1 00:00:00 --> 00:00:00 Today, I'm going to take a critical look at Ampere's Law. 2 00:00:00 --> 00:00:08,246 Today, I'm going to take a critical look at Ampere's Law. 3 00:00:08,246 --> 00:00:14,283 I'm going to run a current through a wire, 4 00:00:14,283 --> 00:00:21,352 as we did before, but now I'm going to also put a 5 00:00:21,352 --> 00:00:29,745 capacitor in that line and so we are charging a capacitor. 6 00:00:29,745 --> 00:00:37,058 Here is that capacitor. And here is the wire. 7 00:00:37,058 --> 00:00:43,622 We are running a current I. And as we are running this 8 00:00:43,622 --> 00:00:48,948 current, clearly, we get a changing electric 9 00:00:48,948 --> 00:00:55,884 field inside the capacitor. The electric field inside the 10 00:00:55,884 --> 00:01:02,2 capacitor, sigma free divided by kappa epsilon zero, 11 00:01:02,2 --> 00:01:08,516 which is also Q free divided by the area. 12 00:01:08,516 --> 00:01:12,743 This is a circular plate capacitor. 13 00:01:12,743 --> 00:01:17,963 Capital R, is the radius of this capacitor, 14 00:01:17,963 --> 00:01:23,06 so we get pi R squared kappa epsilon zero. 15 00:01:23,06 --> 00:01:30,269 But since I run a current the Q free is building up all the 16 00:01:30,269 --> 00:01:36,236 time, and so the current per definition is dQ dT, 17 00:01:36,236 --> 00:01:44,44 and so I now have ex- a changing electric field inside, 18 00:01:44,44 --> 00:01:49,393 de dt, which is the current I divided by pi R squared, 19 00:01:49,393 --> 00:01:53,599 kappa epsilon zero, because I simply take the 20 00:01:53,599 --> 00:01:57,337 derivative of this equation, I get dQ dT, 21 00:01:57,337 --> 00:02:01,636 and dQ dT is I. And only if the current is zero 22 00:02:01,636 --> 00:02:05,562 is there no changing electric field inside. 23 00:02:05,562 --> 00:02:09,487 So how does this affect the magnetic field? 24 00:02:09,487 --> 00:02:15,468 Well, if I take here a point P1 at a 25 00:02:15,468 --> 00:02:20,576 distance little R from the wire, if you fall away from this 26 00:02:20,576 --> 00:02:26,035 capacitor it's hard to believe that Ampere's Law would not give 27 00:02:26,035 --> 00:02:29,909 the right answer. And we will apply that very 28 00:02:29,909 --> 00:02:34,4 shortly, Ampere's Law. It's on the blackboard there. 29 00:02:34,4 --> 00:02:39,507 Suppose you are at the same distance from this line here at 30 00:02:39,507 --> 00:02:43,029 point P2. Well, yeah, you've got to admit 31 00:02:43,029 --> 00:02:47,282 there's an interruption of current now. 32 00:02:47,282 --> 00:02:51,577 There is no current going through this space and so you 33 00:02:51,577 --> 00:02:56,19 expect that the magnetic field here would be a little lower 34 00:02:56,19 --> 00:02:59,531 perhaps than it is here. But not very much. 35 00:02:59,531 --> 00:03:03,269 So the question is, how can we now calculate the 36 00:03:03,269 --> 00:03:07,962 magnetic field here and there, now that we have this opening 37 00:03:07,962 --> 00:03:11,303 in the wire. Well, Biot-Savart could handle 38 00:03:11,303 --> 00:03:15,2 it but I wouldn't know how to do it 39 00:03:15,2 --> 00:03:19,967 because if there's a current flowing like this there's also a 40 00:03:19,967 --> 00:03:23,859 current going up on these plates, and one like so, 41 00:03:23,859 --> 00:03:27,355 and I wouldn't know how to apply Biot-Savart. 42 00:03:27,355 --> 00:03:30,135 In principle, yeah, but in practice, 43 00:03:30,135 --> 00:03:32,201 no. How about Ampere's Law? 44 00:03:32,201 --> 00:03:35,06 Well, let's give Ampere's Law a shot. 45 00:03:35,06 --> 00:03:39,827 This is a cylindrical symmetric problem, so I choose a closed 46 00:03:39,827 --> 00:03:44,116 loop, which of course itself is a circle with radius R, 47 00:03:44,116 --> 00:03:50,207 and I apply -- I attach to this closed loop an open surface. 48 00:03:50,207 --> 00:03:54,111 That's mandatory. And I give myself an easy time, 49 00:03:54,111 --> 00:03:58,421 I make it a flat surface. So now I apply Ampere's Law. 50 00:03:58,421 --> 00:04:01,186 You see it there on the blackboard. 51 00:04:01,186 --> 00:04:05,903 Anywhere on that closed loop, the magnetic fields will have 52 00:04:05,903 --> 00:04:09,319 the same strength, for reasons of symmetry, 53 00:04:09,319 --> 00:04:13,955 and so we get B times two pi R equals mu zero times I pen, 54 00:04:13,955 --> 00:04:20,704 and pen means the current that penetrates my open surface. 55 00:04:20,704 --> 00:04:25,401 Well, that's I. I goes right through that 56 00:04:25,401 --> 00:04:29,746 surface. And so the magnetic fields at 57 00:04:29,746 --> 00:04:35,618 that point, P1 mu zero times I divided by two pi R. 58 00:04:35,618 --> 00:04:39,845 We've seen this several times before. 59 00:04:39,845 --> 00:04:45,717 Now I wonder about P2. Can I apply Ampere's Law for 60 00:04:45,717 --> 00:04:51,61 point P2? Well, yeah, you can try. 61 00:04:51,61 --> 00:04:56,17 So now I attach a closed loop to this point. 62 00:04:56,17 --> 00:04:59,176 Circle again, radius little R, 63 00:04:59,176 --> 00:05:04,565 and I use this flat surface and I apply Ampere's Law. 64 00:05:04,565 --> 00:05:10,369 Well, I'm in for a shock, because B times two pi R is not 65 00:05:10,369 --> 00:05:16,691 changing but there is no current that penetrates that surface. 66 00:05:16,691 --> 00:05:23,47 And so I is zero, and so I have to conclude that 67 00:05:23,47 --> 00:05:28,956 the magnetic field at point P2 is zero which is absurd. 68 00:05:28,956 --> 00:05:33,121 Couldn't be. I can make the situation even 69 00:05:33,121 --> 00:05:36,778 worse. I'm going to revisit point P1, 70 00:05:36,778 --> 00:05:41,755 and here is my capacitor, and here is my point P1. 71 00:05:41,755 --> 00:05:47,038 My current is flowing like so. Here's my closed loop. 72 00:05:47,038 --> 00:05:54,704 According to Ampere's Law, int- closed loop integral B dot 73 00:05:54,704 --> 00:05:57,504 DL. Why should I choose a flat 74 00:05:57,504 --> 00:06:00,98 surface? I'm entitled to any surface! 75 00:06:00,98 --> 00:06:06,29 I like surfaces like this. They are attached to a closed 76 00:06:06,29 --> 00:06:10,635 loop, so I will choose that kind of a surface. 77 00:06:10,635 --> 00:06:16,042 The surface now goes like so. [whistle] Right through the 78 00:06:16,042 --> 00:06:21,353 capacitor plates, and I apply Ampere's Law, 79 00:06:21,353 --> 00:06:24,083 so it's open here. B times two pi R, 80 00:06:24,083 --> 00:06:27,125 the radius is little R. Mu zero times I, 81 00:06:27,125 --> 00:06:30,557 but there is no I going through that surface. 82 00:06:30,557 --> 00:06:34,302 Nowhere through this surface is a current poking, 83 00:06:34,302 --> 00:06:38,514 because there is no current going between the capacitor 84 00:06:38,514 --> 00:06:42,883 plates, so now I have to conclude that the magnetic field 85 00:06:42,883 --> 00:06:47,407 at P1, which we first concluded was this, is now also zero. 86 00:06:47,407 --> 00:06:52,555 So something stinks. So Ampere's Law is inadequate. 87 00:06:52,555 --> 00:06:55,79 And so of course, Faraday and Ampere were both 88 00:06:55,79 --> 00:06:59,384 perfectly aware of this. But yet it was Maxwell who 89 00:06:59,384 --> 00:07:03,768 zeroed in on this and he argued that any open surface that you 90 00:07:03,768 --> 00:07:07,722 attach to a closed loop should give you exactly the same 91 00:07:07,722 --> 00:07:11,1 result, same answer. And so he suggested that we 92 00:07:11,1 --> 00:07:14,406 amend Ampere's Law, and so he asked himself the 93 00:07:14,406 --> 00:07:18,575 question, what is so special about in-between the capacitor 94 00:07:18,575 --> 00:07:22,959 plates? Well, what is special there is 95 00:07:22,959 --> 00:07:28,64 in-between the capacitor plates there is a changing electric 96 00:07:28,64 --> 00:07:31,24 field. And Maxwell reasoned, 97 00:07:31,24 --> 00:07:36,631 gee, Faraday's Law tells me that a changing magnetic flux 98 00:07:36,631 --> 00:07:42,312 gives rise to an electric field, so he says maybe a changing 99 00:07:42,312 --> 00:07:46,548 electric flux gives rise to a magnetic field. 100 00:07:46,548 --> 00:07:52,422 And I want to remind you what an electric flux is. 101 00:07:52,422 --> 00:07:57,044 Phi of e is the integral. In this case it would an open 102 00:07:57,044 --> 00:08:00,982 surface of E dot DA. That is an electric flux. 103 00:08:00,982 --> 00:08:05,519 With Gauss's Law that you see on the blackboard there, 104 00:08:05,519 --> 00:08:10,056 we had a closed surface. I'm talking now about an open 105 00:08:10,056 --> 00:08:12,796 surface. That is an open surface. 106 00:08:12,796 --> 00:08:17,247 This is an open surface, and this is an open surface. 107 00:08:17,247 --> 00:08:22,041 And so Maxwell suggested that we have to add a term which 108 00:08:22,041 --> 00:08:28,633 contains the derivative of the electric 109 00:08:28,633 --> 00:08:33,461 flux. And that's what I'm going to do 110 00:08:33,461 --> 00:08:38,691 there now, walking over to Ampere's Law. 111 00:08:38,691 --> 00:08:45,799 I'm going to amend it in a way that Maxwell suggested. 112 00:08:45,799 --> 00:08:51,029 He adds a term here, epsilon zero kappa, 113 00:08:51,029 --> 00:08:58,003 ddT, of the integral over an open surface, 114 00:08:58,003 --> 00:09:02,173 attached to that closed loop of E dot DA. 115 00:09:02,173 --> 00:09:05,718 This current, which is the one that 116 00:09:05,718 --> 00:09:11,14 penetrates, remember, through the surface is really a 117 00:09:11,14 --> 00:09:14,059 real current. This term here, 118 00:09:14,059 --> 00:09:17,812 Maxwell called "displacement current. 119 00:09:17,812 --> 00:09:23,026 I want to make sure that I have no slip of the pen, 120 00:09:23,026 --> 00:09:28,552 because I hate slips of the pen. 121 00:09:28,552 --> 00:09:32,753 That is correct. I have everything in place. 122 00:09:32,753 --> 00:09:38,617 You may think now that we can start a party because all four 123 00:09:38,617 --> 00:09:42,135 Maxwell's equations are now in place. 124 00:09:42,135 --> 00:09:45,946 Not quite. We're going to make one small 125 00:09:45,946 --> 00:09:51,907 adjustment after spring break, and that adjustment is going to 126 00:09:51,907 --> 00:09:56,792 be made in this one, and then we'll have our party. 127 00:09:56,792 --> 00:10:04,806 So now, I would like to use the new law and see whether we can 128 00:10:04,806 --> 00:10:09,062 clean up that mess. So I'm going to revisit my 129 00:10:09,062 --> 00:10:14,738 point P1 and I'm going to apply the new law by first having a 130 00:10:14,738 --> 00:10:18,9 flat surface, that surface that we have here, 131 00:10:18,9 --> 00:10:24,103 and then trying this surface. And I want to get the same 132 00:10:24,103 --> 00:10:26,846 answer. If I use that surface, 133 00:10:26,846 --> 00:10:31,86 do we agree that there is a current going through that 134 00:10:31,86 --> 00:10:37,489 surface but there is no electric flux going 135 00:10:37,489 --> 00:10:42,066 through that surface? So that second term, 136 00:10:42,066 --> 00:10:48,876 that displacement current term, is zero for that flat surface. 137 00:10:48,876 --> 00:10:52,672 So this answer is completely valid. 138 00:10:52,672 --> 00:10:56,58 But now, I want to pursue this case. 139 00:10:56,58 --> 00:11:02,72 And so I'll make a new drawing. We have here this point, 140 00:11:02,72 --> 00:11:07,52 P1. This is my radius little R. 141 00:11:07,52 --> 00:11:12,647 This is my surface going right through here. 142 00:11:12,647 --> 00:11:17,893 Here's the current I, and here is my changing 143 00:11:17,893 --> 00:11:23,258 electric field. And so I get B times two pi R, 144 00:11:23,258 --> 00:11:25,881 mu zero. I pen is zero. 145 00:11:25,881 --> 00:11:31,603 There is no current penetrating through this bag. 146 00:11:31,603 --> 00:11:38,279 This is open here. So the first part is zero. 147 00:11:38,279 --> 00:11:44,38 So I only deal with the second part, which is epsilon zero K, 148 00:11:44,38 --> 00:11:50,378 kappa, displacement current. And now I have to put in there 149 00:11:50,378 --> 00:11:54,648 d phi e dt. Phi E is very easy to calculate 150 00:11:54,648 --> 00:12:00,545 because E and da right here- think of this part being flat. 151 00:12:00,545 --> 00:12:06,238 Wherever you were inside the capacitor, if we assume that 152 00:12:06,238 --> 00:12:10,778 there are no [inaudible] fields, 153 00:12:10,778 --> 00:12:15,405 then there is an electric field only where you're inside the 154 00:12:15,405 --> 00:12:19,796 capacitor, and so the electric flux is simply E times the 155 00:12:19,796 --> 00:12:22,698 surface area, E and da are in the same 156 00:12:22,698 --> 00:12:27,481 direction, so it is the electric field times this pi capital R 157 00:12:27,481 --> 00:12:29,206 squared. And therefore, 158 00:12:29,206 --> 00:12:32,343 if I want to know what the derivative is, 159 00:12:32,343 --> 00:12:36,891 then I get this pi R squared which is that surface area and 160 00:12:36,891 --> 00:12:42,62 now I need there de dt. And the de dt we have, 161 00:12:42,62 --> 00:12:48,81 that is I divided by pi R square kappa epsilon zero. 162 00:12:48,81 --> 00:12:54,151 I divided by pi R squared kappa epsilon zero. 163 00:12:54,151 --> 00:12:59,006 So this is the area A, and this is de dt, 164 00:12:59,006 --> 00:13:05,924 and this is the area of the part inside the capacitor that 165 00:13:05,924 --> 00:13:13,722 has a flux going through it, cause outside here there is no 166 00:13:13,722 --> 00:13:17,561 flux going through there, so there's no contribution. 167 00:13:17,561 --> 00:13:20,219 There's no contribution here, either. 168 00:13:20,219 --> 00:13:22,877 There's no contribution here, either. 169 00:13:22,877 --> 00:13:25,904 The electric field is only existent there. 170 00:13:25,904 --> 00:13:29,743 That's my assumption. And so the whole thing here is 171 00:13:29,743 --> 00:13:32,548 now d phi E dt. Well, let's look at our 172 00:13:32,548 --> 00:13:34,025 results. I lose a pi, 173 00:13:34,025 --> 00:13:37,494 I lose my R squared, I lose my kappa and epsilon 174 00:13:37,494 --> 00:13:41,038 zero, and look what I get. I get mu zero times I. 175 00:13:41,038 --> 00:13:46,943 That is truly amazing, so I find now that B equals mu 176 00:13:46,943 --> 00:13:51,596 zero times I divided by two pi little R, which is exactly what 177 00:13:51,596 --> 00:13:53,731 we had before. Hooray for Mr. 178 00:13:53,731 --> 00:13:58,459 Maxwell, because now it doesn't matter anymore whether you take 179 00:13:58,459 --> 00:14:02,501 the flat surface or whether you take the back surface. 180 00:14:02,501 --> 00:14:05,552 You now get the same answer. In one case, 181 00:14:05,552 --> 00:14:10,051 there is no contribution from the displacement current term, 182 00:14:10,051 --> 00:14:14,627 and in the other case there is no contribution from the first 183 00:14:14,627 --> 00:14:20,27 term, the real current. Let me make sure whether I'm 184 00:14:20,27 --> 00:14:24,748 happy with my results. Yup, I think that's fine. 185 00:14:24,748 --> 00:14:30,084 We can now also go one step further, and we can calculate 186 00:14:30,084 --> 00:14:34,849 anywhere in between the capacitor what the magnetic 187 00:14:34,849 --> 00:14:38,374 field is. I'll make another drawing of 188 00:14:38,374 --> 00:14:41,233 the capacitor. It's right here. 189 00:14:41,233 --> 00:14:45,807 I have this E field. I will not repeat that every 190 00:14:45,807 --> 00:14:50,392 time. And here I have my point P2 191 00:14:50,392 --> 00:14:55,94 now, which is inside the capacitor at a radius little R 192 00:14:55,94 --> 00:14:59,844 from the center. And this is capital R, 193 00:14:59,844 --> 00:15:04,262 circular plates. I have here my closed loop. 194 00:15:04,262 --> 00:15:07,344 It's a circle, radius little R. 195 00:15:07,344 --> 00:15:11,556 I apply now the new law, B times two pi R. 196 00:15:11,556 --> 00:15:15,049 And there we go. We have a mu zero, 197 00:15:15,049 --> 00:15:20,327 we have an epsilon zero, we have a kappa. 198 00:15:20,327 --> 00:15:23,505 There's no current going through here, 199 00:15:23,505 --> 00:15:26,682 so it's non-negotiable. I pen is zero, 200 00:15:26,682 --> 00:15:29,344 right? That's not even an issue. 201 00:15:29,344 --> 00:15:32,006 So we get mu zero, epsilon zero. 202 00:15:32,006 --> 00:15:35,698 I get kappa. But now, the surface area right 203 00:15:35,698 --> 00:15:39,906 here is not pi capital R squared, where there is a 204 00:15:39,906 --> 00:15:44,199 changing electric field, but it is only pi little R 205 00:15:44,199 --> 00:15:47,119 squared. I take a flat surface now. 206 00:15:47,119 --> 00:15:51,499 And so now we multiply this by pi 207 00:15:51,499 --> 00:15:57,023 little R squared, and then of course de dt is the 208 00:15:57,023 --> 00:16:04,044 same, so we get our current I divided by pi capital R squared, 209 00:16:04,044 --> 00:16:10,835 divided by kappa epsilon zero. And now you're again losing a 210 00:16:10,835 --> 00:16:14,403 lot. You lose your epsilon zero, 211 00:16:14,403 --> 00:16:18,086 you lose your kappa. I lose a pi. 212 00:16:18,086 --> 00:16:23,495 And look, I have a little R here and 213 00:16:23,495 --> 00:16:26,345 I have a l- little R square there. 214 00:16:26,345 --> 00:16:31,267 So now we're going to get a result which is something that 215 00:16:31,267 --> 00:16:35,843 you may actually have anticipated, namely that you get 216 00:16:35,843 --> 00:16:40,506 a- a field inside the capacitor that is growing with R, 217 00:16:40,506 --> 00:16:45,774 because if I make up my balance I get upstairs mu zero times I 218 00:16:45,774 --> 00:16:50,868 but I get one little R upstairs. You see, you have R squared 219 00:16:50,868 --> 00:16:57,512 here and you have R here. And downstairs I get two pi and 220 00:16:57,512 --> 00:17:04,02 then I get a capital R squared, and I believe that's correct. 221 00:17:04,02 --> 00:17:09,552 Let me check my notes. And yes, I'm happy with that. 222 00:17:09,552 --> 00:17:16,06 And this is proportional with little R, whereas here falling 223 00:17:16,06 --> 00:17:21,05 off one over R. And so I can now make a plot of 224 00:17:21,05 --> 00:17:26,691 the magnetic field as a function of 225 00:17:26,691 --> 00:17:30,943 little R when I'm inside the capacitor plates. 226 00:17:30,943 --> 00:17:34,629 Little R, these are the magnetic fields, 227 00:17:34,629 --> 00:17:38,882 and this is the radius of the capacitor plate. 228 00:17:38,882 --> 00:17:43,512 It's going to be a straight line up to that point, 229 00:17:43,512 --> 00:17:49,183 and then it will fall off as one over little R and you can do 230 00:17:49,183 --> 00:17:54,664 your own work on that and it's very trivial to calculate to 231 00:17:54,664 --> 00:18:00,329 demonstrate that when you go beyond the edge of the 232 00:18:00,329 --> 00:18:04,074 capacitor that then it falls off as one over R, 233 00:18:04,074 --> 00:18:07,574 just in the same way that point P1 is doing. 234 00:18:07,574 --> 00:18:11,807 So now we have a tool to calculate the magnetic field 235 00:18:11,807 --> 00:18:15,471 even inside capacitors while we were charging, 236 00:18:15,471 --> 00:18:19,215 which we didn't have before. The strength here, 237 00:18:19,215 --> 00:18:22,96 the maximum magnetic field here, you'll find by 238 00:18:22,96 --> 00:18:26,542 substituting in there for little R capital R. 239 00:18:26,542 --> 00:18:31,751 And when you do this, if this becomes capital R, 240 00:18:31,751 --> 00:18:34,126 this becomes one over capital R. 241 00:18:34,126 --> 00:18:38,186 If you had substituted in here for little R capital R, 242 00:18:38,186 --> 00:18:40,79 you would've found the same result. 243 00:18:40,79 --> 00:18:44,313 This part is not kosher. It can not be correct, 244 00:18:44,313 --> 00:18:46,994 and I can not make it right for you. 245 00:18:46,994 --> 00:18:51,513 And the reason why that part can not be kosher is because we 246 00:18:51,513 --> 00:18:54,577 have made the assumption, which is wrong, 247 00:18:54,577 --> 00:18:59,096 that there is no fringe field. And so we have assumed in our 248 00:18:59,096 --> 00:19:03,769 calculations that the electric field 249 00:19:03,769 --> 00:19:07,473 is only here and there, but it's zero here so that 250 00:19:07,473 --> 00:19:09,771 there is nothing, no de dt here, 251 00:19:09,771 --> 00:19:12,661 no changing magnetic, uh, electric flux. 252 00:19:12,661 --> 00:19:16,365 And that's not true. So clearly, when you get close 253 00:19:16,365 --> 00:19:18,737 to the edge, this is not correct. 254 00:19:18,737 --> 00:19:21,775 And there's no way I can correct for that, 255 00:19:21,775 --> 00:19:26,221 because the fringe fields will be different from capacitor to 256 00:19:26,221 --> 00:19:30,963 capacitor and those calculations of course are not even very easy 257 00:19:30,963 --> 00:19:35,632 to make. But Maxwell had introduced his 258 00:19:35,632 --> 00:19:39,397 displacement current term. He was a very smart man. 259 00:19:39,397 --> 00:19:43,239 He predicted that as a consequence of that term that 260 00:19:43,239 --> 00:19:47,457 radio waves should exist. There was a time that we didn't 261 00:19:47,457 --> 00:19:51,9 know that radio waves existed. He predicted their existence, 262 00:19:51,9 --> 00:19:55,139 but not only did he predict their existence, 263 00:19:55,139 --> 00:19:59,508 he even was able to calculate what their speed was going to 264 00:19:59,508 --> 00:20:01,617 be. We call that the speed of 265 00:20:01,617 --> 00:20:04,177 light. And we will do that in a few 266 00:20:04,177 --> 00:20:08,031 weeks ourselves in eight oh two. 267 00:20:08,031 --> 00:20:11,832 In 1879, which was the year that Maxwell died, 268 00:20:11,832 --> 00:20:16,647 the German physicist Helmholtz asked once of his students, 269 00:20:16,647 --> 00:20:21,885 Hertz- he was twenty-two years at the time, he was a junior- to 270 00:20:21,885 --> 00:20:25,94 try to demonstrate that radio waves indeed exist. 271 00:20:25,94 --> 00:20:29,403 Hertz declined, because he argued that the 272 00:20:29,403 --> 00:20:34,472 equipment that was available at the time was not good enough. 273 00:20:34,472 --> 00:20:41,346 But seven years later when new equipment had been developed, 274 00:20:41,346 --> 00:20:45,566 he accepted the challenge and it took him two years, 275 00:20:45,566 --> 00:20:50,612 but then he indeed was able to demonstrate that radio waves do 276 00:20:50,612 --> 00:20:53,342 exist. Imagine what a victory that 277 00:20:53,342 --> 00:20:55,41 was! Someone like Maxwell, 278 00:20:55,41 --> 00:21:00,126 who predicts out of nothing that radio waves should exist, 279 00:21:00,126 --> 00:21:04,511 and here comes someone who actually shows that they do 280 00:21:04,511 --> 00:21:10,054 exist. Hertz died five years after his 281 00:21:10,054 --> 00:21:14,046 great experiments. He was thirty-seven years old. 282 00:21:14,046 --> 00:21:17,794 He was very young. Had he lived ten more years, 283 00:21:17,794 --> 00:21:22,438 there is no doubt in my mind that he would've been awarded 284 00:21:22,438 --> 00:21:26,675 with the Nobel Prize for physics, but the first Nobel 285 00:21:26,675 --> 00:21:31,319 prize was only given in 1901, so he died just a little bit 286 00:21:31,319 --> 00:21:34,497 too early. Maxwell also died very young, 287 00:21:34,497 --> 00:21:37,838 age forty-eight. Why did Maxwell call that 288 00:21:37,838 --> 00:21:42,277 strange term displacement current? 289 00:21:42,277 --> 00:21:45,791 In the presence of a dielectric, if you put a 290 00:21:45,791 --> 00:21:49,624 dielectric in there, the changing electric fields 291 00:21:49,624 --> 00:21:53,537 will indeed cause a current in-between the plates, 292 00:21:53,537 --> 00:21:57,451 because the polarization will change all the time. 293 00:21:57,451 --> 00:22:01,364 You get a re-eras- re-arrangement of these induced 294 00:22:01,364 --> 00:22:05,916 charges, so there is indeed a current, but in vacuum there 295 00:22:05,916 --> 00:22:10,308 shouldn't be any current. Any electric field changing or 296 00:22:10,308 --> 00:22:13,688 not changing will not cause a 297 00:22:13,688 --> 00:22:16,892 current in vacuum. But Maxwell believed that 298 00:22:16,892 --> 00:22:20,544 vacuum in a way behaves like any other dielectric, 299 00:22:20,544 --> 00:22:24,493 just a special dielectric, happened to be a dielectric 300 00:22:24,493 --> 00:22:28,367 with kappa equals one. And so he really believed that 301 00:22:28,367 --> 00:22:32,242 there was an actual current going between the plates, 302 00:22:32,242 --> 00:22:36,191 even though we now know of course that that is not the 303 00:22:36,191 --> 00:22:38,352 case. So the name displacement 304 00:22:38,352 --> 00:22:42,674 current was perhaps not a very lucky one, but the term is a 305 00:22:42,674 --> 00:22:46,815 must, and it completes the theory of 306 00:22:46,815 --> 00:22:51,207 electricity and magnetism. The name is obviously of no 307 00:22:51,207 --> 00:22:54,687 consequence. After all, Shakespeare said it 308 00:22:54,687 --> 00:22:58,499 himself, in Romeo and Juliet, what's in a name? 309 00:22:58,499 --> 00:23:03,057 Remember, what's in a name? That which we call a rose by 310 00:23:03,057 --> 00:23:05,957 any other name would smell as sweet. 311 00:23:05,957 --> 00:23:08,857 Those were the words by Shakespeare. 312 00:23:08,857 --> 00:23:12,752 I will abandon for now the displacement current, 313 00:23:12,752 --> 00:23:17,06 but we will revisit it later when we 314 00:23:17,06 --> 00:23:22,171 will deal with radio waves and with the propagation of 315 00:23:22,171 --> 00:23:27,474 electromagnetic radiation, and I will return now to good 316 00:23:27,474 --> 00:23:33,356 old Faraday, and I will return to electric generators that run 317 00:23:33,356 --> 00:23:37,502 our economy. We've discussed that at length, 318 00:23:37,502 --> 00:23:41,648 and I want to revisit that to you- with you. 319 00:23:41,648 --> 00:23:47,24 Remember that if you rotate conducting loops in 320 00:23:47,24 --> 00:23:51,765 magnetic fields. that you create induced EMFs, 321 00:23:51,765 --> 00:23:55,988 currents, and that keeps our economy going. 322 00:23:55,988 --> 00:23:59,205 Here is again one of those loops. 323 00:23:59,205 --> 00:24:03,428 Conducting wire, and I don't care about the 324 00:24:03,428 --> 00:24:09,059 direction of the magnetic field. If you want it this way, 325 00:24:09,059 --> 00:24:12,879 that's fine. What matters is that we're 326 00:24:12,879 --> 00:24:17,705 going to rotate it about this axis, 327 00:24:17,705 --> 00:24:23,714 and as we rotate it about this axis we're going to get an 328 00:24:23,714 --> 00:24:27,255 induced EMF. And that induced EMF, 329 00:24:27,255 --> 00:24:31,976 which we derived I think it was last lecture, 330 00:24:31,976 --> 00:24:37,019 as a function of time, will be a sinusoidal or a 331 00:24:37,019 --> 00:24:40,56 cosinusoidal curve, and therefore, 332 00:24:40,56 --> 00:24:46,783 will look something like this. I call this loop number one, 333 00:24:46,783 --> 00:24:53,651 and so this is the EMF produced by loop number one. 334 00:24:53,651 --> 00:24:57,771 But now I'm going to add two more loops which are not 335 00:24:57,771 --> 00:25:01,099 electrically connected physically separate. 336 00:25:01,099 --> 00:25:05,695 If you look from this direction you will see the following. 337 00:25:05,695 --> 00:25:10,449 This would be your loop number one, because you're looking in 338 00:25:10,449 --> 00:25:14,887 this direction and you would only see the conducting wire 339 00:25:14,887 --> 00:25:17,819 like so. I have now a second one which 340 00:25:17,819 --> 00:25:22,573 is rotated hundred and twenty degrees, and so in this picture 341 00:25:22,573 --> 00:25:25,605 you will see it like so. 342 00:25:25,605 --> 00:25:29,338 Look number two, and this is hundred and twenty 343 00:25:29,338 --> 00:25:32,34 degrees. Physically hundred and twenty 344 00:25:32,34 --> 00:25:35,748 degree rotated. And then I have a third one 345 00:25:35,748 --> 00:25:39,724 which is again hundred and twenty degrees rotated. 346 00:25:39,724 --> 00:25:43,294 It is like so. And so this angle here is also 347 00:25:43,294 --> 00:25:48 hundred and twenty degrees and so this angle is hundred and 348 00:25:48 --> 00:25:51,327 twenty degrees. And this is my look number 349 00:25:51,327 --> 00:25:54,167 three. And so each one of those will 350 00:25:54,167 --> 00:25:58,874 give an EMF that has this shape but they 351 00:25:58,874 --> 00:26:04,718 are offset now in phase by a hundred twenty degrees. 352 00:26:04,718 --> 00:26:10,562 And so they're all rotating in exactly the same way, 353 00:26:10,562 --> 00:26:17,552 like so, and so the second one will give me an EMF if I try to 354 00:26:17,552 --> 00:26:22,365 estimate that roughly, something like this, 355 00:26:22,365 --> 00:26:29,011 so this is loop number two. It comes a little later in time 356 00:26:29,011 --> 00:26:35,542 and number three will again be offset, 357 00:26:35,542 --> 00:26:39,006 will look like this. Number three. 358 00:26:39,006 --> 00:26:43,938 And what we- we call this a three phase current. 359 00:26:43,938 --> 00:26:49,815 And a three phase current can produce a rotating magnetic 360 00:26:49,815 --> 00:26:53,383 field. We will make one for you but 361 00:26:53,383 --> 00:26:57,581 I'll first explain to you how that works. 362 00:26:57,581 --> 00:27:02,303 So if the period of number one is sixty Hertz, 363 00:27:02,303 --> 00:27:07,026 then the period of number two is 364 00:27:07,026 --> 00:27:11,09 also sixty Hertz, and number three is also sixty 365 00:27:11,09 --> 00:27:16,106 Hertz, but they're just offset in terms of the phase angle. 366 00:27:16,106 --> 00:27:20,517 Suppose you're looking down onto a horizontal table, 367 00:27:20,517 --> 00:27:25,446 so this is a horizontal table. And I have here a solenoid. 368 00:27:25,446 --> 00:27:28,3 This is one and the same solenoid. 369 00:27:28,3 --> 00:27:33,403 When the current runs clockwise here it will also run s- run 370 00:27:33,403 --> 00:27:36,43 clockwise there. But it's open here. 371 00:27:36,43 --> 00:27:40,494 Going to put something in there. 372 00:27:40,494 --> 00:27:45,646 We call this number one. Then I have another one which 373 00:27:45,646 --> 00:27:50,993 is rotated, physically rotated a hundred twenty degrees. 374 00:27:50,993 --> 00:27:53,034 It's here. Also coils. 375 00:27:53,034 --> 00:27:58,769 And I'm going to feed current number two through those coals 376 00:27:58,769 --> 00:28:03,24 later, through those coils. This is number two. 377 00:28:03,24 --> 00:28:08,781 And I have a third one and I'm going to run current number 378 00:28:08,781 --> 00:28:11,922 three through those. 379 00:28:11,922 --> 00:28:15,202 So here are coils, here are coils, 380 00:28:15,202 --> 00:28:20,271 this is number three. And so one sees current number 381 00:28:20,271 --> 00:28:25,737 one, two sees current number two, and three sees current 382 00:28:25,737 --> 00:28:30,011 number three. At the moment that the current 383 00:28:30,011 --> 00:28:35,875 through number one reaches a maximum, the current in two and 384 00:28:35,875 --> 00:28:39,155 three are down by a factor of two. 385 00:28:39,155 --> 00:28:44,026 You can check that [break in tape]. 386 00:28:44,026 --> 00:28:48,439 During my lecture I went a little bit too fast over the 387 00:28:48,439 --> 00:28:52,688 part that is coming up now, so I'm going to redo it a 388 00:28:52,688 --> 00:28:55,549 little slower to make it more clear. 389 00:28:55,549 --> 00:28:59,716 When the current through loop one reaches a maximum, 390 00:28:59,716 --> 00:29:04,048 let's say then that the magnetic field due to loop one 391 00:29:04,048 --> 00:29:08,052 is in this direction. The current through this one 392 00:29:08,052 --> 00:29:12,547 and the current through this loop are two times smaller. 393 00:29:12,547 --> 00:29:18,484 You may want to check that. But it just so happens that the 394 00:29:18,484 --> 00:29:23,169 vectorial sum of the magnetic field produced by loop number 395 00:29:23,169 --> 00:29:27,45 two and by loop number three also happen to be in this 396 00:29:27,45 --> 00:29:32,055 direction, so the net magnetic field is in this direction. 397 00:29:32,055 --> 00:29:36,094 Let's now look one third of a period later in time. 398 00:29:36,094 --> 00:29:40,375 Now, the current in loop number two reaches a maximum, 399 00:29:40,375 --> 00:29:44,091 so its magnetic field is now in this direction, 400 00:29:44,091 --> 00:29:49,538 and you guessed it of course, that it just so happens that 401 00:29:49,538 --> 00:29:53,345 the vectorial sum of the magnetic field produced by the 402 00:29:53,345 --> 00:29:56,517 other two loops is now also in this direction. 403 00:29:56,517 --> 00:30:00,182 And if we now look again one third of a period later, 404 00:30:00,182 --> 00:30:04,411 when the current through loop number three reaches a maximum, 405 00:30:04,411 --> 00:30:08,429 then the magnetic fields will be in this direction and the 406 00:30:08,429 --> 00:30:12,447 vectorial sum of the magnetic field of the other two loops 407 00:30:12,447 --> 00:30:17,875 will also be in this direction. And look now what has happened. 408 00:30:17,875 --> 00:30:22,745 In one complete period, the magnetic fields started out 409 00:30:22,745 --> 00:30:26,352 like this. One third of a period later it 410 00:30:26,352 --> 00:30:30,411 was like this, and one third of a period later 411 00:30:30,411 --> 00:30:34,65 it was like this. So what we have created is now 412 00:30:34,65 --> 00:30:39,52 a rotating magnetic field, and it rotates in one period 413 00:30:39,52 --> 00:30:43,759 all the way around, three hundred sixty degrees. 414 00:30:43,759 --> 00:30:48,99 OK, let's now go back to my original lecture. 415 00:30:48,99 --> 00:30:53,227 [break in tape] rotates once around in the period of your 416 00:30:53,227 --> 00:30:56,557 alternating current. If that is a sixty Hertz 417 00:30:56,557 --> 00:31:00,493 current, then it will rotate around with sixty Hertz, 418 00:31:00,493 --> 00:31:03,671 sixty times per second. And so if we put a, 419 00:31:03,671 --> 00:31:07,152 a magnet in here, then this magnet will want to 420 00:31:07,152 --> 00:31:11,617 go around [inaudible] wants to follow this rotating magnetic 421 00:31:11,617 --> 00:31:14,342 field. And we call that a synchronous 422 00:31:14,342 --> 00:31:16,461 motor. So the rotor of such a 423 00:31:16,461 --> 00:31:20,913 synchronous motor itself would be a magnet 424 00:31:20,913 --> 00:31:24,957 and it would rotate around with the frequency of your 425 00:31:24,957 --> 00:31:28,534 alternating current. But you need a three-phase 426 00:31:28,534 --> 00:31:32,501 current for that so that the magnetic field rotates. 427 00:31:32,501 --> 00:31:36,623 I can also place in here -- this is again a horizontal 428 00:31:36,623 --> 00:31:40,745 surface, you have it here, you're going to do it right 429 00:31:40,745 --> 00:31:43,467 here. Here is that -- here are those 430 00:31:43,467 --> 00:31:46,577 crazy loops with the three-phase current. 431 00:31:46,577 --> 00:31:51,321 We can also put in here um conducting sphere, 432 00:31:51,321 --> 00:31:54,631 or in my case I will use a conducting egg. 433 00:31:54,631 --> 00:31:58,021 And when the magnetic field rotates around, 434 00:31:58,021 --> 00:32:02,863 there's a continuous magnetic flux change with the surface of 435 00:32:02,863 --> 00:32:07,625 that conducting sphere or egg, and so it's going to run cur- 436 00:32:07,625 --> 00:32:10,693 eddy currents. Now, if you have an eddy 437 00:32:10,693 --> 00:32:14,809 current going around, and you have a magnetic field, 438 00:32:14,809 --> 00:32:19,813 then the magnetic field in the area current will cause a torque 439 00:32:19,813 --> 00:32:23,302 on the current. In a similar way, 440 00:32:23,302 --> 00:32:26,944 when we discussed earlier the idea of a motor that you were 441 00:32:26,944 --> 00:32:29,769 going to build, there was a magnetic field and 442 00:32:29,769 --> 00:32:33,537 there was a current and that caused a torque and the same way 443 00:32:33,537 --> 00:32:36,99 you get a torque on the eddy current and so it starts to 444 00:32:36,99 --> 00:32:39 torque up this conducting sphere. 445 00:32:39 --> 00:32:42,39 And all the time there will be eddy current because the 446 00:32:42,39 --> 00:32:45,907 magnetic fields keep going around, and so you're going to 447 00:32:45,907 --> 00:32:49,549 get a torque which will always be in the same direction and 448 00:32:49,549 --> 00:32:54,384 this conducting object will now start to rotate and we call 449 00:32:54,384 --> 00:32:58,296 that an induction motor. Induction motors have no 450 00:32:58,296 --> 00:33:01,23 brushes. How fast the induction motor 451 00:33:01,23 --> 00:33:04,49 will go depends on the conducting object. 452 00:33:04,49 --> 00:33:08,076 If it is a sphere, it will probably come very 453 00:33:08,076 --> 00:33:12,885 close to sixty Hertz because a sphere has many possibilities 454 00:33:12,885 --> 00:33:17,694 for eddy currents to run around, whereas if you take a ring, 455 00:33:17,694 --> 00:33:21,85 and we will try that, if you try to spin a ring in a 456 00:33:21,85 --> 00:33:26,414 rotating magnetic field then of course then of course the 457 00:33:26,414 --> 00:33:30,95 various paths that are available for 458 00:33:30,95 --> 00:33:36,57 eddy currents are very limited and only go around in the ring. 459 00:33:36,57 --> 00:33:41,453 Many of the stationary tools that you find in people's 460 00:33:41,453 --> 00:33:46,152 workshops and in the basements are induction motors. 461 00:33:46,152 --> 00:33:51,68 A table saw and drill presses, also electric grass mowers are 462 00:33:51,68 --> 00:33:55,826 induction motors. I want to demonstrate now to 463 00:33:55,826 --> 00:34:00,34 you what three-phase currents can do, 464 00:34:00,34 --> 00:34:06,172 and the first thing I'm going to do is show you that unit that 465 00:34:06,172 --> 00:34:12,195 we have here which is the- which are the coils that I described, 466 00:34:12,195 --> 00:34:17,644 through which we are going to run the three-phase current. 467 00:34:17,644 --> 00:34:21,659 Must get my lights right. There you see it. 468 00:34:21,659 --> 00:34:25,197 Coils are wound in a very strange way. 469 00:34:25,197 --> 00:34:30,264 After class, you can come a little closer, 470 00:34:30,264 --> 00:34:34,524 and so in here you would have a rotating magnetic field. 471 00:34:34,524 --> 00:34:38,01 We use sixty Hertz, which rotates around sixty 472 00:34:38,01 --> 00:34:41,573 times per second. And the first thing I'm going 473 00:34:41,573 --> 00:34:45,137 to do is something wild, a little bit in style, 474 00:34:45,137 --> 00:34:47,848 I suppose. I will put on top there a 475 00:34:47,848 --> 00:34:50,559 cardboard cover with little magnets. 476 00:34:50,559 --> 00:34:54,743 They're randomly oriented. There's no way that they can 477 00:34:54,743 --> 00:34:58,074 ever rotate. They th- thee- are these little 478 00:34:58,074 --> 00:35:02,567 magnets, flat, a lot of friction. 479 00:35:02,567 --> 00:35:06,977 If I expose them to a rotating magnetic field, 480 00:35:06,977 --> 00:35:10,31 then they will go nuts. I told you, 481 00:35:10,31 --> 00:35:15,015 they were going nuts. You're not supposed to show 482 00:35:15,015 --> 00:35:17,466 these to students, but OK. 483 00:35:17,466 --> 00:35:20,602 Now here I have a conducting egg. 484 00:35:20,602 --> 00:35:25,797 And this now has ample possibilities for eddy currents 485 00:35:25,797 --> 00:35:32,266 to flow, and so now if I give these coils the 486 00:35:32,266 --> 00:35:35,341 right current, a three-phase current, 487 00:35:35,341 --> 00:35:39,098 it's spun up, the magnetic fields acts on the 488 00:35:39,098 --> 00:35:42,599 eddy currents, and it starts to spin and I 489 00:35:42,599 --> 00:35:46,698 have actually tried to measure the rotation rate. 490 00:35:46,698 --> 00:35:51,053 It's only a little bit under thirty-six hundred RPM. 491 00:35:51,053 --> 00:35:54,725 Thirty-six hundred RPM would be sixty Hertz. 492 00:35:54,725 --> 00:35:59,165 It's very close to that. If I spin this object in the 493 00:35:59,165 --> 00:36:04,719 direction in which the magnetic field is not rotating, 494 00:36:04,719 --> 00:36:06,64 then it says sorry, no way. 495 00:36:06,64 --> 00:36:10,113 It just rehearses, because the magnetic field is 496 00:36:10,113 --> 00:36:14,029 going to slave it in the direction that it wants it to 497 00:36:14,029 --> 00:36:16,32 go. So we're looking there at an 498 00:36:16,32 --> 00:36:18,906 induction motor. I have here a ring. 499 00:36:18,906 --> 00:36:23,487 Now a ring doesn't have as many possibilities for eddy currents 500 00:36:23,487 --> 00:36:26,295 to run. Could only go around like this, 501 00:36:26,295 --> 00:36:27,698 or like this, right? 502 00:36:27,698 --> 00:36:31,688 But I can still make it spin probably if I do the right 503 00:36:31,688 --> 00:36:34,563 thing. First of all, 504 00:36:34,563 --> 00:36:37,643 I have to rotate it in the right direction, 505 00:36:37,643 --> 00:36:39,99 which would be this one, I think. 506 00:36:39,99 --> 00:36:43,144 There it goes. It doesn't go anywhere nearly 507 00:36:43,144 --> 00:36:47,324 as fast as the egg because of the restrictive paths of the 508 00:36:47,324 --> 00:36:49,451 eddy currents. But it rotates. 509 00:36:49,451 --> 00:36:53,484 It's trying to follow that magnetic field to the best it 510 00:36:53,484 --> 00:36:56,345 can, but its abilities are very limited. 511 00:36:56,345 --> 00:36:59,718 And needless to say, if I try to spin it in the 512 00:36:59,718 --> 00:37:03,165 wrong direction, that of course it will stop and 513 00:37:03,165 --> 00:37:07,237 it has no way like the egg to 514 00:37:07,237 --> 00:37:12,342 reverse its direction because of its peculiar geometry. 515 00:37:12,342 --> 00:37:16,312 I owe you an explanation to the secret top. 516 00:37:16,312 --> 00:37:19,81 If you haven't found one yourself yet. 517 00:37:19,81 --> 00:37:25,483 Let me first come to a simple conclusion, and all of you must 518 00:37:25,483 --> 00:37:30,966 have come to that conclusion. That top, when I showed it to 519 00:37:30,966 --> 00:37:37,867 you during my exam review was spinning for more than an hour. 520 00:37:37,867 --> 00:37:40,125 In fact, it was spinning the next day. 521 00:37:40,125 --> 00:37:43,116 Energy has to come from somewhere, and so the only 522 00:37:43,116 --> 00:37:46,716 conclusion that you could've drawn that the energy came from 523 00:37:46,716 --> 00:37:49,462 inside the box, there must be something inside 524 00:37:49,462 --> 00:37:51,842 the box. Clearly there must be a battery 525 00:37:51,842 --> 00:37:55,198 in that box, and there is. But that doesn't tell you how 526 00:37:55,198 --> 00:37:57,273 it works yet. And I can assure you, 527 00:37:57,273 --> 00:38:00,996 I can a- a- admit that it took me quite a while before I fully 528 00:38:00,996 --> 00:38:04,23 understand how it works. And I want to explain that to 529 00:38:04,23 --> 00:38:07,708 you, and then I will demonstrate it to 530 00:38:07,708 --> 00:38:12,612 you again. Remember what it looks like. 531 00:38:12,612 --> 00:38:18,806 In the top itself is a magnet. So here is a top. 532 00:38:18,806 --> 00:38:26,161 Let's say this is north and this is south and this is that 533 00:38:26,161 --> 00:38:29 top. We're rotating it. 534 00:38:29 --> 00:38:33,258 We're spinning it. Inside the box, 535 00:38:33,258 --> 00:38:41,516 right at the center of the box, is a solenoid. 536 00:38:41,516 --> 00:38:44,068 The switch and a nine-volt battery. 537 00:38:44,068 --> 00:38:47,745 Inside this solenoid is also a little bit of iron. 538 00:38:47,745 --> 00:38:50,747 We have not discussed that in our course. 539 00:38:50,747 --> 00:38:53,598 It's not important for the explanation. 540 00:38:53,598 --> 00:38:58,026 You'll later understand why there is also some iron in here. 541 00:38:58,026 --> 00:39:02,078 It makes the magnetic fields so it's a little stronger. 542 00:39:02,078 --> 00:39:06,58 This is right at the center of the- of the little platform on 543 00:39:06,58 --> 00:39:10,332 which I was running this. It is a concave platform, 544 00:39:10,332 --> 00:39:14,235 and here is a little plastic nod so 545 00:39:14,235 --> 00:39:17,499 when the top hits it it bounces off. 546 00:39:17,499 --> 00:39:22,722 Imagine for now that it's rotating in such a way that the 547 00:39:22,722 --> 00:39:28,412 North Pole is approaching that solenoid, coming in from above. 548 00:39:28,412 --> 00:39:32,515 What's going to happen now, in this solenoid, 549 00:39:32,515 --> 00:39:36,433 in this coil, you are changing the magnetic 550 00:39:36,433 --> 00:39:42,216 flux through the surface of this coil and so you're introducing 551 00:39:42,216 --> 00:39:46,693 an induced EMF, an induced current. 552 00:39:46,693 --> 00:39:51,992 And this current is sensed by a transistor which I have not put 553 00:39:51,992 --> 00:39:56,95 in here, and the transistor throws the switch and now sucks 554 00:39:56,95 --> 00:40:00,625 energy out of the battery and runs currents, 555 00:40:00,625 --> 00:40:05,839 very high current through this coil, such that the top becomes 556 00:40:05,839 --> 00:40:09,515 the south pole. Remember if you have a coil, 557 00:40:09,515 --> 00:40:14,302 and you run current through here, that you get a magnetic 558 00:40:14,302 --> 00:40:17,477 field like so. In this case, 559 00:40:17,477 --> 00:40:21,012 this would be north pole and this would be south pole. 560 00:40:21,012 --> 00:40:24,814 If you reverse the current, then this is south and this is 561 00:40:24,814 --> 00:40:27,215 north. That magnetic field that comes 562 00:40:27,215 --> 00:40:31,35 out there is fanning out in all directions three dimensionally. 563 00:40:31,35 --> 00:40:34,752 It's going like this and it's fanning out like this. 564 00:40:34,752 --> 00:40:38,22 So when it approaches this coil, there is a change in 565 00:40:38,22 --> 00:40:41,155 magnetic flux. And this becomes a south pole. 566 00:40:41,155 --> 00:40:44,557 The north pole is being attracted by the south pole. 567 00:40:44,557 --> 00:40:48,437 I make you look at this from above now. 568 00:40:48,437 --> 00:40:52,713 Here is the top seen from above, so it's spinning in this 569 00:40:52,713 --> 00:40:55,462 direction. And let's say here is this 570 00:40:55,462 --> 00:40:58,211 coil. This is the north pole and this 571 00:40:58,211 --> 00:41:01,8 is the south pole. And I just discussed with you 572 00:41:01,8 --> 00:41:06,611 that the current that's going to flow from the battery will make 573 00:41:06,611 --> 00:41:10,123 this a south pole. The current can only flow in 574 00:41:10,123 --> 00:41:14,018 that coil in one direction. That's just the way it's 575 00:41:14,018 --> 00:41:16,843 designed. So whenever the current goes 576 00:41:16,843 --> 00:41:21,119 it's always this becomes a south pole. 577 00:41:21,119 --> 00:41:25,997 The north pole is being attracted by the south pole. 578 00:41:25,997 --> 00:41:29,918 You'll notice it's going to be torqued up. 579 00:41:29,918 --> 00:41:33,648 So far, so good. A little later in time, 580 00:41:33,648 --> 00:41:38,43 looking from above, the north pole will be here and 581 00:41:38,43 --> 00:41:43,785 the south pole will be there, it has rotated a little bit 582 00:41:43,785 --> 00:41:48,95 further, and the coil is here. So now the north pole is 583 00:41:48,95 --> 00:41:52,393 leaving. It's receding. 584 00:41:52,393 --> 00:41:54,851 It's not approaching, it's receding. 585 00:41:54,851 --> 00:41:59,065 If this were to remain a south pole, that would be disastrous 586 00:41:59,065 --> 00:42:03,279 because south poles and north poles would attract each other. 587 00:42:03,279 --> 00:42:06,58 You don't want that. Well, the transistor senses 588 00:42:06,58 --> 00:42:09,601 that the EMF in the coil reverses direction. 589 00:42:09,601 --> 00:42:13,745 It has to reverse direction, because if the north pole comes 590 00:42:13,745 --> 00:42:18,029 in, the EMF is in one direction but when the north pole leaves 591 00:42:18,029 --> 00:42:22,313 the EMF of course goes in the other direction. 592 00:42:22,313 --> 00:42:26,665 You've got a reversal. And so what the transistor 593 00:42:26,665 --> 00:42:31,651 does, it opens the switch, and so there is no north pole 594 00:42:31,651 --> 00:42:37,362 here and there is no south pole here, and so the thing starts to 595 00:42:37,362 --> 00:42:41,804 go around further. What happens now when the south 596 00:42:41,804 --> 00:42:47,244 pole approaches that solenoid? OK, here is the situation that 597 00:42:47,244 --> 00:42:50,235 the south pole is now approaching. 598 00:42:50,235 --> 00:42:53,046 It's rotating in this direction. 599 00:42:53,046 --> 00:42:58,576 And here is the coil. South pole is coming in. 600 00:42:58,576 --> 00:43:01,942 From Faraday's point of view, there is no difference between 601 00:43:01,942 --> 00:43:04,966 the north pole receding or the south pole approaching. 602 00:43:04,966 --> 00:43:07,59 You should be able to reason that for yourself. 603 00:43:07,59 --> 00:43:10,842 That's exactly the same thing, and so the transistor knows 604 00:43:10,842 --> 00:43:13,98 that indeed the current is still in the wrong direction. 605 00:43:13,98 --> 00:43:16,319 It keeps the switch open. It does nothing, 606 00:43:16,319 --> 00:43:19,743 so as the south pole approaches no current through this coil. 607 00:43:19,743 --> 00:43:22,424 We must remember, the current can only go in one 608 00:43:22,424 --> 00:43:24,821 direction, can only make this a south pole. 609 00:43:24,821 --> 00:43:28,073 It could have been designed in such a way that the current 610 00:43:28,073 --> 00:43:31,34 could go in both directions. 611 00:43:31,34 --> 00:43:34,583 It would have made it more expensive. 612 00:43:34,583 --> 00:43:39,357 Just a matter of economy. So nothing will happen here. 613 00:43:39,357 --> 00:43:44,581 But now, there comes a time that the south pole is leaving, 614 00:43:44,581 --> 00:43:48,094 is receding, and so let us have here our 615 00:43:48,094 --> 00:43:50,706 coil. A south pole receding is 616 00:43:50,706 --> 00:43:54,94 exactly the same for Mr. Faraday as a north pole 617 00:43:54,94 --> 00:43:58,543 approaching. And so now the EMF is in the 618 00:43:58,543 --> 00:44:02,459 same direction in the coil as it was 619 00:44:02,459 --> 00:44:04,847 here. And so now the transistor says 620 00:44:04,847 --> 00:44:07,986 yippee, that's fine. I close the switch and I'm 621 00:44:07,986 --> 00:44:11,875 going to run a current and so this becomes the south pole. 622 00:44:11,875 --> 00:44:15,9 South pole and south pole repel each other, so now the thing 623 00:44:15,9 --> 00:44:18,629 gets a kick again. So when the north pole 624 00:44:18,629 --> 00:44:22,518 approaches, it pulls on the north pole, and when the south 625 00:44:22,518 --> 00:44:25,315 pole recedes, it pushes on the south pole. 626 00:44:25,315 --> 00:44:29,477 And so it is an induction motor which is only powered half per 627 00:44:29,477 --> 00:44:32,451 full rotation, but a very, 628 00:44:32,451 --> 00:44:35,96 very clever design. And I'm going to demonstrate it 629 00:44:35,96 --> 00:44:38,977 to you again. I want you to see that as this 630 00:44:38,977 --> 00:44:42,766 top approaches the center that actually, you can see it 631 00:44:42,766 --> 00:44:46,345 starting spinning up. It really gets its energy when 632 00:44:46,345 --> 00:44:49,222 it gets close to this coil. It also works, 633 00:44:49,222 --> 00:44:52,379 doesn't matter in which direction you spin it. 634 00:44:52,379 --> 00:44:55,607 That's also great. You can spin it clockwise or 635 00:44:55,607 --> 00:44:58,273 counter-clockwise. Makes no difference. 636 00:44:58,273 --> 00:45:02,063 And so, you're going to see that top 637 00:45:02,063 --> 00:45:04,298 here, I think. There it is. 638 00:45:04,298 --> 00:45:08,682 And this is probably the best way for you to see it. 639 00:45:08,682 --> 00:45:13,41 We have here this box in which there is this very simple 640 00:45:13,41 --> 00:45:16,935 circuit, very simple, and here is the top. 641 00:45:16,935 --> 00:45:21,749 Has little bar magnet in it. I will try to spin it just a 642 00:45:21,749 --> 00:45:26,305 little bit, to make you see that it actually spins up. 643 00:45:26,305 --> 00:45:32,065 It may not be so easy for you to see, but I can s- ah, 644 00:45:32,065 --> 00:45:34,511 you see it's really spinning up now. 645 00:45:34,511 --> 00:45:37,656 And then it loses to friction, rotation rates. 646 00:45:37,656 --> 00:45:41,571 It always comes back to the center because the surface is 647 00:45:41,571 --> 00:45:45,975 concave, and then it gets to the center there and gets its kicks 648 00:45:45,975 --> 00:45:49,47 again, gets spun up. And this can go on for as long 649 00:45:49,47 --> 00:45:52,825 as your battery lasts, which is about a few days. 650 00:45:52,825 --> 00:45:55,411 I can also rotate it counterclockwise. 651 00:45:55,411 --> 00:45:57,368 It's not so easy, it's funny. 652 00:45:57,368 --> 00:46:01,073 Have you ever tried to rotate a top counter-clockwise? 653 00:46:01,073 --> 00:46:05,359 It's very hard! I don't know why that is, 654 00:46:05,359 --> 00:46:08,263 because maybe because I'm right-handed. 655 00:46:08,263 --> 00:46:10,325 I'll try. You see, I failed. 656 00:46:10,325 --> 00:46:14,222 Ah, this is a nice one. I gave it a teeny-wee little 657 00:46:14,222 --> 00:46:16,055 spin. It doesn't like it. 658 00:46:16,055 --> 00:46:19,646 It stays near the center. Oh, doesn't like that. 659 00:46:19,646 --> 00:46:23,161 It has to be a little bit away from the center. 660 00:46:23,161 --> 00:46:25,911 Ah, I think, I think I've got it now. 661 00:46:25,911 --> 00:46:26,981 Oh, no. Oh, no. 662 00:46:26,981 --> 00:46:30,495 Too optimistic. Isn't it strange that it's hard 663 00:46:30,495 --> 00:46:34,239 for a person to rotate something counterclockwise? 664 00:46:34,239 --> 00:46:36,531 OK, I did it. Slowly coming in, 665 00:46:36,531 --> 00:46:41,89 to friction now. And when it gets close to the 666 00:46:41,89 --> 00:46:46,099 center, there it gets its kicks. Now it's spinning up. 667 00:46:46,099 --> 00:46:49,99 Ah, you can really see it now. It's being spun up. 668 00:46:49,99 --> 00:46:52,214 You see that? Really spun up. 669 00:46:52,214 --> 00:46:56,423 I have another fantastic toy for you, which is also an 670 00:46:56,423 --> 00:46:59,918 induction motor. And that one you're going to 671 00:46:59,918 --> 00:47:04,524 see there, first want to explain to you how that one works. 672 00:47:04,524 --> 00:47:08,495 That's a real beauty. It is an induction motor that 673 00:47:08,495 --> 00:47:13,897 runs on a two-phase current. Here we have solenoids. 674 00:47:13,897 --> 00:47:16,716 It's this, this baby here, big one. 675 00:47:16,716 --> 00:47:21,608 And we're going to run sixty Hertz AC current through there, 676 00:47:21,608 --> 00:47:25,754 and here we have one, also going to run sixty Hertz 677 00:47:25,754 --> 00:47:28,491 AC through there. Here's the coil. 678 00:47:28,491 --> 00:47:31,725 This one is easy to show. The other one, 679 00:47:31,725 --> 00:47:35,041 very heavy. These two currents are ninety 680 00:47:35,041 --> 00:47:38,358 degrees out of phase. Not hundred twenty, 681 00:47:38,358 --> 00:47:42,255 but ninety. So it's a two-phase 682 00:47:42,255 --> 00:47:45,041 current. So when the current is maximum 683 00:47:45,041 --> 00:47:48,339 through this one, it is zero through this one. 684 00:47:48,339 --> 00:47:52,956 When it is maximum through this one, it's zero through this one. 685 00:47:52,956 --> 00:47:57,281 Let's look at the moment that the current is maximum through 686 00:47:57,281 --> 00:47:59,846 this one. And let's say the magnetic 687 00:47:59,846 --> 00:48:04,024 field is in this direction, which is created by this coil. 688 00:48:04,024 --> 00:48:08,202 Then there is no current here. But one quarter of a period 689 00:48:08,202 --> 00:48:12,893 later, this one has no current but this one does. 690 00:48:12,893 --> 00:48:17,433 Let's assume that now the magnetic field from this is in 691 00:48:17,433 --> 00:48:21,231 this direction. And so what you're going to see 692 00:48:21,231 --> 00:48:25,028 now is that again, you have a rotating magnetic 693 00:48:25,028 --> 00:48:29,321 field which goes like so. And if I put in here a can, 694 00:48:29,321 --> 00:48:31,963 a paint can, we use a coffee can, 695 00:48:31,963 --> 00:48:35,843 it's right here, and at the surface of that can, 696 00:48:35,843 --> 00:48:39,971 so I will draw the can here, but it's really there. 697 00:48:39,971 --> 00:48:45,406 At the surface of that can, you're going to have eddy 698 00:48:45,406 --> 00:48:49,892 currents, because you have change of magnetic flux all the 699 00:48:49,892 --> 00:48:54,299 time and these eddy currents with the magnetic field will 700 00:48:54,299 --> 00:48:58,706 cause a torque on this can. And the torque will always be 701 00:48:58,706 --> 00:49:02,955 in the same direction and the thing is going to rotate. 702 00:49:02,955 --> 00:49:06,497 So it's another example of an induction motor. 703 00:49:06,497 --> 00:49:10,353 It's a very cute one. And I want to show it to you 704 00:49:10,353 --> 00:49:13,579 and for that you're going to see it there. 705 00:49:13,579 --> 00:49:17,436 Needless to say that the can is a 706 00:49:17,436 --> 00:49:21,557 very special can, Maxwell House coffee. 707 00:49:21,557 --> 00:49:24,485 Of course. And you see that? 708 00:49:24,485 --> 00:49:29,365 Maxwell House. All right, so let's see whether 709 00:49:29,365 --> 00:49:33,378 we can get this to run. There it goes. 710 00:49:33,378 --> 00:49:39,885 Nice example of an induction motor, and now I'm going to test 711 00:49:39,885 --> 00:49:43,03 you. I'm going to ask you what 712 00:49:43,03 --> 00:49:48,018 happens if I take this coil here, 713 00:49:48,018 --> 00:49:51,586 which I can do, and flip over from here to 714 00:49:51,586 --> 00:49:54,457 here. Who thinks that nothing will 715 00:49:54,457 --> 00:49:57,415 happen? And you're all afraid of me 716 00:49:57,415 --> 00:50:01,069 now, right? Who thinks that it will come to 717 00:50:01,069 --> 00:50:03,679 a grinding halt? Grinding halt. 718 00:50:03,679 --> 00:50:08,464 Who thinks that the direction of the motor will reverse? 719 00:50:08,464 --> 00:50:11,944 Good for you. It's clear that when I flip 720 00:50:11,944 --> 00:50:15,772 this one over, you can easily go through that 721 00:50:15,772 --> 00:50:19,252 for yourself, that this magnetic field is 722 00:50:19,252 --> 00:50:23,464 then not rotating this way, 723 00:50:23,464 --> 00:50:29,051 but is rotating that way, and so clearly the motor will 724 00:50:29,051 --> 00:50:33,5 reverse direction. I'm going to do that now. 725 00:50:33,5 --> 00:50:37,224 Watch it. So it's torquing now in the 726 00:50:37,224 --> 00:50:42,397 opposite direction. It's coming to a grinding halt. 727 00:50:42,397 --> 00:50:46,639 You were right. The other people were also 728 00:50:46,639 --> 00:50:51,088 right, because now it's reversing direction. 729 00:50:51,088 --> 00:50:58,342 And you see there it goes. Another striking example of an 730 00:50:58,342 --> 00:51:01,354 induction motor. Next lecture, 731 00:51:01,354 --> 51:06 Friday, I'm going to elevate a woman.