:06,525 show you that paperclips are hanging on this. 340 00:20:06,525 --> 00:20:10,876 I could also show you that aluminum is not hanging on this. 341 00:20:10,876 --> 00:20:13,652 But you won't find that very exciting. 342 00:20:13,652 --> 00:20:17,554 And therefore I decided on a different demonstration, 343 00:20:17,554 --> 00:20:22,056 whereby my goal is to show you that ferromagnetic material is 344 00:20:22,056 --> 00:20:26,332 pulled with huge forces towards the strong magnetic field, 345 00:20:26,332 --> 00:20:30,684 provided that I have a magnetic field which is non-uniform. 346 00:20:30,684 --> 00:20:35,261 And the way I will do that is with this piece of ferromagnetic 347 00:20:35,261 --> 00:20:39,462 material. And this piece of ferromagnetic 348 00:20:39,462 --> 00:20:41,593 material is actually quite heavy. 349 00:20:41,593 --> 00:20:44,989 And you are going to tell the class how heavy it is. 350 00:20:44,989 --> 00:20:47,252 Be very careful. What do you think? 351 00:20:47,252 --> 00:20:48,384 Wow! Good for you! 352 00:20:48,384 --> 00:20:49,915 [laughter]. Do it again! 353 00:20:49,915 --> 00:20:52,246 Sounds go-- looks great. [laughter]. 354 00:20:52,246 --> 00:20:55,109 It's fifteen kilograms. Fifteen kilograms of 355 00:20:55,109 --> 00:20:58,571 ferromagnetic material. It is not a permanent magnet. 356 00:20:58,571 --> 00:21:02,099 There may be a little bit of permanent magnetism left, 357 00:21:02,099 --> 00:21:05,894 of course, because once you have exposed it to an external 358 00:21:05,894 --> 00:21:10,954 field, yes, there may be some permanent magnetism left. 359 00:21:10,954 --> 00:21:14,929 So now I'm going to hold this -- let's first make sure that 360 00:21:14,929 --> 00:21:17,67 nothing happens to Galileo's thermometer. 361 00:21:17,67 --> 00:21:19,794 So we're going to put this here. 362 00:21:19,794 --> 00:21:23,357 See what the temperature is -- oh man, it's going up. 363 00:21:23,357 --> 00:21:26,441 I must be sweating here. Seventy-four degrees, 364 00:21:26,441 --> 00:21:30,278 yeah, seventy-four degrees now. OK, so here is my magnet, 365 00:21:30,278 --> 00:21:33,156 producing about three hundred twenty gauss. 366 00:21:33,156 --> 00:21:36,993 But what counts is that the magnetic field is non-uniform 367 00:21:36,993 --> 00:21:40,214 here and also here. And so I am going to turn on 368 00:21:40,214 --> 00:21:44,371 the magnet -- I believe I have to 369 00:21:44,371 --> 00:21:48,756 push a button here. And the first thing I will do 370 00:21:48,756 --> 00:21:53,049 is now power this magnet. So this is a solenoid. 371 00:21:53,049 --> 00:21:57,252 I put my hand in here, my hand is paramagnetic, 372 00:21:57,252 --> 00:22:00,997 it's not being sucked in. Really it isn't. 373 00:22:00,997 --> 00:22:04,926 I feel nothing. The force is -- I can't even 374 00:22:04,926 --> 00:22:08,58 feel anything. But I'm not ferromagnetic, 375 00:22:08,58 --> 00:22:11,138 thank goodness. Now this one. 376 00:22:11,138 --> 00:22:17,532 *Whssht*, fifteen kilograms, just sucked in like that. 377 00:22:17,532 --> 00:22:20,717 And I'm very lucky that when it's overshoots here that it 378 00:22:20,717 --> 00:22:23,333 wants to go back, because it always wants to go 379 00:22:23,333 --> 00:22:26,404 to the strongest field. Doesn't matter whether you have 380 00:22:26,404 --> 00:22:28,963 it here or there. The reason why that's lucky, 381 00:22:28,963 --> 00:22:32,319 because if that were not the case, this fifteen kilogram bar 382 00:22:32,319 --> 00:22:34,65 would go like a bullet coming out of here. 383 00:22:34,65 --> 00:22:38,006 So the one thing you don't want to do when it goes in there, 384 00:22:38,006 --> 00:22:41,247 you don't want to break the current, because then it would 385 00:22:41,247 --> 00:22:44,091 come out as a bullet. And I'm not going to do that, 386 00:22:44,091 --> 00:22:46,423 believe me. But I want to show you that -- 387 00:22:46,423 --> 00:22:47,958 there it goes. It's amazing, 388 00:22:47,958 --> 00:22:50,853 ferromagnetic material. 389 00:22:50,853 --> 00:22:51,794 *Aagh*. OK. 390 00:22:51,794 --> 00:22:56,405 So ferromagnetic material, there's enormous force. 391 00:22:56,405 --> 00:23:01,77 If you have a s- a field that is -- has a strong gradient, 392 00:23:01,77 --> 00:23:07,04 that it's very non-uniform, is sucked, pulled towards the 393 00:23:07,04 --> 00:23:11,087 strong side. That's why it hangs on magnets. 394 00:23:11,087 --> 00:23:15,887 That's the basic idea. I have another demonstration. 395 00:23:15,887 --> 00:23:21,157 And another demonstration is to make you sort of see in a 396 00:23:21,157 --> 00:23:25,506 non-kosher way magnetic domains. 397 00:23:25,506 --> 00:23:29,007 But I will tell you why it's non-kosher. 398 00:23:29,007 --> 00:23:33,944 I have here an array of eight by eight magnetic needles, 399 00:23:33,944 --> 00:23:37,893 compass needles. And you're going to see them 400 00:23:37,893 --> 00:23:41,214 there. And I will change the situation 401 00:23:41,214 --> 00:23:46,331 so that you have better light. And when I have an external 402 00:23:46,331 --> 00:23:50,37 magnetic field and I march over here a little, 403 00:23:50,37 --> 00:23:55,978 and I just let it go, and wait, you will see areas 404 00:23:55,978 --> 00:24:01,352 whereby these magnetic needles point in the same direction and 405 00:24:01,352 --> 00:24:06,638 you will see areas where they point in a different direction. 406 00:24:06,638 --> 00:24:12,011 We'll just give it some chance. And so that may make you think 407 00:24:12,011 --> 00:24:16,064 that this is the way that domains are formed in 408 00:24:16,064 --> 00:24:20,292 ferromagnetic material. Oh, in fact we have now a 409 00:24:20,292 --> 00:24:26,282 situation that almost all are aligned in this direction, 410 00:24:26,282 --> 00:24:29,19 and there's only a group here that is pointing in this 411 00:24:29,19 --> 00:24:30,726 direction. I can change that, 412 00:24:30,726 --> 00:24:32,976 of course, by changing the magnetic field. 413 00:24:32,976 --> 00:24:36,268 Why is this not really a kosher demonstration to convince you 414 00:24:36,268 --> 00:24:38,023 that domains exist? First of all, 415 00:24:38,023 --> 00:24:40,986 there is no thermal agitation, whereas in ferromagnetic 416 00:24:40,986 --> 00:24:42,906 material there is thermal agitation. 417 00:24:42,906 --> 00:24:45,704 Some may be oriented like this and others like that, 418 00:24:45,704 --> 00:24:48,393 where here you only have two preferred directions. 419 00:24:48,393 --> 00:24:50,642 You don't need quantum mechanics for that, 420 00:24:50,642 --> 00:24:53,275 simply a matter of minimum energy considerations. 421 00:24:53,275 --> 00:24:56,458 And so they either are pointed like 422 00:24:56,458 --> 00:25:00,46 this or they are pointed like that, and so already that shows 423 00:25:00,46 --> 00:25:03,662 you that it's very different from ferromagnetism. 424 00:25:03,662 --> 00:25:07,664 But the reason why we show it to you is it still gives you an 425 00:25:07,664 --> 00:25:11,2 interesting idea of the fact that you can have various 426 00:25:11,2 --> 00:25:13,935 orientations and that they come in groups. 427 00:25:13,935 --> 00:25:17,737 That the groups stick together and are not all in the same 428 00:25:17,737 --> 00:25:19,338 direction. But as I said, 429 00:25:19,338 --> 00:25:23,207 it is not really a good way to explain to you why there are 430 00:25:23,207 --> 00:25:25,408 domains in ferromagnetic material. 431 00:25:25,408 --> 00:25:30,79 Ah, now you see again, you have some nicely aligned 432 00:25:30,79 --> 00:25:35,704 here and others are in very different direction here. 433 00:25:35,704 --> 00:25:40,712 So the basic idea is there. It's a nice demonstration, 434 00:25:40,712 --> 00:25:45,91 but it shows you something that really is not related to 435 00:25:45,91 --> 00:25:50,068 ferromagnetism. The demonstration that is one 436 00:25:50,068 --> 00:25:54,32 of my favorites, one of my absolute favorites, 437 00:25:54,32 --> 00:25:58,856 is one whereby I can make you listen 438 00:25:58,856 --> 00:26:03,164 to the flip-over of these domains. 439 00:26:03,164 --> 00:26:08,776 I have ferromagnetic material inside a coil. 440 00:26:08,776 --> 00:26:15,562 I have here a coil and I'm going to put ferromagnetic 441 00:26:15,562 --> 00:26:21,566 material in here. And I have here a loudspeaker 442 00:26:21,566 --> 00:26:27,7 -- an amplifier as well, called it an amplifier. 443 00:26:27,7 --> 00:26:36,576 And this is a loudspeaker. Let's first assume there is no 444 00:26:36,576 --> 00:26:38,696 ferromagnetic material in there. 445 00:26:38,696 --> 00:26:41,775 That's the way I will start the demonstration. 446 00:26:41,775 --> 00:26:45,401 And I approach this with a magnet, and I go very fast. 447 00:26:45,401 --> 00:26:48,411 *Whssht*, what will happen? Faraday will say, 448 00:26:48,411 --> 00:26:52,448 oh, there's a magnetic flux change, and there will be an EMF 449 00:26:52,448 --> 00:26:55,116 in this coil. That means there will be a 450 00:26:55,116 --> 00:26:57,647 current in this coil, induced current. 451 00:26:57,647 --> 00:27:01,342 And it will be amplified and you will hear some sissing 452 00:27:01,342 --> 00:27:03,326 noise. And you will hear that. 453 00:27:03,326 --> 00:27:05,652 If, however, I come in very slowly, 454 00:27:05,652 --> 00:27:10,502 you won't hear anything, because D phi DT is then so 455 00:27:10,502 --> 00:27:13,913 low, because the time scale of my motion is so large, 456 00:27:13,913 --> 00:27:15,947 that you won't hear any current. 457 00:27:15,947 --> 00:27:18,834 The induced current is insignificantly small. 458 00:27:18,834 --> 00:27:22,639 Because remember the induced current is proportional to the 459 00:27:22,639 --> 00:27:26,51 induced EMF, and the induced EMF is proportional to the time 460 00:27:26,51 --> 00:27:30,315 change of the magnetic flux. So I can make that flux change 461 00:27:30,315 --> 00:27:33,268 very, very small if I bring it in very slowly. 462 00:27:33,268 --> 00:27:36,154 Now I will put in the ferromagnetic material, 463 00:27:36,154 --> 00:27:39,839 and I will approach it again very slowly. 464 00:27:39,839 --> 00:27:43,136 And now, there comes a time that some of those domains go 465 00:27:43,136 --> 00:27:45,845 *cluk*, *cluk*. But when the domains flip over, 466 00:27:45,845 --> 00:27:48,849 there is a magnetic flux change inside the material, 467 00:27:48,849 --> 00:27:51,558 and so the magnetic flux change means D phi DT, 468 00:27:51,558 --> 00:27:53,972 and it's on an extremely short time scale. 469 00:27:53,972 --> 00:27:57,329 And so now you get an EMF, you get a current going through 470 00:27:57,329 --> 00:28:00,097 the wire, and you hear a cracking noise over the 471 00:28:00,097 --> 00:28:02,57 loudspeaker. And for every group of domains 472 00:28:02,57 --> 00:28:05,868 that flip, you can hear that. And that's an amazing thing 473 00:28:05,868 --> 00:28:08,872 when you think about it, that some ten to the twenty 474 00:28:08,872 --> 00:28:12,903 atoms go clunk and that you can hear 475 00:28:12,903 --> 00:28:15,921 that. And so this is what we're going 476 00:28:15,921 --> 00:28:20,449 to do here, and I will do it then in, in several steps, 477 00:28:20,449 --> 00:28:24,726 so that you first can hear the noise if I don't have 478 00:28:24,726 --> 00:28:28,919 ferromagnetic material, and then -- so here is the, 479 00:28:28,919 --> 00:28:32,441 here's the coil. This is a very small coil. 480 00:28:32,441 --> 00:28:36,801 And here is a magnet. And I'll come very fast towards 481 00:28:36,801 --> 00:28:40,155 the coil. What you heard now is Faraday's 482 00:28:40,155 --> 00:28:44,516 Law. You simply have a magnetic flux 483 00:28:44,516 --> 00:28:50,241 change in the coil -- oh, I shouldn't touch it. 484 00:28:50,241 --> 00:28:56,465 Now I come in very slowly, and go away very slowly. 485 00:28:56,465 --> 00:29:01,692 You hear nothing. D phi DT is just too low. 486 00:29:01,692 --> 00:29:06,547 Now I put in the ferromagnetic material. 487 00:29:06,547 --> 00:29:12,895 Put it inside the coil. And now I approach it again, 488 00:29:12,895 --> 00:29:17,625 very slowly. There they go. 489 00:29:17,625 --> 00:29:21,919 You hear them? Those are, those are domains 490 00:29:21,919 --> 00:29:25,498 that go. I'll come in with the other 491 00:29:25,498 --> 00:29:27,441 side. There it goes, 492 00:29:27,441 --> 00:29:30,611 the domains. Isn't that amazing? 493 00:29:30,611 --> 00:29:34,496 You hear atoms switch, groups of atoms. 494 00:29:34,496 --> 00:29:38,893 I'll turn it over again. Now they flip back. 495 00:29:38,893 --> 00:29:42,574 They don't like it that that's there. 496 00:29:42,574 --> 00:29:47,892 This is called the Barkhausen effect. 497 00:29:47,892 --> 00:29:51,807 I find it truly amazing that you hear groups of atoms, 498 00:29:51,807 --> 00:29:55,575 ten to the twenty atoms at the time, they flip over, 499 00:29:55,575 --> 00:29:59,121 and when they do, there is a magnetic flux change 500 00:29:59,121 --> 00:30:03,258 inside the ferromagnetic material, is sensed by the coil, 501 00:30:03,258 --> 00:30:06,435 and you hear a current. And if I do it fast, 502 00:30:06,435 --> 00:30:09,39 uh, these, these, these, these domains go 503 00:30:09,39 --> 00:30:11,237 haywire. They go nuts now. 504 00:30:11,237 --> 00:30:15,743 Imagine that you were a domain and I would treat you that way. 505 00:30:15,743 --> 00:30:18,034 You'd go *cluk*, *cluk*, *cluk*, 506 00:30:18,034 --> 00:30:22,794 *cluk*, *cluk*. But the fact that you can hear 507 00:30:22,794 --> 00:30:25,342 it is absolutely amazing, isn't it. 508 00:30:25,342 --> 00:30:29,539 So that's actually a nice way of demonstrating that these 509 00:30:29,539 --> 00:30:32,087 domains exist. If you did that with 510 00:30:32,087 --> 00:30:36,059 faramagnetic- paramagnetic material, you wouldn't hear 511 00:30:36,059 --> 00:30:37,633 that. So in all cases, 512 00:30:37,633 --> 00:30:41,455 whether we have diamagnetic material or paramagnetic 513 00:30:41,455 --> 00:30:44,303 material or ferromagnetic material, uh, 514 00:30:44,303 --> 00:30:48,575 the magnetic field inside is different from what the field 515 00:30:48,575 --> 00:30:52,088 would be without the material. 516 00:30:52,088 --> 00:30:56,038 And what the field would be without the material we've 517 00:30:56,038 --> 00:30:59,765 called external field. I've called it vacuum field. 518 00:30:59,765 --> 00:31:03,269 And in many cases, but not all -- next lecture I 519 00:31:03,269 --> 00:31:07,89 will discuss the issues of not all -- in many cases but not all 520 00:31:07,89 --> 00:31:12,214 cases, is the field inside the material proportional to the 521 00:31:12,214 --> 00:31:14,972 vacuum field. And if that is the case, 522 00:31:14,972 --> 00:31:20,265 then you can write down that the field inside is linearly 523 00:31:20,265 --> 00:31:24,244 proportional -- so this is the field inside the material, 524 00:31:24,244 --> 00:31:28,223 regardless of whether it's diamagnetic or paramagnetic or 525 00:31:28,223 --> 00:31:31,279 ferromagnetic, is proportional to the vacuum 526 00:31:31,279 --> 00:31:33,695 field. I will write down vacuum for 527 00:31:33,695 --> 00:31:35,755 this. And this proportionality 528 00:31:35,755 --> 00:31:39,806 constant I call kappa of M. I -- our book calls it K of M. 529 00:31:39,806 --> 00:31:42,719 And it's called the relative permeability. 530 00:31:42,719 --> 00:31:46,556 And so now we can look at these values for the relative 531 00:31:46,556 --> 00:31:50,322 permeability and we can immediately understand now the 532 00:31:50,322 --> 00:31:54,972 difference between diamagnetic material, 533 00:31:54,972 --> 00:31:59,688 paramagnetic material, and ferromagnetic material. 534 00:31:59,688 --> 00:32:03,922 Since in the case of diamagnetic material and 535 00:32:03,922 --> 00:32:08,541 paramagnetic material, the B field inside is only 536 00:32:08,541 --> 00:32:12,39 slightly different from the vacuum field, 537 00:32:12,39 --> 00:32:17,587 it is common to express kappa of M in terms of one plus 538 00:32:17,587 --> 00:32:23,746 something which we call the magnetic susceptibility, 539 00:32:23,746 --> 00:32:27,014 which is xi of M. Because if it is very close to 540 00:32:27,014 --> 00:32:30,143 one, then it is easier to simply list xi of M. 541 00:32:30,143 --> 00:32:32,785 And let's look at diamagnetic material. 542 00:32:32,785 --> 00:32:36,818 Notice that these values for xi of M are all negative -- of 543 00:32:36,818 --> 00:32:40,573 course, they have to be negative, otherwise it wouldn't 544 00:32:40,573 --> 00:32:43,702 be diamagnetic. It means that the field inside 545 00:32:43,702 --> 00:32:47,11 is slightly, a hair smaller than the vacuum field, 546 00:32:47,11 --> 00:32:50,934 because these induced dipoles oppose the external field, 547 00:32:50,934 --> 00:32:53,298 remember. It has nothing to do with 548 00:32:53,298 --> 00:32:56,688 Lenz's Law, but they oppose it 549 00:32:56,688 --> 00:32:59,801 nevertheless. And so you express it in terms 550 00:32:59,801 --> 00:33:02,335 of the, um, magnetic susceptibility, 551 00:33:02,335 --> 00:33:06,535 and so you have to take one minus one point seven times ten 552 00:33:06,535 --> 00:33:10,734 to the minus four to get kappa of M, which is very close to 553 00:33:10,734 --> 00:33:13,124 one. If now you go to paramagnetic 554 00:33:13,124 --> 00:33:15,875 materials, the minus signs become plus. 555 00:33:15,875 --> 00:33:20,002 Again, the numbers are small. But the fact that it is plus 556 00:33:20,002 --> 00:33:24,419 means that inside paramagnetic material, the magnetic field is 557 00:33:24,419 --> 00:33:28,331 a little, a hair larger than the vacuum 558 00:33:28,331 --> 00:33:30,076 field. But now if you go to 559 00:33:30,076 --> 00:33:33,432 ferromagnetic material, it is really absurd to ever 560 00:33:33,432 --> 00:33:37,056 list the value for xi of M, because xi of M is so large 561 00:33:37,056 --> 00:33:41,15 that you can forget about the one, and so xi of M is about the 562 00:33:41,15 --> 00:33:44,17 same as kappa of M. And so you deal there with 563 00:33:44,17 --> 00:33:47,661 numbers that are a hundred, a thousand, ten thousand, 564 00:33:47,661 --> 00:33:49,875 and even larger than ten thousand. 565 00:33:49,875 --> 00:33:52,896 That means that if kappa of M is ten thousand, 566 00:33:52,896 --> 00:33:56,856 you would have a field inside ferromagnetic material that is 567 00:33:56,856 --> 00:34:01,659 ten thousand times larger than your vacuum field. 568 00:34:01,659 --> 00:34:06,405 Next lecture I will tell you that there is a limit to as far 569 00:34:06,405 --> 00:34:09,139 as you can go, but for now we will, 570 00:34:09,139 --> 00:34:12,839 we will leave it with this. So paramagnetic and 571 00:34:12,839 --> 00:34:16,86 ferromagnetic properties depend on the temperature. 572 00:34:16,86 --> 00:34:21,284 Diamagnetic properties do not depend on the temperature. 573 00:34:21,284 --> 00:34:25,788 So at very low temperatures, there is very little thermal 574 00:34:25,788 --> 00:34:30,373 agitation, and so you can then easier align 575 00:34:30,373 --> 00:34:33,911 these dipoles, and so the values for kappa of 576 00:34:33,911 --> 00:34:38,092 M will then be different. For ferromagnetic material, 577 00:34:38,092 --> 00:34:41,792 if you cool it, you expect the kappa of M going 578 00:34:41,792 --> 00:34:44,847 up, so you got a stronger field inside. 579 00:34:44,847 --> 00:34:49,592 So it's temperature-dependent. If you make the material very 580 00:34:49,592 --> 00:34:54,498 hot, then it can lose completely its ferromagnetic properties. 581 00:34:54,498 --> 00:34:59,081 What happens at a certain temperature, that these dosmain- 582 00:34:59,081 --> 00:35:02,538 domains fall apart, so the domains 583 00:35:02,538 --> 00:35:05,171 themselves no longer exist. They annihilate. 584 00:35:05,171 --> 00:35:07,987 And that happens at a very precise temperature. 585 00:35:07,987 --> 00:35:10,865 It's very strange. That's also something that is 586 00:35:10,865 --> 00:35:14,477 very difficult to understand, and you need quantum mechanics 587 00:35:14,477 --> 00:35:17,049 for that too. But at a certain temperature, 588 00:35:17,049 --> 00:35:20,416 which we call the Curie temperature, which for iron is a 589 00:35:20,416 --> 00:35:23,967 thousand forty-three degrees Kelvin, which is seven hundred 590 00:35:23,967 --> 00:35:27,273 seventy degrees centigrade, all of a sudden the domains 591 00:35:27,273 --> 00:35:30,151 disappear and the material becomes paramagnetic. 592 00:35:30,151 --> 00:35:34,756 In other words, if ferromagnetic material would 593 00:35:34,756 --> 00:35:39,68 be hanging on a magnet and you would heat it up above the Curie 594 00:35:39,68 --> 00:35:43,969 point, it would fall off. It would become paramagnetic, 595 00:35:43,969 --> 00:35:48,178 but paramagnetic material in general doesn't hang on a 596 00:35:48,178 --> 00:35:52,229 magnet, because the forces involved are quite small. 597 00:35:52,229 --> 00:35:56,994 And the change is very abrupt, and I am going to show that to 598 00:35:56,994 --> 00:36:01,124 you with a demonstration. I have a ferromagnetic nut. 599 00:36:01,124 --> 00:36:04,777 It's right there. You will see it very shortly. 600 00:36:04,777 --> 00:36:09,134 And this nut, or washer, hanging on a steel 601 00:36:09,134 --> 00:36:11,47 cable, and there is here a magnet. 602 00:36:11,47 --> 00:36:14,514 I don't know whether this is north or south. 603 00:36:14,514 --> 00:36:17,629 It doesn't matter. And here we have a thermal 604 00:36:17,629 --> 00:36:20,178 shield. And so this washer is against 605 00:36:20,178 --> 00:36:23,576 the thermal shield, because it's being attracted. 606 00:36:23,576 --> 00:36:26,975 It wants to go towards the strong magnetic field. 607 00:36:26,975 --> 00:36:30,231 It's ferromagnetic. So it will be sitting here. 608 00:36:30,231 --> 00:36:34,125 And now I'm going to heat this up above the Curie point, 609 00:36:34,125 --> 00:36:39,222 seven hundred seventy degrees centigrade, and you will 610 00:36:39,222 --> 00:36:43,732 see it fall off. And when it cools again, 611 00:36:43,732 --> 00:36:48,58 it goes back on again. So I can make you see 612 00:36:48,58 --> 00:36:52,413 ferromagnetic properties disappear. 613 00:36:52,413 --> 00:36:57,712 And let me make sure I have the proper settings. 614 00:36:57,712 --> 00:37:00,869 I see nothing. I see nothing. 615 00:37:00,869 --> 00:37:04,928 But there it is. So here is this nut, 616 00:37:04,928 --> 00:37:12,369 and here is this shield, and the magnet is behind it, 617 00:37:12,369 --> 00:37:15,945 you can't see it, but it's right there. 618 00:37:15,945 --> 00:37:21,309 And so it goes against it, right, it goes just towards the 619 00:37:21,309 --> 00:37:24,885 magnetic poles. It goes into the strong 620 00:37:24,885 --> 00:37:28,273 magnetic field. The magnetic field is 621 00:37:28,273 --> 00:37:33,167 non-uniform outside a magnet, and it goes towards it. 622 00:37:33,167 --> 00:37:36,084 And so now I'm going to heat it. 623 00:37:36,084 --> 00:37:39,19 It will take a while, because, um, 624 00:37:39,19 --> 00:37:45,025 seven hundred seventy degrees centigrade is not 625 00:37:45,025 --> 00:37:50,661 so easy to achieve. The three most common 626 00:37:50,661 --> 00:37:56,579 ferromagnetic materials are cobalt, nickel, 627 00:37:56,579 --> 00:38:01,652 and iron. Nickel has a Curie point of 628 00:38:01,652 --> 00:38:08,556 only three hundred fifty-eight degrees centigrade, 629 00:38:08,556 --> 00:38:16,87 so if this were nickel -- ooh. If this were nickel -- uh-uh. 630 00:38:16,87 --> 00:38:21,676 [laughter]. Oh, you like that, 631 00:38:21,676 --> 00:38:24,711 huh. I think I need strong hands. 632 00:38:24,711 --> 00:38:27,271 A strong hand is coming. OK. 633 00:38:27,271 --> 00:38:30,401 I think I fixed it. I'm a big boy, 634 00:38:30,401 --> 00:38:33,815 I did it myself today. I lost my pen, 635 00:38:33,815 --> 00:38:37,608 but that's a detail. OK, let's try again. 636 00:38:37,608 --> 00:38:42,634 So I'm going to heat it up, and I was mentioning that, 637 00:38:42,634 --> 00:38:49,367 um, nickel has a Curie point of three hundred fifty-eight 638 00:38:49,367 --> 00:38:52,529 degrees centigrade. So that's quite low. 639 00:38:52,529 --> 00:38:57,07 This is seven hundred seventy. Cobalt is fourteen hundred 640 00:38:57,07 --> 00:39:01,53 degrees Kelvin Curie point. Gadolinium is a very special 641 00:39:01,53 --> 00:39:04,693 material. Gadolinium is ferromagnetic in 642 00:39:04,693 --> 00:39:09,234 the winter, when the temperature is below sixteen degrees 643 00:39:09,234 --> 00:39:13,126 centigrade, but it is paramagnetic in the summer, 644 00:39:13,126 --> 00:39:17,667 when the temperature is above sixteen degrees centigrade. 645 00:39:17,667 --> 00:39:21,559 It's beginning to be red-hot now. 646 00:39:21,559 --> 00:39:26,147 Seven hundred seventy degrees centigrade, you expect some 647 00:39:26,147 --> 00:39:30,652 visible light in the form of red light -- there it goes. 648 00:39:30,652 --> 00:39:35,158 And I will keep it heating, I will keep the torch on it, 649 00:39:35,158 --> 00:39:40,237 so that you can see that indeed it's no longer attracted by the 650 00:39:40,237 --> 00:39:42,94 magnet. And the moment that I stop 651 00:39:42,94 --> 00:39:45,971 heating it, it will very quickly cool. 652 00:39:45,971 --> 00:39:51,623 It will become ferromagnetic again, and it will go back. 653 00:39:51,623 --> 00:39:55,506 Just watch it. There it goes. 654 00:39:55,506 --> 00:39:59,805 So now it's again ferromagnetic. 655 00:39:59,805 --> 00:40:04,797 So the transition is extremely sharp. 656 00:40:04,797 --> 00:40:07,155 All right. Uh, OK. 657 00:40:07,155 --> 00:40:14,782 So paramagnetic materials, as I mentioned several times, 658 00:40:14,782 --> 00:40:19,496 in general cannot hang on a magnet. 659 00:40:19,496 --> 00:40:25,829 The attractive force is there's not enough. 660 00:40:25,829 --> 00:40:29,428 To hang on a magnet, the force has to be larger than 661 00:40:29,428 --> 00:40:32,181 its own weight. And diamagn- diamagnetic 662 00:40:32,181 --> 00:40:35,286 materials is of course completely out because 663 00:40:35,286 --> 00:40:39,732 diamagnetic materials are always pushed towards the weak part of 664 00:40:39,732 --> 00:40:41,99 the field. It's only paramagnetic 665 00:40:41,99 --> 00:40:45,8 materials and ferromagnetic materials that experience a 666 00:40:45,8 --> 00:40:50,317 force towards the strong part of the field if the field itself is 667 00:40:50,317 --> 00:40:52,646 non-uniform. Now there is one very 668 00:40:52,646 --> 00:40:57,504 interesting exception. And I want to draw your 669 00:40:57,504 --> 00:41:01,044 attention to this, um, transparency here. 670 00:41:01,044 --> 00:41:04,319 Look here at oxygen at one atmosphere. 671 00:41:04,319 --> 00:41:09,629 Oxygen at one atmosphere and three hundred degrees Kelvin has 672 00:41:09,629 --> 00:41:14,851 a value for xi of M which is two times ten to the minus six. 673 00:41:14,851 --> 00:41:19,63 But now look at liquid oxygen at ninety degrees Kelvin. 674 00:41:19,63 --> 00:41:26,003 That value is eighteen hundred times larger than this value. 675 00:41:26,003 --> 00:41:29,032 Why is that so much higher? Well, liquid, 676 00:41:29,032 --> 00:41:33,349 in general, is about thousand times denser than gas at one 677 00:41:33,349 --> 00:41:36,53 atmosphere. So you have thousand times more 678 00:41:36,53 --> 00:41:40,392 dipoles per cubic meter that in principle can align. 679 00:41:40,392 --> 00:41:44,028 And so clearly you expect an immediate one-to-one 680 00:41:44,028 --> 00:41:48,193 correspondence between the density, how many dipoles you 681 00:41:48,193 --> 00:41:51,904 have per cubic meter, and the value for kappa M -- 682 00:41:51,904 --> 00:41:56,373 for xi of M. And so you see indeed that this 683 00:41:56,373 --> 00:42:00,313 value is substantially larger. The reason why it is more than 684 00:42:00,313 --> 00:42:04,123 a factor of thousand higher is that the temperature is also 685 00:42:04,123 --> 00:42:06,159 lower. You go from three hundred 686 00:42:06,159 --> 00:42:09,574 degrees to ninety degrees, and that gives you another 687 00:42:09,574 --> 00:42:12,53 factor of two, because when the temperature is 688 00:42:12,53 --> 00:42:16,34 lower, there is less thermal agitation, and so the external 689 00:42:16,34 --> 00:42:18,901 field can align the dipoles more easily. 690 00:42:18,901 --> 00:42:22,382 And so that's why you end up with a factor of eighteen 691 00:42:22,382 --> 00:42:24,812 hundred. Even though this value for xi 692 00:42:24,812 --> 00:42:28,293 of M is extraordinarily high for a 693 00:42:28,293 --> 00:42:32,198 paramagnetic material, notice that the field inside 694 00:42:32,198 --> 00:42:36,884 would only be point three five percent higher than the vacuum 695 00:42:36,884 --> 00:42:41,336 field, because if xi of M is three point five times ten to 696 00:42:41,336 --> 00:42:44,538 the minus three, that means that the field 697 00:42:44,538 --> 00:42:49,302 inside is only point three five percent higher than the vacuum 698 00:42:49,302 --> 00:42:52,036 field. But that is enough for liquid 699 00:42:52,036 --> 00:42:55,628 oxygen to be attracted by a very strong magnet, 700 00:42:55,628 --> 00:43:01,669 provided that it also has a very non-uniform field outside 701 00:43:01,669 --> 00:43:05,165 the magnet. And so the force with which 702 00:43:05,165 --> 00:43:10,962 liquid oxygen is pulled towards a magnet can be made larger than 703 00:43:10,962 --> 00:43:16,759 the weight of the liquid oxygen. And so I can make you see today 704 00:43:16,759 --> 00:43:21,451 that I can have liquid oxygen hanging from a magnet. 705 00:43:21,451 --> 00:43:25,04 And that's what we are going to do here. 706 00:43:25,04 --> 00:43:29,364 Make sure I have the right setting. 707 00:43:29,364 --> 00:43:33,564 Ah, this is it. Now we're going to have some 708 00:43:33,564 --> 00:43:38,057 changes in the lights. So there you see the two 709 00:43:38,057 --> 00:43:41,573 magnetic poles. It's a electromagnet. 710 00:43:41,573 --> 00:43:46,262 And so we can turn the magnetic field on at will. 711 00:43:46,262 --> 00:43:49,68 So here are the poles of the magnet. 712 00:43:49,68 --> 00:43:53,978 And the first thing I will do is very boring. 713 00:43:53,978 --> 00:43:58,763 I will throw some, uh, liquid nitrogen between the 714 00:43:58,763 --> 00:44:02,676 poles. Now I don't have the value for 715 00:44:02,676 --> 00:44:05,778 liquid nitrogen there, but nitrogen is diamagnetic, 716 00:44:05,778 --> 00:44:09,252 so it's not even an issue. Diamagnetic material is pushed 717 00:44:09,252 --> 00:44:12,85 away from the strong field. So even though the value for xi 718 00:44:12,85 --> 00:44:16,635 of M will be very different for liquid nitrogen than it is for 719 00:44:16,635 --> 00:44:18,806 gaseous nitrogen, it doesn't matter. 720 00:44:18,806 --> 00:44:20,915 So certainly it will be pushed out. 721 00:44:20,915 --> 00:44:24,452 So that's the first thing I want to do, just to bore you a 722 00:44:24,452 --> 00:44:26,933 little bit. Because I have to keep you on 723 00:44:26,933 --> 00:44:31,835 the edge of your seat before you're going to see this oxygen, 724 00:44:31,835 --> 00:44:38,035 which will be hanging in there. So let's first power this 725 00:44:38,035 --> 00:44:43,46 magnet -- I hope I did that -- yes, I think I did. 726 00:44:43,46 --> 00:44:47,225 And here comes the liquid nitrogen. 727 00:44:47,225 --> 00:44:51,211 Boring like hell, just falls through. 728 00:44:51,211 --> 00:44:55,086 Now comes the oxygen. Liquid oxygen. 729 00:44:55,086 --> 00:44:59,293 It's hanging in there. I challenge you, 730 00:44:59,293 --> 00:45:06,158 you've never in your life seen liquid hanging on a magnet. 731 00:45:06,158 --> 00:45:10,442 You can tell your parents about it -- and of course your 732 00:45:10,442 --> 00:45:13,012 grandchildren. It's hanging there. 733 00:45:13,012 --> 00:45:17,452 I'll put some more in -- make sure I have the right stuff, 734 00:45:17,452 --> 00:45:19,166 yeah. Put some more in. 735 00:45:19,166 --> 00:45:22,904 There is liquid oxygen. When I break the current, 736 00:45:22,904 --> 00:45:26,565 it's no longer a magnet, it will fall of course. 737 00:45:26,565 --> 00:45:28,746 Don't worry, you'll get more. 738 00:45:28,746 --> 00:45:33,03 Who has ever in his life seen a liquid hang on a magnet? 739 00:45:33,03 --> 00:45:37,537 It's paramagnetic, it's not ferromagnetic, 740 00:45:37,537 --> 00:45:41,906 but because the density is so high and because it's so cold, 741 00:45:41,906 --> 00:45:46,274 the value for xi of M is high enough that the force on it is 742 00:45:46,274 --> 00:45:50,42 larger than its own weight. If you do this with aluminum, 743 00:45:50,42 --> 00:45:54,196 not a chance in the world. Aluminum will not hang in 744 00:45:54,196 --> 00:45:57,824 there, even though aluminum, as you can see there, 745 00:45:57,824 --> 00:46:01,23 is paramagnetic. But the value two times ten to 746 00:46:01,23 --> 00:46:05,525 the minus five is way too small, and it will not stick to a 747 00:46:05,525 --> 00:46:07,456 magnet. OK. 748 00:46:07,456 --> 00:46:09,974 You have something to think about. 749 00:46:09,974 --> 46:15 I will see you Friday.