1 00:00:00 --> 00:00:00,276 2 00:00:00,276 --> 00:00:06,16 So last lecture was arguably the most important of all my 3 00:00:06,16 --> 00:00:10,258 lectures. We saw how a changing magnetic 4 00:00:10,258 --> 00:00:15,932 field can produce a current, an induced electric field, 5 00:00:15,932 --> 00:00:20,555 an induced EMF. And Faraday expressed that in 6 00:00:20,555 --> 00:00:25,178 his famous law, his famous equation which we 7 00:00:25,178 --> 00:00:32,424 see there on the blackboard. You select a closed loop in 8 00:00:32,424 --> 00:00:34,926 your circuit. Any loop is OK. 9 00:00:34,926 --> 00:00:39,037 You attach an open surface to that closed loop. 10 00:00:39,037 --> 00:00:43,773 Any open surface is OK. And you then get an EMF in the 11 00:00:43,773 --> 00:00:48,777 loop, and that's the time derivative of the magnetic flux 12 00:00:48,777 --> 00:00:53,156 through that surface. And the minus sign indicates 13 00:00:53,156 --> 00:00:58,517 that the induced current itself produces a magnetic flux that 14 00:00:58,517 --> 00:01:02,372 opposes the flux change, 15 00:01:02,372 --> 00:01:06,962 and that we refer to as Lenz's Law. 16 00:01:06,962 --> 00:01:12,633 Today, I will expand on this a lot further. 17 00:01:12,633 --> 00:01:19,519 So let's start with a conducting loop and a magnetic 18 00:01:19,519 --> 00:01:23,84 field. This is a conducting loop. 19 00:01:23,84 --> 00:01:31,806 Let the dimensions be Y X and let- I have a uniform magnetic 20 00:01:31,806 --> 00:01:38,152 field. Magnetic field B is like so. 21 00:01:38,152 --> 00:01:43,942 And I choose as the perpendicular vector to my 22 00:01:43,942 --> 00:01:51,148 surface, this is the surface that I attach to that closed 23 00:01:51,148 --> 00:01:54,88 loop. I choose it pointing up. 24 00:01:54,88 --> 00:02:02,472 And so the angle between DA and B, [inaudible] B is uniform. 25 00:02:02,472 --> 00:02:07,104 So the flux, phi B, is defined as the 26 00:02:07,104 --> 00:02:12,895 integral of B dot DA, over 27 00:02:12,895 --> 00:02:17,233 this open surface. Flux is a scalar. 28 00:02:17,233 --> 00:02:21,696 It's plus or it's minus or it's zero. 29 00:02:21,696 --> 00:02:28,142 Flux has no direction. So the flux in this case would 30 00:02:28,142 --> 00:02:35,084 be X Y, which is the area of this loop since the magnetic 31 00:02:35,084 --> 00:02:41,034 field is uniform. That's a very easy integral and 32 00:02:41,034 --> 00:02:45,84 then I get the magnetic field B, 33 00:02:45,84 --> 00:02:49,988 and then I get the cosine of the angle. 34 00:02:49,988 --> 00:02:56,1 So now according to Faraday, it is the time derivative of 35 00:02:56,1 --> 00:03:00,138 this quantity that determines the EMF. 36 00:03:00,138 --> 00:03:04,068 Now, you can do that in several ways. 37 00:03:04,068 --> 00:03:09,307 You can have dB dT, changing the magnetic fields. 38 00:03:09,307 --> 00:03:16,729 This is the area A of the loop. You can change the area. 39 00:03:16,729 --> 00:03:21,564 You can have da dt. But you can also change theta. 40 00:03:21,564 --> 00:03:27,19 You can have a d theta dt. And I will look at those today. 41 00:03:27,19 --> 00:03:31,631 This number here, the way I have chosen my da, 42 00:03:31,631 --> 00:03:35,875 is a positive number. If somehow this number 43 00:03:35,875 --> 00:03:41,303 increases in positive value, the induced current that is 44 00:03:41,303 --> 00:03:47,323 going to run will try to create a magnetic field to oppose the 45 00:03:47,323 --> 00:03:51,653 change. So in that case if the flux, 46 00:03:51,653 --> 00:03:55,776 which is now positive, is getting larger positive, 47 00:03:55,776 --> 00:04:00,067 then the current that's going to run will be in this 48 00:04:00,067 --> 00:04:02,591 direction. That's Lenz for you. 49 00:04:02,591 --> 00:04:06,798 So it creates by itself, this current will create a 50 00:04:06,798 --> 00:04:09,491 magnetic field in this direction. 51 00:04:09,491 --> 00:04:14,035 And if the magnetic flux, which is now positive the way 52 00:04:14,035 --> 00:04:16,727 I've defined it, were decreasing, 53 00:04:16,727 --> 00:04:21,019 then the current would go the other 54 00:04:21,019 --> 00:04:24,356 way around. Last time, I did several 55 00:04:24,356 --> 00:04:27,599 demonstration whereby we changed B. 56 00:04:27,599 --> 00:04:31,7 We had dB dT's. And there was one particular 57 00:04:31,7 --> 00:04:37,422 demonstration that blew your mind and that you will tell your 58 00:04:37,422 --> 00:04:42,477 grandchildren about and that you will always remember, 59 00:04:42,477 --> 00:04:45,624 I hope. Today, I'm going to change 60 00:04:45,624 --> 00:04:51,251 theta and I'm going to change the area, which will also give 61 00:04:51,251 --> 00:04:57,641 me then induced EMF's and therefore induced currents 62 00:04:57,641 --> 00:05:05,407 into a closed conducting loop. So let me make another drawing 63 00:05:05,407 --> 00:05:13,044 of the closed conducting loop. This has lengths Y and widths 64 00:05:13,044 --> 00:05:20,682 X, and I'm going to rotate this. My idea is you can see this 65 00:05:20,682 --> 00:05:27,154 three-dimensionally. I'm going to rotate this about 66 00:05:27,154 --> 00:05:31,231 this axis with angular frequency 67 00:05:31,231 --> 00:05:34,423 omega. Omega is two pi divided by the 68 00:05:34,423 --> 00:05:37,703 periods. The period is the time of one 69 00:05:37,703 --> 00:05:40,895 rotation. Normally we choose for that 70 00:05:40,895 --> 00:05:44,353 capital T. I don't want to do that today 71 00:05:44,353 --> 00:05:47,546 because T can confuse you with Tesla. 72 00:05:47,546 --> 00:05:52,954 And so I'm going to rotate this around so the angle theta that 73 00:05:52,954 --> 00:05:56,856 you have there, theta then becomes theta zero 74 00:05:56,856 --> 00:06:00,403 plus omega T, going back 75 00:06:00,403 --> 00:06:04,872 to eight oh one. And I choose this theta zero 76 00:06:04,872 --> 00:06:09,748 such that a T zero, I choose my theta to be zero, 77 00:06:09,748 --> 00:06:14,116 and so I have nothing to do with theta zero. 78 00:06:14,116 --> 00:06:17,367 So what now is the magnetic flux? 79 00:06:17,367 --> 00:06:21,836 This is my loop. I have to commit myself to a 80 00:06:21,836 --> 00:06:25,595 surface. Well, I will just choose this 81 00:06:25,595 --> 00:06:30,572 flat surface, just like I did there. 82 00:06:30,572 --> 00:06:36,504 I chose that flat surface. I'm free to choose any surface, 83 00:06:36,504 --> 00:06:42,331 why not taking the flat one. And so the flux of that flat 84 00:06:42,331 --> 00:06:46,805 surface is then the area which is X times A, 85 00:06:46,805 --> 00:06:50,863 X times Y, that's the area of this loop. 86 00:06:50,863 --> 00:06:54,401 And then I have the magnetic field. 87 00:06:54,401 --> 00:07:00,644 And then I have cosine omega T. Maxwell tells me it's not the 88 00:07:00,644 --> 00:07:06,409 flux that matters. It is the change in the flux 89 00:07:06,409 --> 00:07:09,039 that matters. OK, so d phi dt. 90 00:07:09,039 --> 00:07:12,939 I got the A, the area, I've got the magnetic 91 00:07:12,939 --> 00:07:15,116 field. An omega pops out, 92 00:07:15,116 --> 00:07:19,651 and I get a sign of omega T and I get a minus sign. 93 00:07:19,651 --> 00:07:24,73 Normally I don't care about minus signs, because I'm only 94 00:07:24,73 --> 00:07:28,902 interested in the magnitude of the induced EMF. 95 00:07:28,902 --> 00:07:33,437 I always know in which direction the 96 00:07:33,437 --> 00:07:35,75 current will flow, I really do, 97 00:07:35,75 --> 00:07:39,913 because I know Lenz's law. So you should never have too 98 00:07:39,913 --> 00:07:44,385 many hang-ups on those minus signs, but since I'm getting a 99 00:07:44,385 --> 00:07:49,011 minus sign out of this now here, it would be a little foolish 100 00:07:49,011 --> 00:07:53,792 not to put a minus here and make this into a plus because that, 101 00:07:53,792 --> 00:07:58,495 then, according to Faraday is immediately the EMF and that EMF 102 00:07:58,495 --> 00:08:02,967 is changing with time because you have this sign omega T in 103 00:08:02,967 --> 00:08:05,357 here. And so the current that is 104 00:08:05,357 --> 00:08:09,5 going to flow, the induced current, 105 00:08:09,5 --> 00:08:12,313 which will also be time-dependent, 106 00:08:12,313 --> 00:08:16,403 is the EMF divided by the resistance in the loop, 107 00:08:16,403 --> 00:08:20,324 and this is the total resistance of that entire 108 00:08:20,324 --> 00:08:23,477 network. There could be light bulbs in 109 00:08:23,477 --> 00:08:27,056 there, there could be resistances in there. 110 00:08:27,056 --> 00:08:30,721 It's the total resistance. And this current, 111 00:08:30,721 --> 00:08:34,982 when I rotate this loop, is going to alternate in a 112 00:08:34,982 --> 00:08:40,862 sinusoidal fashion. And we call that alternating 113 00:08:40,862 --> 00:08:45,311 current, AC. That's what's coming out of the 114 00:08:45,311 --> 00:08:49,243 wall, AC. Suppose this loop was double, 115 00:08:49,243 --> 00:08:53,589 and what I mean by double is the following, 116 00:08:53,589 --> 00:08:58,763 that it works like this. Follow my picture closely. 117 00:08:58,763 --> 00:09:02,074 I will go slowly. It's like this, 118 00:09:02,074 --> 00:09:07,144 like this, like this, so back and I close it here, 119 00:09:07,144 --> 00:09:12,215 so it's one closed loop, but I have 120 00:09:12,215 --> 00:09:15,39 two windings. I have to attach a surface to 121 00:09:15,39 --> 00:09:17,96 this closed loop. That's mandatory. 122 00:09:17,96 --> 00:09:22,118 Farado- Faraday insists I attach an open surface to this 123 00:09:22,118 --> 00:09:24,764 closed loop. What will it look like? 124 00:09:24,764 --> 00:09:28,317 Well, I advise you to take that, dip it in soap, 125 00:09:28,317 --> 00:09:31,492 and look at it, and what you will see then, 126 00:09:31,492 --> 00:09:35,877 because the soap will attach everywhere to the closed loop, 127 00:09:35,877 --> 00:09:38,221 you're going to see one surface. 128 00:09:38,221 --> 00:09:42,53 It's not two separate surface. You don't have two separate 129 00:09:42,53 --> 00:09:46,385 loops. It's one surface but sort 130 00:09:46,385 --> 00:09:50,906 of two layers. One is lower and the other one 131 00:09:50,906 --> 00:09:55,323 comes on top. And so, the magnetic flux will 132 00:09:55,323 --> 00:10:01,795 double now, because you're going to see that this magnetic field 133 00:10:01,795 --> 00:10:07,548 penetrates both this soap film and the one that is below, 134 00:10:07,548 --> 00:10:13,404 and so you get twice the EMF and if you have N windings in 135 00:10:13,404 --> 00:10:17,307 one closed loop, capital N, 136 00:10:17,307 --> 00:10:25,145 then the EMF that you get would be N times larger and you can 137 00:10:25,145 --> 00:10:31,545 make N one thousand. There's no problem with that. 138 00:10:31,545 --> 00:10:39,774 I'm going to do a demonstration for you whereby I'm going to use 139 00:10:39,774 --> 00:10:49,048 the earth's magnetic field and a loop that you see here that has 140 00:10:49,048 --> 00:10:55,56 forty-two windings. So my capital N is forty-two. 141 00:10:55,56 --> 00:11:00,579 Not just two like here, but forty-two. 142 00:11:00,579 --> 00:11:05,327 And it is circular. It has a radius. 143 00:11:05,327 --> 00:11:10,346 I think it's about thirty centimeters. 144 00:11:10,346 --> 00:11:16,722 Here you have it. It's about thirty centimeters. 145 00:11:16,722 --> 00:11:21,234 So the area, pi r squared, 146 00:11:21,234 --> 00:11:26,803 which is my capital A, pi R squared is about oh point 147 00:11:26,803 --> 00:11:32,264 two eight square meters. You may want to check that. 148 00:11:32,264 --> 00:11:38,047 I use the Earth's magnetic field, which is about half a 149 00:11:38,047 --> 00:11:43,83 Gauss, so that's about five times ten to the minus five 150 00:11:43,83 --> 00:11:49,828 Tesla, if we work in SI units. And I'm going to rotate it 151 00:11:49,828 --> 00:11:54,219 around with a period, periods 152 00:11:54,219 --> 00:11:58,567 of about one second. That means omega, 153 00:11:58,567 --> 00:12:05,502 two pi divided by the periods, is then about six radians per 154 00:12:05,502 --> 00:12:09,145 second. I call that six for now. 155 00:12:09,145 --> 00:12:16,197 And so what is the EMF that I'm going to get when I rotate it 156 00:12:16,197 --> 00:12:22,427 once around per second? Well, the EMF will change as a 157 00:12:22,427 --> 00:12:27,814 function of time. We're going to get forty-two, 158 00:12:27,814 --> 00:12:29,982 that's N. We're going to get A, 159 00:12:29,982 --> 00:12:33,451 that is oh point two eight. We're going to get B, 160 00:12:33,451 --> 00:12:37,86 that is five times ten to the minus five, and then we're going 161 00:12:37,86 --> 00:12:39,667 to get omega, that is six, 162 00:12:39,667 --> 00:12:42,125 and then we get this sign of six T. 163 00:12:42,125 --> 00:12:46,244 You see the equation there. The only difference is we have 164 00:12:46,244 --> 00:12:50,581 a capital N out here because we have N windings in the closed 165 00:12:50,581 --> 00:12:53,038 loop. And this number here in front 166 00:12:53,038 --> 00:12:57,986 of the sign six T, you should check that, 167 00:12:57,986 --> 00:13:01,824 is about three and a half millivolts. 168 00:13:01,824 --> 00:13:08,114 Three point five times ten to the minus three times the sign 169 00:13:08,114 --> 00:13:11,739 of six T, and that now is in volts. 170 00:13:11,739 --> 00:13:16,963 So you get an alternating EMF, positive, negative, 171 00:13:16,963 --> 00:13:23,253 and the maximum value that you would get is three and a half 172 00:13:23,253 --> 00:13:30,322 millivolts. If I look at the EMF as a 173 00:13:30,322 --> 00:13:37,956 function of time, it would be something like 174 00:13:37,956 --> 00:13:42,75 this. And from here to here, 175 00:13:42,75 --> 00:13:52,869 would then be one second if I really rotated around in one 176 00:13:52,869 --> 00:14:01,746 second. And so the current, 177 00:14:01,746 --> 00:14:05,158 the induced EMF, according to Ohm's Law, 178 00:14:05,158 --> 00:14:10,057 is always the induced current times the resistance of the 179 00:14:10,057 --> 00:14:14,693 whole loop, so the induced current will also have this 180 00:14:14,693 --> 00:14:18,892 shape, of course. And how high that is depends on 181 00:14:18,892 --> 00:14:22,392 how large R is. The EMF is independent of 182 00:14:22,392 --> 00:14:25,628 capital R. The EMF follows exclusively 183 00:14:25,628 --> 00:14:29,827 from those numbers. It's the current that depends 184 00:14:29,827 --> 00:14:33,354 on what the resistance is. 185 00:14:33,354 --> 00:14:36,368 Suppose now I rotate twice as fast. 186 00:14:36,368 --> 00:14:40,181 I double omega. Two things are changing now. 187 00:14:40,181 --> 00:14:43,994 For one thing, that the full period now goes 188 00:14:43,994 --> 00:14:47,54 from here to here, only in half a second. 189 00:14:47,54 --> 00:14:50,998 But there's something else that changes. 190 00:14:50,998 --> 00:14:55,254 The EMF now doubles, because look at my equation. 191 00:14:55,254 --> 00:14:58,978 It's hiding behind the blackboard, I think. 192 00:14:58,978 --> 00:15:05,234 There is an omega in there. It's linearly proportional to 193 00:15:05,234 --> 00:15:08,689 omega, because it's d phi dt that matters. 194 00:15:08,689 --> 00:15:13,155 See, the omega pops out, and so you now get double the 195 00:15:13,155 --> 00:15:18,127 EMF, so the three and a half millivolts maximum would become 196 00:15:18,127 --> 00:15:23,267 seven, and so if I try to make a drawing of that twice as high 197 00:15:23,267 --> 00:15:27,649 here, twice as low here, then you would get something 198 00:15:27,649 --> 00:15:32,957 like this, and so this omega is now twice this one. 199 00:15:32,957 --> 00:15:38,381 You get double the maximum value of the EMF. 200 00:15:38,381 --> 00:15:45,444 We're going to show that here. I'm going to improve on my 201 00:15:45,444 --> 00:15:49,984 lights. You see there a current meter 202 00:15:49,984 --> 00:15:55,281 with a sign sensitive, can go to the right, 203 00:15:55,281 --> 00:16:01,209 can go to the left. And I'm going to rotate this 204 00:16:01,209 --> 00:16:05,245 loop. When you rotate a loop in a 205 00:16:05,245 --> 00:16:10,605 magnetic field, you can even rotate it 206 00:16:10,605 --> 00:16:13,691 in such a way that you get no EMF. 207 00:16:13,691 --> 00:16:18,365 I can show that to you easily. If this is the loop, 208 00:16:18,365 --> 00:16:23,134 and if somehow the magnetic field came in like this, 209 00:16:23,134 --> 00:16:27,528 if you rotated this loop now around this access, 210 00:16:27,528 --> 00:16:32,577 there would never be an EMF, because the DA and B would 211 00:16:32,577 --> 00:16:38,468 always be perpendicular to each other, so there's never any flux 212 00:16:38,468 --> 00:16:41,539 going through this system. 213 00:16:41,539 --> 00:16:43,417 No flux change. But of course, 214 00:16:43,417 --> 00:16:47,043 if you rotate it around this direction, it would be fine. 215 00:16:47,043 --> 00:16:50,021 So think about this. Don't fall into that trap. 216 00:16:50,021 --> 00:16:53,711 You can rotate in such a way that there is no flux change. 217 00:16:53,711 --> 00:16:57,596 We don't have that problem at all because the magnetic fields 218 00:16:57,596 --> 00:16:59,992 here on earth, in Boston, doesn't come 219 00:16:59,992 --> 00:17:03,359 straight from heaven down, but it comes rather steep, 220 00:17:03,359 --> 00:17:05,495 so there's never any problem here. 221 00:17:05,495 --> 00:17:07,567 I don't have to worry about that. 222 00:17:07,567 --> 00:17:11,743 So here is that loop, forty-two windings. 223 00:17:11,743 --> 00:17:14,465 The scale there is in microamperes, 224 00:17:14,465 --> 00:17:19,029 so if you want to you can calculate what the resistance of 225 00:17:19,029 --> 00:17:23,032 the loop is when I rotate, but that's really not my 226 00:17:23,032 --> 00:17:26,155 objective. I want you to see that when I 227 00:17:26,155 --> 00:17:29,838 rotate it, that you get an alternating current. 228 00:17:29,838 --> 00:17:33,12 Very modest, because I rotate very slowly. 229 00:17:33,12 --> 00:17:36,723 Now I rotate faster, and it is proportional to 230 00:17:36,723 --> 00:17:42,969 omega, and so if I rotate faster you get a much larger maximum 231 00:17:42,969 --> 00:17:45,664 induced current. A larger EMF, 232 00:17:45,664 --> 00:17:50,126 a larger current. I don't know how fast I can go. 233 00:17:50,126 --> 00:17:53,194 This is about as fast as I can go. 234 00:17:53,194 --> 00:17:57,191 Gets almost up to four microamperes maximum, 235 00:17:57,191 --> 00:18:02,024 and so we are producing here AC, alternating current. 236 00:18:02,024 --> 00:18:07,23 We have slipping contacts here so that the system doesn't 237 00:18:07,23 --> 00:18:12,25 break, and we could put a light bulb here 238 00:18:12,25 --> 00:18:17,935 somewhere in this line and then the light bulb may glow. 239 00:18:17,935 --> 00:18:22,689 In United States, what comes out of the wall is 240 00:18:22,689 --> 00:18:27,031 sixty Hertz. So that means that the current 241 00:18:27,031 --> 00:18:33,129 through a light bulb becomes zero a hundred twenty times per 242 00:18:33,129 --> 00:18:36,54 second. A hundred twenty times per 243 00:18:36,54 --> 00:18:42,432 second do you go [inaudible] zero if you have sixty Hertz. 244 00:18:42,432 --> 00:18:47,084 Does it mean that hundred twenty 245 00:18:47,084 --> 00:18:51,1 times per second there is no light from the light bulb? 246 00:18:51,1 --> 00:18:55,265 No, it doesn't mean that because filaments get hot and so 247 00:18:55,265 --> 00:18:58,611 they still glow even when the current is zero. 248 00:18:58,611 --> 00:19:03,148 But they don't cool that fast. If you take a fluorescent bulb, 249 00:19:03,148 --> 00:19:05,602 then indeed, fluorescent tube goes 250 00:19:05,602 --> 00:19:09,024 completely off and on, hundred twenty times per 251 00:19:09,024 --> 00:19:12,891 second, and therefore you can use them very nicely as 252 00:19:12,891 --> 00:19:16,089 stroboscopes, but of course the frequency is 253 00:19:16,089 --> 00:19:20,18 fixed. You can't change the frequency. 254 00:19:20,18 --> 00:19:23,153 It's a hundred and twenty Hertz. 255 00:19:23,153 --> 00:19:28,43 So now you're getting the idea of an electric generator, 256 00:19:28,43 --> 00:19:31,404 or what we call, if you want to, 257 00:19:31,404 --> 00:19:35,913 a dynamo, which produces AC. You have a turbine, 258 00:19:35,913 --> 00:19:40,614 and a turbine rotates conducting loops in magnetic 259 00:19:40,614 --> 00:19:46,274 fields, and that according to Faraday will then produce your 260 00:19:46,274 --> 00:19:49,152 EMF. And that runs our economy. 261 00:19:49,152 --> 00:19:53,949 You have a permanent magnet and you 262 00:19:53,949 --> 00:19:58,558 rotate conducting loops, windings, in that magnetic 263 00:19:58,558 --> 00:20:01,97 field. The higher your magnetic field, 264 00:20:01,97 --> 00:20:05,75 the higher the EMF. The faster you rotate, 265 00:20:05,75 --> 00:20:09,991 the higher the EMF. The more windings you have, 266 00:20:09,991 --> 00:20:14,601 the higher the EMF. And the larger the area of your 267 00:20:14,601 --> 00:20:19,764 loops, the higher the EMF. As you can see on the equation 268 00:20:19,764 --> 00:20:23,729 that I keep hiding, but that's 269 00:20:23,729 --> 00:20:27,241 where it is. In the United States we have 270 00:20:27,241 --> 00:20:31,807 sixty Hertz as I mentioned, and we are committed to a 271 00:20:31,807 --> 00:20:36,812 maximum voltage coming out, that is the maximum value that 272 00:20:36,812 --> 00:20:41,73 you get from your alternating voltage, of hundred and ten 273 00:20:41,73 --> 00:20:46,91 times the square root of two volts, and we call that hundred 274 00:20:46,91 --> 00:20:50,423 ten volts. In Europe, we have fifty hertz 275 00:20:50,423 --> 00:20:56,042 and the maximum voltage there in the oscillation is 276 00:20:56,042 --> 00:20:59,624 two hundred and twenty times the square root of two. 277 00:20:59,624 --> 00:21:03,628 You can not change omega and go faster somewhere where you 278 00:21:03,628 --> 00:21:07,491 generate this electricity, because that would have major 279 00:21:07,491 --> 00:21:10,511 consequences. Number one, the EMF that comes 280 00:21:10,511 --> 00:21:14,022 out of the wall would go up, so you might blow your 281 00:21:14,022 --> 00:21:17,042 television, your circuits. But besides that, 282 00:21:17,042 --> 00:21:20,765 you would change also the frequency of the alternating 283 00:21:20,765 --> 00:21:24,768 current, and there are many systems that run in such a way 284 00:21:24,768 --> 00:21:28,771 that they're locked into that frequency, 285 00:21:28,771 --> 00:21:31,775 for instance, many electric clocks and 286 00:21:31,775 --> 00:21:35,51 certainly record players if you still have one. 287 00:21:35,51 --> 00:21:40,299 I locked into the sixty Hertz and so if you were to increase 288 00:21:40,299 --> 00:21:45,332 omega your record player would go around faster and your clocks 289 00:21:45,332 --> 00:21:47,93 would go faster. A long time ago, 290 00:21:47,93 --> 00:21:52,801 when I came over from Europe, I brought my record player with 291 00:21:52,801 --> 00:21:55,48 me. The record player requires two 292 00:21:55,48 --> 00:21:59,945 hundred and twenty volts, so I bought a transformer here 293 00:21:59,945 --> 00:22:03,162 to that, the hundred and ten 294 00:22:03,162 --> 00:22:05,84 volts at my home would become two twenty. 295 00:22:05,84 --> 00:22:08,653 That was fine. And so the record player was 296 00:22:08,653 --> 00:22:10,059 happy. It was running. 297 00:22:10,059 --> 00:22:13,943 But it ran twenty percent too fast because I had overlooked 298 00:22:13,943 --> 00:22:17,761 that there are sixty Hertz here and fifty Hertz in Europe. 299 00:22:17,761 --> 00:22:21,578 It was going a little bit too fast, and you know what that 300 00:22:21,578 --> 00:22:25,529 means when it goes too fast -- [inaudible] so you can't even 301 00:22:25,529 --> 00:22:28,074 here the music, and that's exactly what 302 00:22:28,074 --> 00:22:31,757 happened with my record player. So if we look at a power 303 00:22:31,757 --> 00:22:36,31 station, as we discussed earlier in this 304 00:22:36,31 --> 00:22:40,925 course, and let us suppose to get some- some numbers, 305 00:22:40,925 --> 00:22:45,54 that the maximum EMF that the power station produces, 306 00:22:45,54 --> 00:22:50,599 let's say, is three hundred kilovolts which it puts on the 307 00:22:50,599 --> 00:22:53,439 line. And let's say we have a- we 308 00:22:53,439 --> 00:22:58,231 have loops that have an area of about one square meter, 309 00:22:58,231 --> 00:23:03,29 and that they use magnetic fields which are let's say half 310 00:23:03,29 --> 00:23:06,573 a Tesla. It's by no means unreasonable 311 00:23:06,573 --> 00:23:12,144 numbers. And if now you want sixty Hertz 312 00:23:12,144 --> 00:23:18,86 frequency, so your frequency F sixty Hertz, so your omega is 313 00:23:18,86 --> 00:23:23,073 about six times higher, two pi higher. 314 00:23:23,073 --> 00:23:28,651 It's about three hundred sixty radians per second. 315 00:23:28,651 --> 00:23:34,115 If now you have about seventeen hundred windings, 316 00:23:34,115 --> 00:23:40,377 and you can check that at home, there you get your three 317 00:23:40,377 --> 00:23:45,386 hundred kilovolts. Power is induced EMF times 318 00:23:45,386 --> 00:23:51,989 current and with Ohm's Law you can replace E 319 00:23:51,989 --> 00:23:55,273 by IR, and so you get I square R. 320 00:23:55,273 --> 00:24:01,021 This is joules per second, and so someone has to do work. 321 00:24:01,021 --> 00:24:06,256 Someone has to put in the energy, for which you need 322 00:24:06,256 --> 00:24:11,081 perhaps fossil fuel, have to burn oil or coal to 323 00:24:11,081 --> 00:24:15,392 keep the turbines going, or nuclear energy, 324 00:24:15,392 --> 00:24:17,753 or waterfalls, or winds. 325 00:24:17,753 --> 00:24:23,983 But something gotta keep those windings going, 326 00:24:23,983 --> 00:24:30,885 to keep our economy going. A typical power station in this 327 00:24:30,885 --> 00:24:37,909 country has about one thousand, produces about one thousand 328 00:24:37,909 --> 00:24:42,752 megawatts. It is about one thousand times 329 00:24:42,752 --> 00:24:49,655 a million joules per second. I have here a generator which 330 00:24:49,655 --> 00:24:54,74 is run by manpower, and for this 331 00:24:54,74 --> 00:24:58,839 I need a strong man. Who wants to volunteer? 332 00:24:58,839 --> 00:25:01,413 You look very strong, there. 333 00:25:01,413 --> 00:25:04,844 Ah, you don't want to look at me now. 334 00:25:04,844 --> 00:25:08,467 Come on. Every morning we talk a little 335 00:25:08,467 --> 00:25:13,9 bit, but now you didn't see me. This is a power generator, 336 00:25:13,9 --> 00:25:17,617 magnetic field. You see the magnet here. 337 00:25:17,617 --> 00:25:22,955 And there are current loops, windings, and when you crank 338 00:25:22,955 --> 00:25:27,189 this you turn those windings into 339 00:25:27,189 --> 00:25:31,342 these magnetic fields. There's a light bulb here, 340 00:25:31,342 --> 00:25:35,062 twenty watts, and this gentleman is go- what 341 00:25:35,062 --> 00:25:37,571 is your name? Student: Naveen. 342 00:25:37,571 --> 00:25:40,513 Naveen. That's almost my last name. 343 00:25:40,513 --> 00:25:45,618 Can you start turning and see whether you can produce twenty 344 00:25:45,618 --> 00:25:48,646 watts? Put your foot on the -- yeah, 345 00:25:48,646 --> 00:25:52,28 yeah, keep going. Ah, man, a little better! 346 00:25:52,28 --> 00:25:55,654 Keep going! That's not twenty watts yet! 347 00:25:55,654 --> 00:26:00,413 Are you sure you had a good breakfast 348 00:26:00,413 --> 00:26:05,841 this morning? He's producing twenty- roughly 349 00:26:05,841 --> 00:26:12,405 twenty joules per second now. Will you stop a minute? 350 00:26:12,405 --> 00:26:18,591 We have six light bulbs here. Naveen, be my guest. 351 00:26:18,591 --> 00:26:24,146 Hundred twenty watts. Man, where is Superman? 352 00:26:24,146 --> 00:26:29,069 I see nothing! Hundred-twenty joules per 353 00:26:29,069 --> 00:26:34,553 second, he doesn't even come close! 354 00:26:34,553 --> 00:26:37,765 Keep going, man, keep going. 355 00:26:37,765 --> 00:26:44,07 You want me to stop the whole [inaudible], keep going. 356 00:26:44,07 --> 00:26:46,449 Forget it! Forget it. 357 00:26:46,449 --> 00:26:50,969 You tried, and that's all that matters. 358 00:26:50,969 --> 00:26:57,631 But you see how difficult it is to produce hundred twenty 359 00:26:57,631 --> 00:27:03,841 joules per second. Now, think about it, 360 00:27:03,841 --> 00:27:07,98 when you run your hundred watt light bulb at home, 361 00:27:07,98 --> 00:27:12,71 and you do that for ten hours, that is one kilowatt hour. 362 00:27:12,71 --> 00:27:17,61 That costs you only ten cents. Would you run that ten hours 363 00:27:17,61 --> 00:27:20,566 for ten cents? You can't even do it, 364 00:27:20,566 --> 00:27:22,931 man! I'll show you something. 365 00:27:22,931 --> 00:27:27,999 I do a lot of mountaineering, and in the mountains you want a 366 00:27:27,999 --> 00:27:32,223 light that always works. When you need it the most, 367 00:27:32,223 --> 00:27:36,108 the batteries are flat, so you 368 00:27:36,108 --> 00:27:41,635 always have with you a dynamo. This is my dynamo, 369 00:27:41,635 --> 00:27:44,629 hand-powered. You see that? 370 00:27:44,629 --> 00:27:50,847 That is Superman for you! This is a hundred-twenty watt 371 00:27:50,847 --> 00:27:55,683 light bulb! And I can keep it going all the 372 00:27:55,683 --> 00:27:59,022 time. I can do better for you. 373 00:27:59,022 --> 00:28:04,434 I have a radio here. And this radio has a little 374 00:28:04,434 --> 00:28:08,924 generator. Magnetic field, 375 00:28:08,924 --> 00:28:14,381 constant magnets, permanent magnet, 376 00:28:14,381 --> 00:28:23,689 and windings which you turn around, and when I do that I do 377 00:28:23,689 --> 00:28:31,231 work, and I generate an EMF. I charge batteries. 378 00:28:31,231 --> 00:28:39,577 And then I can play this radio. [radio voice] 379 00:28:39,577 --> 00:28:45,061 I don't know about that. And it's designed in such a way 380 00:28:45,061 --> 00:28:50,545 that if you turn just for a minute that you have several 381 00:28:50,545 --> 00:28:53,836 hours that you can play the radio. 382 00:28:53,836 --> 00:28:58,722 It's quite amazing. Now, we're going to change the 383 00:28:58,722 --> 00:29:01,913 area. So far we've changed theta. 384 00:29:01,913 --> 00:29:05,303 Now we're going to change the area. 385 00:29:05,303 --> 00:29:10,014 I have again a conducting loop here. 386 00:29:10,014 --> 00:29:14,347 But now I have a crossbar here which I can move. 387 00:29:14,347 --> 00:29:18,865 I can move it with a velocity V in this direction, 388 00:29:18,865 --> 00:29:23,843 or I can move it to the left. Let this be L and let the 389 00:29:23,843 --> 00:29:27,623 lengths be X. My surface that I'm going to 390 00:29:27,623 --> 00:29:32,232 choose, I always have to commit to an open surface, 391 00:29:32,232 --> 00:29:36,657 is a flat surface. And I'll make life very simple 392 00:29:36,657 --> 00:29:40,714 for all of us, let's assume that the magnetic 393 00:29:40,714 --> 00:29:44,282 field going straight up. 394 00:29:44,282 --> 00:29:48,273 Let my DA, it's perpendicular to the surface, 395 00:29:48,273 --> 00:29:51,719 B straight up, B and DA are in the same 396 00:29:51,719 --> 00:29:54,893 direction now. Makes my life simple. 397 00:29:54,893 --> 00:29:59,7 And so what is the flux now, going through my surface? 398 00:29:59,7 --> 00:30:02,874 Well, that's the area, which is L X, 399 00:30:02,874 --> 00:30:07,862 times the magnetic field, which I will assume is uniform 400 00:30:07,862 --> 00:30:12,579 throughout this surface. So as simple as you can have 401 00:30:12,579 --> 00:30:15,571 it. Faraday says, 402 00:30:15,571 --> 00:30:21,741 "I don't care what the magnetic flux is!" I want to know how 403 00:30:21,741 --> 00:30:26,447 that magnetic flux is changing. All right, OK, 404 00:30:26,447 --> 00:30:31,257 Mister Faraday. D phi dt equals L times B times 405 00:30:31,257 --> 00:30:34,498 dx dt. But dx dt is my velocity, 406 00:30:34,498 --> 00:30:37,949 and so I get here times the speed. 407 00:30:37,949 --> 00:30:43,282 Dx dt is the velocity. And this now is the magnitude 408 00:30:43,282 --> 00:30:48,055 of the EMF. Notice I don't care about minus 409 00:30:48,055 --> 00:30:50,609 signs. I just want to know how large 410 00:30:50,609 --> 00:30:52,945 the EMF is in terms of magnitude. 411 00:30:52,945 --> 00:30:57,106 I always know the direction, because I know if I move this 412 00:30:57,106 --> 00:31:01,487 to the right that the flux is positive, the way I have chosen 413 00:31:01,487 --> 00:31:05,794 my DA, and as I move it to the right this flux is increasing 414 00:31:05,794 --> 00:31:09,882 and so I know that the current is going to run like this, 415 00:31:09,882 --> 00:31:15,284 which then creates a magnetic field that opposes the change. 416 00:31:15,284 --> 00:31:20,827 And if I go in the other direction with the velocity, 417 00:31:20,827 --> 00:31:24,985 then of course the current will reverse. 418 00:31:24,985 --> 00:31:28,29 Phi L X B, I can live with that. 419 00:31:28,29 --> 00:31:33,194 D phi dt, I can put a B here, if you like that, 420 00:31:33,194 --> 00:31:38,844 to remind you that we're dealing with magnetic fluxes, 421 00:31:38,844 --> 00:31:40,55 L B V. I'm happy. 422 00:31:40,55 --> 00:31:46,094 If I look here at this rod, try to make you see three 423 00:31:46,094 --> 00:31:54,267 dimensionally this rod is coming straight out of the blackboard. 424 00:31:54,267 --> 00:31:58,041 Then the current is now coming to you. 425 00:31:58,041 --> 00:32:03,958 The magnetic field is pointing straight up, and so remember 426 00:32:03,958 --> 00:32:09,467 that the Lawrence force is always in the direction of I 427 00:32:09,467 --> 00:32:15,588 cross B, is in this direction. That means the Lawrence force, 428 00:32:15,588 --> 00:32:20,077 F L, which in this case would be the current, 429 00:32:20,077 --> 00:32:26,198 times the length of this bar which is the length 430 00:32:26,198 --> 00:32:30,147 of this bar times B. That is the force that I have 431 00:32:30,147 --> 00:32:34,821 to apply if I put it to the right, because that force is to 432 00:32:34,821 --> 00:32:39,254 the left, so the force of [inaudible] is the same but in 433 00:32:39,254 --> 00:32:42,8 this direction. I have to overcome the force, 434 00:32:42,8 --> 00:32:45,782 the Lawrence force, in this direction. 435 00:32:45,782 --> 00:32:49,005 And so it's clear that I have to do work. 436 00:32:49,005 --> 00:32:53,277 I have a force in this direction and I move it in this 437 00:32:53,277 --> 00:32:57,468 direction, and so I do positive work. 438 00:32:57,468 --> 00:33:02,028 What happens with that work, well, that comes out in the 439 00:33:02,028 --> 00:33:06,009 form of heat in the resistance of this conductor. 440 00:33:06,009 --> 00:33:09,906 I'm creating an EMF. A current is going to flow, 441 00:33:09,906 --> 00:33:14,384 and the power is the EMF times the current, I square R. 442 00:33:14,384 --> 00:33:17,037 It comes out in the form of heat. 443 00:33:17,037 --> 00:33:21,93 If I change the direction when I push in, velocity is now in 444 00:33:21,93 --> 00:33:25,413 this direction, then clearly the current is 445 00:33:25,413 --> 00:33:30,588 going to change direction. And so when I push in, 446 00:33:30,588 --> 00:33:35,27 the Lawrence force will also flip over and so the force for 447 00:33:35,27 --> 00:33:39,145 me will flip over, so again I have to do positive 448 00:33:39,145 --> 00:33:42,051 work. There's no such thing as a free 449 00:33:42,051 --> 00:33:46,733 lunch, no matter what I do. Whether I pull this way or push 450 00:33:46,733 --> 00:33:51,576 in, I always have to do positive work and that work is always 451 00:33:51,576 --> 00:33:55,935 converted then to heat, in the resistance of that loop. 452 00:33:55,935 --> 00:34:00,133 So the work that I do, let me express it in terms of- 453 00:34:00,133 --> 00:34:02,419 of power. 454 00:34:02,419 --> 00:34:10,337 The power that I generate is my force, dot product with my 455 00:34:10,337 --> 00:34:15,754 velocity and remember from eight oh one. 456 00:34:15,754 --> 00:34:22,977 The work that I do is force over a little element dx. 457 00:34:22,977 --> 00:34:30,2 But power is work per unit time, so the dx dt becomes 458 00:34:30,2 --> 00:34:35,598 velocity. And my force and my velocity 459 00:34:35,598 --> 00:34:41,215 are always in the same direction when I push there in this 460 00:34:41,215 --> 00:34:46,141 direction, and when I pull there in this direction. 461 00:34:46,141 --> 00:34:50,969 I always do positive work. And so the power that I 462 00:34:50,969 --> 00:34:55,6 generate is my force. That's the magnitude of my 463 00:34:55,6 --> 00:34:59,542 force, which is I L B times the velocity. 464 00:34:59,542 --> 00:35:04,173 But that must also be the EMF times the current, 465 00:35:04,173 --> 00:35:10,636 and notice now that the EMF therefore I goes is L times B 466 00:35:10,636 --> 00:35:13,56 times V. And so now I have shown you 467 00:35:13,56 --> 00:35:18,323 that the EMF is exactly what I er found before in terms of 468 00:35:18,323 --> 00:35:22,166 magnitude by now I have not used Faraday's Law. 469 00:35:22,166 --> 00:35:26,845 This is purely a derivation based off the work that I do, 470 00:35:26,845 --> 00:35:31,441 and the work per unit time. So it's interesting that you 471 00:35:31,441 --> 00:35:36,12 can also think of it that way. Let me check my equations. 472 00:35:36,12 --> 00:35:40,548 E I, I R squared, I can live with that. 473 00:35:40,548 --> 00:35:45,949 Power, force dotted with the velocity. 474 00:35:45,949 --> 00:35:54,414 I L B V, this is the magnitude of the EMF, and that's fine. 475 00:35:54,414 --> 00:36:02,587 If I have a conducting disk, solid disk, and I move that, 476 00:36:02,587 --> 00:36:08,571 I try to move it through a magnetic field, 477 00:36:08,571 --> 00:36:16,179 north pole, south pole. This is the magnetic field. 478 00:36:16,179 --> 00:36:21,183 It's a little weaker here, little weaker there. 479 00:36:21,183 --> 00:36:25,861 I move this in. Then there comes a time when 480 00:36:25,861 --> 00:36:32,171 this disk is here that magnetic field lines go through this 481 00:36:32,171 --> 00:36:36,088 portion. That means the magnetic flux 482 00:36:36,088 --> 00:36:39,569 through this surface is changing. 483 00:36:39,569 --> 00:36:45,838 Lenz doesn't like that. Farado- Faraday doesn't like 484 00:36:45,838 --> 00:36:48,915 that. And so what's going to happen, 485 00:36:48,915 --> 00:36:53,046 the current is going to go around now like this. 486 00:36:53,046 --> 00:36:57,881 It's not so easy to precisely determine how that current 487 00:36:57,881 --> 00:37:01,661 exactly flows. But this current will be seen 488 00:37:01,661 --> 00:37:06,144 from above clockwise, so that it produces a magnetic 489 00:37:06,144 --> 00:37:10,979 field in this direction to oppose the change in magnetic 490 00:37:10,979 --> 00:37:14,056 flux. And we call these current eddy 491 00:37:14,056 --> 00:37:16,078 currents. Eddy currents. 492 00:37:16,078 --> 00:37:21,024 The eddy current produces heat in here. 493 00:37:21,024 --> 00:37:26,229 The heat is the product in joules per second of the power E 494 00:37:26,229 --> 00:37:29,55 times I. I squared R always comes down 495 00:37:29,55 --> 00:37:34,127 to the same, so this disk will heat up a little bit. 496 00:37:34,127 --> 00:37:37,896 The resistance now is the resistance there. 497 00:37:37,896 --> 00:37:41,755 And that means that the disk will slow down. 498 00:37:41,755 --> 00:37:46,242 At the expense of kinetic energy, heat is produced, 499 00:37:46,242 --> 00:37:51,35 and it won't go as fast through this field than 500 00:37:51,35 --> 00:37:54,945 the situation would be if there were no field. 501 00:37:54,945 --> 00:37:57,661 And we call that magnetic breaking. 502 00:37:57,661 --> 00:38:02,374 And you can easily convince yourself, which you should do at 503 00:38:02,374 --> 00:38:07,247 home, that if you look at the current right here coming out of 504 00:38:07,247 --> 00:38:12,279 the blackboard and you calculate the Lawrence force right there, 505 00:38:12,279 --> 00:38:16,833 you will see that the Lawrence force is in this direction. 506 00:38:16,833 --> 00:38:21,676 It's pushing it out. It opposes the motion. 507 00:38:21,676 --> 00:38:24,866 And I can demonstrate that to you. 508 00:38:24,866 --> 00:38:29,798 I have here a pendulum. The pendulum is a conducting 509 00:38:29,798 --> 00:38:34,149 copper plate like so, which I'm going to swing 510 00:38:34,149 --> 00:38:37,726 between magnetic poles which are here. 511 00:38:37,726 --> 00:38:41,11 Going to swing it in this direction. 512 00:38:41,11 --> 00:38:46,428 In fact, I have two pendulums, one whereby this is solid 513 00:38:46,428 --> 00:38:52,809 copper, and I have another one whereby it is 514 00:38:52,809 --> 00:38:56,332 slotted, like teeth. If I'm going to oscillate this 515 00:38:56,332 --> 00:38:59,925 one in a magnetic field, you're going to get current 516 00:38:59,925 --> 00:39:03,448 there, eddy currents, sometimes clockwise sometimes 517 00:39:03,448 --> 00:39:07,746 counterclockwise depending upon how the magnetic flux for that 518 00:39:07,746 --> 00:39:10,916 surface is changing. Whether it moves into the 519 00:39:10,916 --> 00:39:15,143 magnetic field or whether it moves out of the magnetic field, 520 00:39:15,143 --> 00:39:17,398 it will always oppose its motion. 521 00:39:17,398 --> 00:39:20,075 And so it will damp, you will see that. 522 00:39:20,075 --> 00:39:22,963 And it's at the expense of kinetic energy, 523 00:39:22,963 --> 00:39:26,866 heat will be produced in this copper. 524 00:39:26,866 --> 00:39:30,987 If you do it with something like this, the damping will be 525 00:39:30,987 --> 00:39:34,313 substantially less. Not zero, but substantially 526 00:39:34,313 --> 00:39:38,434 less, because now if there is an EMF that wants to drive a 527 00:39:38,434 --> 00:39:42,772 current, this current has to go through this opening which is 528 00:39:42,772 --> 00:39:46,098 air, which has a huge resistance, and remember, 529 00:39:46,098 --> 00:39:49,713 power is E times I. And if the- and it's I square R 530 00:39:49,713 --> 00:39:53,617 and if the, if the current is extremely low because the 531 00:39:53,617 --> 00:39:58,046 resistance is so absurdly high then you don't 532 00:39:58,046 --> 00:40:01,975 dissipate much power, and so there's not much damping 533 00:40:01,975 --> 00:40:05,905 and I can show that to you. By the way, this damping, 534 00:40:05,905 --> 00:40:10,287 this magnetic damping is used sometimes for scales that you 535 00:40:10,287 --> 00:40:14,67 weigh yourself on so that it doesn't oscillate for too long 536 00:40:14,67 --> 00:40:18,523 so it damps very quickly. So you're going to see the 537 00:40:18,523 --> 00:40:22,15 oscillations there, and it's going to be a little 538 00:40:22,15 --> 00:40:27,44 dark but that's the best way that I can make you see it. 539 00:40:27,44 --> 00:40:30,343 Turn on the power. So you see there, 540 00:40:30,343 --> 00:40:33,661 the loop -- I'll give you a little light. 541 00:40:33,661 --> 00:40:38,388 And first I will oscillate it without any magnetic fields. 542 00:40:38,388 --> 00:40:42,37 I can power this magnet because it has solenoids. 543 00:40:42,37 --> 00:40:46,186 So we'll just oscillate it, no magnetic fields. 544 00:40:46,186 --> 00:40:49,172 Give you a feeling how it oscillates. 545 00:40:49,172 --> 00:40:53,651 What you see on the left is the reflection, by the way, 546 00:40:53,651 --> 00:40:59,291 against the magnetic poles. So this gives you an idea of 547 00:40:59,291 --> 00:41:02,681 how it oscillates. And now I will turn on the 548 00:41:02,681 --> 00:41:04,145 magnetic field, now. 549 00:41:04,145 --> 00:41:07,457 Just likes going into mud. I'll do it again. 550 00:41:07,457 --> 00:41:11,309 Oh, hitting the magnetic poles. We don't want that. 551 00:41:11,309 --> 00:41:13,003 Now, amazing, isn't it? 552 00:41:13,003 --> 00:41:17,471 And it doesn't matter whether it goes in or whether it goes 553 00:41:17,471 --> 00:41:19,859 out. And now I will use the ones 554 00:41:19,859 --> 00:41:22,941 with the teeth, and you will see there is 555 00:41:22,941 --> 00:41:27,177 damping, but it's substantially less, 556 00:41:27,177 --> 00:41:32,514 so this is without magnetic fields. 557 00:41:32,514 --> 00:41:35,106 And now with, now. 558 00:41:35,106 --> 00:41:44,102 You can see there's damping, but it's nowhere nearly as much 559 00:41:44,102 --> 00:41:52,641 as there was on the one that was- that didn't have teeth. 560 00:41:52,641 --> 00:42:00,418 I have here a remarkable example of 561 00:42:00,418 --> 00:42:04,497 how our economy is run. I have there some windings, 562 00:42:04,497 --> 00:42:07,923 not just some. We don't even know how many, 563 00:42:07,923 --> 00:42:11,921 thousands, copper wire going around, going around, 564 00:42:11,921 --> 00:42:14,042 going around, going around. 565 00:42:14,042 --> 00:42:17,632 It's one wire, and then there is a light bulb 566 00:42:17,632 --> 00:42:20,405 in that loop. And here is a magnet. 567 00:42:20,405 --> 00:42:24,974 We don't know the strength, but I would say it's not more 568 00:42:24,974 --> 00:42:28,237 than a kilogauss, probably a little less. 569 00:42:28,237 --> 00:42:32,724 And when I move this between these poles, magnetic field 570 00:42:32,724 --> 00:42:36,725 let's say is going in this direction. 571 00:42:36,725 --> 00:42:39,238 I don't know whether it's in this or that. 572 00:42:39,238 --> 00:42:42,732 I don't know the color code. But there is a magnetic field 573 00:42:42,732 --> 00:42:45,49 going through here, so there's a change in the 574 00:42:45,49 --> 00:42:47,574 magnetic flux through this surface. 575 00:42:47,574 --> 00:42:50,577 Very crazy surface. If there are a thousand wires, 576 00:42:50,577 --> 00:42:53,274 this surface goes a thousand times like this, 577 00:42:53,274 --> 00:42:55,604 remember? And then there is going to be 578 00:42:55,604 --> 00:42:58,117 an induced EMF, and there's going to be an 579 00:42:58,117 --> 00:43:01,12 induced current and this light will glow a little. 580 00:43:01,12 --> 00:43:04,43 If I go in very slowly, you just see teeny weeny little 581 00:43:04,43 --> 00:43:07,856 light. If I go very fast, 582 00:43:07,856 --> 00:43:12,32 then the magnetic flux change is high, high EMF, 583 00:43:12,32 --> 00:43:15,55 lot of light. So I'll make it dark, 584 00:43:15,55 --> 00:43:18,589 darker, so that you can see that. 585 00:43:18,589 --> 00:43:23,339 Oh, we don't want this. In fact, we don't need that 586 00:43:23,339 --> 00:43:26,853 display at all. So, if you can see me, 587 00:43:26,853 --> 00:43:32,742 I have it now and I'm going to bring it near the magnetic poles 588 00:43:32,742 --> 00:43:36,843 and I go very slowly. I do it now. 589 00:43:36,843 --> 00:43:39,106 You see? I pull out, a little bit of 590 00:43:39,106 --> 00:43:41,499 light, I go in, a little bit of light. 591 00:43:41,499 --> 00:43:43,762 I'm right in now, holding it steady, 592 00:43:43,762 --> 00:43:45,056 nothing happens. Why? 593 00:43:45,056 --> 00:43:48,936 Because there's no flux change. Magnetic field is very strong 594 00:43:48,936 --> 00:43:52,493 now through these loops. Faraday doesn't care how strong 595 00:43:52,493 --> 00:43:54,886 it is. He only cares about the change. 596 00:43:54,886 --> 00:43:57,214 I pull it out, a little bit of light. 597 00:43:57,214 --> 00:43:59,284 Put it in, a little bit of light. 598 00:43:59,284 --> 00:44:02,776 Whether I pull in or whether I pull out doesn't matter. 599 00:44:02,776 --> 00:44:05,945 If I do it very fast, I may be able to generate so 600 00:44:05,945 --> 00:44:10,565 much current that the bulb may even blow. 601 00:44:10,565 --> 00:44:14,625 I'll try that, because I know you like the 602 00:44:14,625 --> 00:44:17,992 idea of breaking things. We all do. 603 00:44:17,992 --> 00:44:22,448 You're not along. Let's see whether I managed. 604 00:44:22,448 --> 00:44:25,121 Yes, I did. It's broken now. 605 00:44:25,121 --> 00:44:29,776 So you got something for your money, didn't you. 606 00:44:29,776 --> 00:44:34,826 That runs our economy. Windings, conducting windings 607 00:44:34,826 --> 00:44:41,757 that are being moved forcefully through magnetic fields. 608 00:44:41,757 --> 00:44:46,998 Faraday was once interviewed by reporters when he came up with 609 00:44:46,998 --> 00:44:50,435 this law, and they said to him, "So what? 610 00:44:50,435 --> 00:44:55,761 So fine, so you moved a winding through a magnetic field and so 611 00:44:55,761 --> 00:44:58,768 you get a little bit of electricity? 612 00:44:58,768 --> 00:45:03,407 So what?" And his answer was, some day you will tax it. 613 00:45:03,407 --> 00:45:06,071 And he was right. He had vision. 614 00:45:06,071 --> 00:45:08,992 The reporters didn't. Part of life. 615 00:45:08,992 --> 00:45:14,53 I can show you another striking example of, um, 616 00:45:14,53 --> 00:45:19,713 of magnetic breaking. I have here a magnet which I 617 00:45:19,713 --> 00:45:25,637 can also power with solenoids, and I have here two rings. 618 00:45:25,637 --> 00:45:31,772 One ring, which is complete in the sense that it's like so, 619 00:45:31,772 --> 00:45:36,849 a conducting ring. I drop it through the magnetic 620 00:45:36,849 --> 00:45:42,349 field and as the flux is changing the eddy 621 00:45:42,349 --> 00:45:46,82 current will flow in such a direction that it will oppose 622 00:45:46,82 --> 00:45:51,37 the change, and so it could either be in this direction or 623 00:45:51,37 --> 00:45:53,844 in this direction. I don't know. 624 00:45:53,844 --> 00:45:56,798 But it will flow to oppose the change. 625 00:45:56,798 --> 00:45:59,831 And so as it enters the magnetic field, 626 00:45:59,831 --> 00:46:03,503 when the flux is increasing, it will be damped. 627 00:46:03,503 --> 00:46:07,574 When it is in the magnetic field and the flux is not 628 00:46:07,574 --> 00:46:12,922 changing very much anymore there will be no damping, 629 00:46:12,922 --> 00:46:16,554 but when it comes out of the magnetic field the flux is 630 00:46:16,554 --> 00:46:18,84 changing again through the surface. 631 00:46:18,84 --> 00:46:21,866 It will be damped again, and you can see that. 632 00:46:21,866 --> 00:46:25,901 And then I will throw through there another ring which is the 633 00:46:25,901 --> 00:46:29,129 same dimension but this ring has an opening here. 634 00:46:29,129 --> 00:46:33,096 Air, the resistance is huge. So the current that is going to 635 00:46:33,096 --> 00:46:36,324 flow, this eddy current, is way lower because the 636 00:46:36,324 --> 00:46:40,157 resistance is so high and so there is no power dissipation 637 00:46:40,157 --> 00:46:45,268 because I is so low and so there is no heat produced at the 638 00:46:45,268 --> 00:46:50,144 expense of kinetic energy, so there is no damping. 639 00:46:50,144 --> 00:46:53,527 There is no force, no strong force, 640 00:46:53,527 --> 00:46:57,508 that opposes it. And I can show you both. 641 00:46:57,508 --> 00:47:01,588 And for this I need the DC power on again, 642 00:47:01,588 --> 00:47:06,266 and we're going to project it there on the wall. 643 00:47:06,266 --> 00:47:11,241 I have to wait and see that I get my carbon arc up. 644 00:47:11,241 --> 00:47:15,72 There it comes. So we're going to project this 645 00:47:15,72 --> 00:47:20,42 slot which is the opening between 646 00:47:20,42 --> 00:47:24,734 the pole shoes on the wall there, light off, 647 00:47:24,734 --> 00:47:28,748 light off, all off. And you see it there. 648 00:47:28,748 --> 00:47:33,163 This is that magnet. And here comes the ring. 649 00:47:33,163 --> 00:47:39,283 The ring, that is going to be decelerated heavily when it goes 650 00:47:39,283 --> 00:47:40,487 in. Watch it. 651 00:47:40,487 --> 00:47:45,203 Oh, small detail. I forgot to turn the power on. 652 00:47:45,203 --> 00:47:50,922 [inaudible] There we go. Power goes on now. 653 00:47:50,922 --> 00:47:56,012 Actually, you see now -- I did that purposely -- you see now 654 00:47:56,012 --> 00:48:00,411 how fast it should go if there is no magnetic field, 655 00:48:00,411 --> 00:48:03,258 and now there is a magnetic field. 656 00:48:03,258 --> 00:48:06,535 Now, did you notice these three phases? 657 00:48:06,535 --> 00:48:10,331 You get damping, and then when it is right in 658 00:48:10,331 --> 00:48:14,558 the magnetic field, when there is very little flux 659 00:48:14,558 --> 00:48:19,561 change, then it picks up speed again and then it slows down 660 00:48:19,561 --> 00:48:21,372 again. Watch it again. 661 00:48:21,372 --> 00:48:26,674 Now, the one with the slot. Amazing, huh? 662 00:48:26,674 --> 00:48:31,656 Now one- once more th- one without the slot. 663 00:48:31,656 --> 00:48:36,639 Magnetic damping. All of that result of eddy 664 00:48:36,639 --> 00:48:42,317 currents, all of that the result of Faraday's law. 665 00:48:42,317 --> 00:48:47,994 Heat is produced at the expense of kinetic energy. 666 00:48:47,994 --> 00:48:53,556 So if I summarize, then when we create an induced 667 00:48:53,556 --> 00:49:00,985 EMF and we run a current, we either have to change 668 00:49:00,985 --> 00:49:05,875 magnetic fields in time, or we have to change the area 669 00:49:05,875 --> 00:49:10,027 in time, or we have to change the angle theta, 670 00:49:10,027 --> 00:49:15,193 but we must make a change in the magnetic flux through an 671 00:49:15,193 --> 00:49:18,515 open surface. And the energy that has 672 00:49:18,515 --> 00:49:21,744 dissipated must come from somewhere. 673 00:49:21,744 --> 00:49:26,726 When you rotate the coils, when you power your dynamo, 674 00:49:26,726 --> 00:49:30,971 you have to do work. When you move the crossbar 675 00:49:30,971 --> 00:49:35,236 around, you have to do work. 676 00:49:35,236 --> 00:49:39,803 When you move the coil as I did there, in-between the magnetic 677 00:49:39,803 --> 00:49:43,471 poles to make the light glow, you have to do work. 678 00:49:43,471 --> 00:49:48,038 You always experience a force that is against the direction of 679 00:49:48,038 --> 00:49:52,305 your motion, which is another manifestation of Lenz's Law. 680 00:49:52,305 --> 00:49:56,498 And thank goodness it is that way, because if it were the 681 00:49:56,498 --> 00:49:59,942 other way around, our universe could not exist, 682 00:49:59,942 --> 00:50:03,985 and I'll give you an example. Suppose we have a growing 683 00:50:03,985 --> 00:50:06,983 magnetic field somewhere. 684 00:50:06,983 --> 00:50:10,437 And this growing magnetic field creates an EMF, 685 00:50:10,437 --> 00:50:13,441 and suppose that EMF supports the growth. 686 00:50:13,441 --> 00:50:17,346 Then the EMF would produce a stronger magnetic field, 687 00:50:17,346 --> 00:50:21,701 and that keeps the EMF going in exactly the same direction, 688 00:50:21,701 --> 00:50:26,057 and so the B field would become even stronger and you get a 689 00:50:26,057 --> 00:50:29,211 runaway process. Situation would get out of 690 00:50:29,211 --> 00:50:32,139 control. It would also be a violation of 691 00:50:32,139 --> 00:50:37,555 the conservation of energy, and thank goodness physics is 692 00:50:37,555 --> 00:50:40,873 the way it is, because if it weren't that way 693 00:50:40,873 --> 00:50:44,644 you and I wouldn't be here. We couldn't even exist. 694 00:50:44,644 --> 50:50 See you Wednesday.