1 00:00:00 --> 00:00:00,061 2 00:00:00,061 --> 00:00:07,383 Well, we have a current going through a wire, 3 00:00:07,383 --> 00:00:13,078 like so. And we look at the magnetic 4 00:00:13,078 --> 00:00:21,702 field in the vicinity of this wire , then we know from 5 00:00:21,702 --> 00:00:33,744 experiment that if you put pieces of magnetite around 6 00:00:33,744 --> 00:00:37,405 the wire that they line up in a circle. 7 00:00:37,405 --> 00:00:42,32 Put around like this. If that circle has a radius R, 8 00:00:42,32 --> 00:00:47,428 then the magnetic fields, that's an experimental fact, 9 00:00:47,428 --> 00:00:52,246 is proportional with the current I and is inversely 10 00:00:52,246 --> 00:00:56,39 proportional with the radius of that circle. 11 00:00:56,39 --> 00:01:00,534 By convention, the direction of the magnetic 12 00:01:00,534 --> 00:01:05,738 fields given by the right-hand corkscrew, 13 00:01:05,738 --> 00:01:08,707 rotate this way, the current goes up. 14 00:01:08,707 --> 00:01:12,09 You've seen before, with electric charges, 15 00:01:12,09 --> 00:01:16,957 when you have a wire which is uniformly distributed say with 16 00:01:16,957 --> 00:01:20,751 positive charge, you've also seen that electric 17 00:01:20,751 --> 00:01:25,701 fields in the vicinity of that straight wire falls off as one 18 00:01:25,701 --> 00:01:30,568 over R, whereas the direction is different than the magnetic 19 00:01:30,568 --> 00:01:35,435 field but it also falls off as one over R, and the reason is 20 00:01:35,435 --> 00:01:40,1 that electric monopoles, individual charges, 21 00:01:40,1 --> 00:01:43,909 the electric fields fall off as one over R squared. 22 00:01:43,909 --> 00:01:48,633 And so when you integrate that out over a straight wire you get 23 00:01:48,633 --> 00:01:51,3 the one over R field. So by analogy, 24 00:01:51,3 --> 00:01:55,947 it would be very plausible that if you took magnetic monopoles 25 00:01:55,947 --> 00:02:00,214 that the magnetic field would also fall off as one over R 26 00:02:00,214 --> 00:02:04,861 squared, but magnetic monopoles as far as we know don't exist. 27 00:02:04,861 --> 00:02:10,33 In principle they could exist, but we've never seen one, 28 00:02:10,33 --> 00:02:15,495 and if any one of you ever find one, that would certainly be a 29 00:02:15,495 --> 00:02:18,882 Nobel Prize. It's by no means impossible. 30 00:02:18,882 --> 00:02:24,131 And so the simple fact that the magnetic field around a current 31 00:02:24,131 --> 00:02:28,958 wire falls off as one over R, sort of suggests that if you 32 00:02:28,958 --> 00:02:33,784 carve this wire up in little elements DL, that each one of 33 00:02:33,784 --> 00:02:38,949 those elements contributes to the magnetic fields 34 00:02:38,949 --> 00:02:44,251 in inverse R-squared law, and by integrating out over the 35 00:02:44,251 --> 00:02:48,702 whole wire you'd then get the one over R fields. 36 00:02:48,702 --> 00:02:54,005 And this behind the idea of the formalism by Biot-Savart, 37 00:02:54,005 --> 00:02:59,308 who introduced the idea that if you have a little current 38 00:02:59,308 --> 00:03:03,853 element DL, and the current is in this direction, 39 00:03:03,853 --> 00:03:08,304 and you want to know what the magnetic field is, 40 00:03:08,304 --> 00:03:12,566 This is small contribution DB to 41 00:03:12,566 --> 00:03:16,283 that little current element, and the distance is R, 42 00:03:16,283 --> 00:03:20,521 and the unit vector from the element DL to the point where 43 00:03:20,521 --> 00:03:23,867 you want to know the magnetic field is R roof. 44 00:03:23,867 --> 00:03:27,659 Then the idea here is DB, it's a little bit of curr- 45 00:03:27,659 --> 00:03:32,194 little bit of magnetic fields. In this case it would be in the 46 00:03:32,194 --> 00:03:36,06 blackboards because of the right-hand corkscrew rule. 47 00:03:36,06 --> 00:03:39,629 The current is in this direction, so these little 48 00:03:39,629 --> 00:03:44,239 elements would contribute to magnetic fields in 49 00:03:44,239 --> 00:03:47,648 this direction perpendicular to the blackboard. 50 00:03:47,648 --> 00:03:51,28 It's some constant, proportional to the current no 51 00:03:51,28 --> 00:03:54,986 doubt, and then it's proportional to the lengths of 52 00:03:54,986 --> 00:03:58,396 that little element DL, if it's longer than the 53 00:03:58,396 --> 00:04:01,954 magnetic field is larger, and in order to get the 54 00:04:01,954 --> 00:04:06,327 direction right perpendicular to the blackboard you take the 55 00:04:06,327 --> 00:04:08,996 cross product with the unit vector R. 56 00:04:08,996 --> 00:04:13,443 The unit vector R has length one so you only do that in order 57 00:04:13,443 --> 00:04:19,069 to get the direction right. And this, and that inversely 58 00:04:19,069 --> 00:04:23,039 proportional to R squared. That's of course key. 59 00:04:23,039 --> 00:04:26,417 And this is, the formalism by Biot-Savart 60 00:04:26,417 --> 00:04:31,4 and you can do experiments and measure the magnetic field in 61 00:04:31,4 --> 00:04:35,286 the vicinity of wires and this formalism works, 62 00:04:35,286 --> 00:04:40,015 so you then calculate the individual contributions of all 63 00:04:40,015 --> 00:04:46,687 these little elements DL and then you do an integration and 64 00:04:46,687 --> 00:04:51,351 this formalism works. You can then also measure what 65 00:04:51,351 --> 00:04:55,557 C is, in SI units. C is ten to the minus seven. 66 00:04:55,557 --> 00:04:59,488 But we write for C something quite peculiar. 67 00:04:59,488 --> 00:05:05,066 We write for C mu zero divided by four pi, and we call this mu 68 00:05:05,066 --> 00:05:08,266 zero the permeability of free space. 69 00:05:08,266 --> 00:05:13,387 You've seen earlier with Coulomb's law that this constant 70 00:05:13,387 --> 00:05:20,213 nine times ten to the ninth, we call that one over four pi 71 00:05:20,213 --> 00:05:23,714 epsilon zero. What is in the name? 72 00:05:23,714 --> 00:05:29,126 And so here we call this mu zero divided by four pi. 73 00:05:29,126 --> 00:05:34,644 So now you can apply Biot-Savart's Law and you can go 74 00:05:34,644 --> 00:05:40,904 to a straight wire and you have a current I, and suppose you 75 00:05:40,904 --> 00:05:47,589 want to know what the magnetic field at that location 76 00:05:47,589 --> 00:05:52,814 is at a distant capital R, and so what you now have to do, 77 00:05:52,814 --> 00:05:57,489 if you carve this up, in an infinite number of small 78 00:05:57,489 --> 00:06:02,806 elements DL, and this distance is R, and the unit vector is 79 00:06:02,806 --> 00:06:06,472 then like so, and you calculate the small 80 00:06:06,472 --> 00:06:11,788 amount of magnetic field due to this little element and you 81 00:06:11,788 --> 00:06:14,905 integrate this over the whole wire. 82 00:06:14,905 --> 00:06:19,122 It's mathematics. You've done it. 83 00:06:19,122 --> 00:06:23,209 You've done it before, where we had uniformly electric 84 00:06:23,209 --> 00:06:26,757 charge on the wire. So I'm not going to do this 85 00:06:26,757 --> 00:06:29,919 again for you. It's a very straightforward 86 00:06:29,919 --> 00:06:33,852 piece of mathematics. The magnetic field by the way, 87 00:06:33,852 --> 00:06:36,474 in this case, would come out of the 88 00:06:36,474 --> 00:06:39,251 blackboards. Thus it's the right-hand 89 00:06:39,251 --> 00:06:42,644 corkscrew rule. And what you find when you do 90 00:06:42,644 --> 00:06:46,346 this, we will find that B equals mu zero times I, 91 00:06:46,346 --> 00:06:50,514 divided by two pi R, this being R, 92 00:06:50,514 --> 00:06:56,478 and so you indeed see that the inverse one over R comes out. 93 00:06:56,478 --> 00:06:59,208 And so if you, for instance, 94 00:06:59,208 --> 00:07:04,565 take a radius of oh point one meters, ten centimeters, 95 00:07:04,565 --> 00:07:10,328 and you have a current through the wire of about a hundred 96 00:07:10,328 --> 00:07:14,877 amperes, then you would end up with a B field. 97 00:07:14,877 --> 00:07:20,841 You use this equation two times ten to the minus four Tesla. 98 00:07:20,841 --> 00:07:25,841 That is about two Gauss. Hundred amperes. 99 00:07:25,841 --> 00:07:28,809 Ten centimeter distance is only two Gauss. 100 00:07:28,809 --> 00:07:31,995 Think about it. The Earth's magnetic field is 101 00:07:31,995 --> 00:07:34,89 half a Gauss. So if you go one meter away 102 00:07:34,89 --> 00:07:37,859 from the wire, so we have a magnetic field 103 00:07:37,859 --> 00:07:41,478 which is ten times lower [inaudible] is one over R, 104 00:07:41,478 --> 00:07:45,315 than the magnetic field of the Earth already dominates 105 00:07:45,315 --> 00:07:48,501 substantially. So you need very high current, 106 00:07:48,501 --> 00:07:51,324 actually, when you do these experiments. 107 00:07:51,324 --> 00:07:57,106 It's nice to see that out of Biot-Savart's formalism the one 108 00:07:57,106 --> 00:08:00,743 over R pops out, but of course you must realize 109 00:08:00,743 --> 00:08:05,566 that Biot-Savart knew that the magnetic field falls off as one 110 00:08:05,566 --> 00:08:08,491 over R. That was an experimental fact. 111 00:08:08,491 --> 00:08:12,84 So the fact that it falls out is logical, because it was 112 00:08:12,84 --> 00:08:16,714 cooked into that formalism. If you think about it, 113 00:08:16,714 --> 00:08:21,063 it all goes back to Newton. Newton was the one who first 114 00:08:21,063 --> 00:08:26,519 suggested that the gravitational field falls off as one 115 00:08:26,519 --> 00:08:29,447 over R squared. And then later a logical 116 00:08:29,447 --> 00:08:33,877 extension was that the electric fields would fall off as one 117 00:08:33,877 --> 00:08:38,532 over R squared and out of that came the idea that the fields of 118 00:08:38,532 --> 00:08:41,461 magnetic monopole, if they only existed, 119 00:08:41,461 --> 00:08:45,816 would fall off as one over R squared, and that's all behind 120 00:08:45,816 --> 00:08:49,796 this and so the person who really deserves most of the 121 00:08:49,796 --> 00:08:52,799 credit for all this in my book is Newton. 122 00:08:52,799 --> 00:08:58,28 Using Biot-Savart, we can calculate now easily the 123 00:08:58,28 --> 00:09:02,59 magnetic fields at the center of a current loop. 124 00:09:02,59 --> 00:09:07,633 Let this be a wire circle and let the current go in this 125 00:09:07,633 --> 00:09:13,318 direction, and I would ask you what is the magnetic field right 126 00:09:13,318 --> 00:09:17,353 at the center. Well, the magnetic field right 127 00:09:17,353 --> 00:09:21,296 at the center of course is pointing upwards. 128 00:09:21,296 --> 00:09:25,239 Each little element along the line here, DL, 129 00:09:25,239 --> 00:09:31,109 each little element will contribute a little bit 130 00:09:31,109 --> 00:09:36,709 magnetic field at that point right in this direction. 131 00:09:36,709 --> 00:09:41,555 And if this radius is R, with Biot-Savart now, 132 00:09:41,555 --> 00:09:47,91 we can calculate quite easily the total field that you would 133 00:09:47,91 --> 00:09:53,079 get at this location, because that total field is 134 00:09:53,079 --> 00:09:59,002 then the integral of DB factorially over the entire wire 135 00:09:59,002 --> 00:10:04,711 so the entire loop... So if you go there, 136 00:10:04,711 --> 00:10:09,574 so you would get your mu zero, divided by four pi, 137 00:10:09,574 --> 00:10:15,133 you get your current and you get your one over R squared, 138 00:10:15,133 --> 00:10:20,493 and now we have to do an integral over that DL cross R. 139 00:10:20,493 --> 00:10:25,158 Well, R is of course always perpendicular to DL. 140 00:10:25,158 --> 00:10:31,014 Any element DL that you choose, the unit vector R is exactly 141 00:10:31,014 --> 00:10:37,069 perpendicular to the element DL, because that's characteristic 142 00:10:37,069 --> 00:10:39,493 of a circle. 143 00:10:39,493 --> 00:10:44,967 And so the sine of the angle between DL and R is one, 144 00:10:44,967 --> 00:10:50,23 and so all we have to do is do an integral over DL, 145 00:10:50,23 --> 00:10:55,282 which is the integral of the circle, which is the 146 00:10:55,282 --> 00:11:00,44 circumference of the circle, and that is two pi R. 147 00:11:00,44 --> 00:11:05,177 And so now you find, lose a pi, you lose an R, 148 00:11:05,177 --> 00:11:11,072 so we find mu zero times I divided by two R. 149 00:11:11,072 --> 00:11:15,079 Just to show you an example, how in this case how easy it is 150 00:11:15,079 --> 00:11:19,359 to use Biot-Savart and calculate the magnetic field right at the 151 00:11:19,359 --> 00:11:21,601 center. If you were asked what the 152 00:11:21,601 --> 00:11:25,065 magnetic field was here or there, that would be also 153 00:11:25,065 --> 00:11:27,307 relatively easy. You've done that. 154 00:11:27,307 --> 00:11:30,703 I've given you a problem earlier where we had point 155 00:11:30,703 --> 00:11:34,983 charges uniformly distributed on a wire and I asked you what the 156 00:11:34,983 --> 00:11:38,515 electric field was here. So that can also be done now 157 00:11:38,515 --> 00:11:43,067 with magnetic fields. If I ever asked you what the 158 00:11:43,067 --> 00:11:46,616 magnetic fields would be here, that of course is an 159 00:11:46,616 --> 00:11:50,592 impossibility to do that with Biot-Savart, practically an 160 00:11:50,592 --> 00:11:53,787 impossibility. I wouldn't know how to do that. 161 00:11:53,787 --> 00:11:57,55 But in principle it could be done and certainly with a 162 00:11:57,55 --> 00:12:00,887 computer you can do it. So we can go to our same 163 00:12:00,887 --> 00:12:05,431 situation, we can take a hundred amperes for I and you can take R 164 00:12:05,431 --> 00:12:09,833 oh point one meters and then the B field, the strength of the B 165 00:12:09,833 --> 00:12:13,951 field right at the center of this loop that I found is then 166 00:12:13,951 --> 00:12:18,671 six times ten to the minus four Tesla. 167 00:12:18,671 --> 00:12:23,668 And that would be six Gauss. It's clear that if you want to 168 00:12:23,668 --> 00:12:27,545 put in some field lines, magnetic field lines, 169 00:12:27,545 --> 00:12:32,025 as a result of this current going around in a circle, 170 00:12:32,025 --> 00:12:37,194 that the- through the center there would be a field line like 171 00:12:37,194 --> 00:12:39,779 so. If you're very close to the 172 00:12:39,779 --> 00:12:44,948 wire here, which goes into the blackboards, I want you to see 173 00:12:44,948 --> 00:12:50,981 this three-dimensionally, then the magnetic fields would 174 00:12:50,981 --> 00:12:53,029 go like this, clockwise. 175 00:12:53,029 --> 00:12:58,284 Here the current comes to you, so would be counterclockwise. 176 00:12:58,284 --> 00:13:02,025 If the magnetic field line is here like so, 177 00:13:02,025 --> 00:13:06,835 and here it is curled up, then clearly I expect them to 178 00:13:06,835 --> 00:13:10,13 be here, sort of like so, and like so, 179 00:13:10,13 --> 00:13:13,693 and like so. This is the kind of magnetic 180 00:13:13,693 --> 00:13:17,612 field line configuration that I would expect, 181 00:13:17,612 --> 00:13:21,531 then, in the vicinity of such a current loop. 182 00:13:21,531 --> 00:13:23,758 183 00:13:23,758 --> 00:13:28,576 And I want to show this to you in a little bit more detail. 184 00:13:28,576 --> 00:13:33,31 I have here a transparency, and you see there on the right 185 00:13:33,31 --> 00:13:38,045 side, current goes into the paper and here it comes out of 186 00:13:38,045 --> 00:13:40,953 the paper. There is a circular loop. 187 00:13:40,953 --> 00:13:44,691 And you see here the field line configuration. 188 00:13:44,691 --> 00:13:49,343 It's not too different from what I have on the blackboard 189 00:13:49,343 --> 00:13:53,663 there. Very close to the wires, 190 00:13:53,663 --> 00:13:58,598 of course, you get circles because the one over R dominates 191 00:13:58,598 --> 00:14:01,662 there. It's so close to the wire that 192 00:14:01,662 --> 00:14:06,513 the one over R relationship makes it come out like circles 193 00:14:06,513 --> 00:14:10,258 and here too, but then if you're farther away 194 00:14:10,258 --> 00:14:13,662 you get configurations like I have there. 195 00:14:13,662 --> 00:14:17,491 When you're very far away from a current loop, 196 00:14:17,491 --> 00:14:21,746 the magnetic field configuration is very similar to 197 00:14:21,746 --> 00:14:27,844 that of an electric dipole. I can show you that in the 198 00:14:27,844 --> 00:14:30,465 following way. Let's first look at the 199 00:14:30,465 --> 00:14:33,087 electric dipole that you see up there. 200 00:14:33,087 --> 00:14:36,772 This is a positive charge, this is a negative charge. 201 00:14:36,772 --> 00:14:39,322 Don't look anywhere near the charges. 202 00:14:39,322 --> 00:14:41,661 Don't look in between the charges. 203 00:14:41,661 --> 00:14:44,566 Look far away. Here you see electric field 204 00:14:44,566 --> 00:14:48,605 lines and you see them here. Now look at your current loop 205 00:14:48,605 --> 00:14:51,014 here. The current is going into the 206 00:14:51,014 --> 00:14:53,494 paper here, coming out of the paper. 207 00:14:53,494 --> 00:14:57,957 There is a loop. And look, you see the same 208 00:14:57,957 --> 00:14:59,868 configuration, field lines, 209 00:14:59,868 --> 00:15:02,073 field lines. This goes like so. 210 00:15:02,073 --> 00:15:05,895 This one goes like so. Here, the electric field lines 211 00:15:05,895 --> 00:15:09,203 coming in, magnetic field lines are coming in. 212 00:15:09,203 --> 00:15:11,702 Electric field lines are going out. 213 00:15:11,702 --> 00:15:14,2 Magnetic field lines are going out. 214 00:15:14,2 --> 00:15:18,022 They look very similar. Gauss's Law tells me that the 215 00:15:18,022 --> 00:15:22,212 closed surface integral of the electric flux is the charge 216 00:15:22,212 --> 00:15:25,005 inside the box divided by epsilon zero, 217 00:15:25,005 --> 00:15:28,974 and so if you have a closed surface 218 00:15:28,974 --> 00:15:33,075 here, it looks like a line but I meant it to be a surface, 219 00:15:33,075 --> 00:15:37,104 then that closed surface integral of the electric flux is 220 00:15:37,104 --> 00:15:40,558 now zero because there's a charge inside the box. 221 00:15:40,558 --> 00:15:45,019 No matter where in the magnetic field you make a closed surface 222 00:15:45,019 --> 00:15:49,264 there is never any magnetic flux going through that surface. 223 00:15:49,264 --> 00:15:53,437 Never, unless you come into twenty-six one hundred and show 224 00:15:53,437 --> 00:15:56,747 me a magnetic monopole. Only then will there be 225 00:15:56,747 --> 00:16:01,889 magnetic flux coming out of a closed 226 00:16:01,889 --> 00:16:07,959 surface, if we put the magnetic monopole inside. 227 00:16:07,959 --> 00:16:13,77 And this, now, brings us to the second of four 228 00:16:13,77 --> 00:16:19,84 Maxwell's equations, the first one being Gauss's 229 00:16:19,84 --> 00:16:27,719 Law, the second one is that the closed surface- closed surface 230 00:16:27,719 --> 00:16:35,338 integral of B dot DA is always zero, unless you come with a 231 00:16:35,338 --> 00:16:39,883 magnetic monopole. 232 00:16:39,883 --> 00:16:45,526 So we now have two of Maxwell's four equations in 233 00:16:45,526 --> 00:16:47,759 place. Historic day. 234 00:16:47,759 --> 00:16:55,047 I want to show you the magnetic field in the vicinity of a wire 235 00:16:55,047 --> 00:16:59,396 like this. I have to use a few hundred 236 00:16:59,396 --> 00:17:04,215 amperes through that wire. I told you why, 237 00:17:04,215 --> 00:17:10,327 because magnetic field falls off 238 00:17:10,327 --> 00:17:13,842 quite rapidly, and I do that with iron file 239 00:17:13,842 --> 00:17:19,031 which I will sprinkle around the wire and these magnetites will 240 00:17:19,031 --> 00:17:23,633 orient themselves in that magnetic field and then I will 241 00:17:23,633 --> 00:17:28,487 try to also make you see this field configuration by having 242 00:17:28,487 --> 00:17:33,591 one wire going into the paper and one coming out of the paper. 243 00:17:33,591 --> 00:17:37,441 So let's first look at the single current wire. 244 00:17:37,441 --> 00:17:41,458 It's coming towards you and it goes 245 00:17:41,458 --> 00:17:44,37 into of course. It is a wire that goes like 246 00:17:44,37 --> 00:17:48,669 this and the reason why you see it here is of course we have to 247 00:17:48,669 --> 00:17:52,482 get the current in somehow. But it really is a wire like 248 00:17:52,482 --> 00:17:55,603 this, and this platform I'm going to show you. 249 00:17:55,603 --> 00:17:58,584 I'm going to put some iron file around this. 250 00:17:58,584 --> 00:18:02,329 We've got magnetites and when they see magnetic fields, 251 00:18:02,329 --> 00:18:06,004 they will try to orient themselves in the direction of 252 00:18:06,004 --> 00:18:09,332 the magnetic fields, so you're going to see these 253 00:18:09,332 --> 00:18:11,828 circles. But appreciate the fact that 254 00:18:11,828 --> 00:18:17,46 you need huge currents for this. Hundreds of amperes we do. 255 00:18:17,46 --> 00:18:21,087 That's why we have car battery here, remember, 256 00:18:21,087 --> 00:18:25,52 that was capable of delivering many hundreds of amperes. 257 00:18:25,52 --> 00:18:29,227 So I close the current now. I tap, you can see, 258 00:18:29,227 --> 00:18:33,579 these circular configurations. I hope you can see that. 259 00:18:33,579 --> 00:18:37,206 Looks like circles. I want to do the same now. 260 00:18:37,206 --> 00:18:40,672 This is a little bit more exciting, perhaps, 261 00:18:40,672 --> 00:18:45,669 with one wire going into the plane and the other 262 00:18:45,669 --> 00:18:49,357 one coming out. Even though it's not a circle, 263 00:18:49,357 --> 00:18:53,865 the idea is that you get a field configuration very much 264 00:18:53,865 --> 00:18:57,226 like you see there. Boy, it's already hot. 265 00:18:57,226 --> 00:19:02,144 These cables are already hot. They don't like the two hundred 266 00:19:02,144 --> 00:19:04,849 amperes. OK, let's do it this way. 267 00:19:04,849 --> 00:19:09,85 So you're going to see a field configuration similar to what I 268 00:19:09,85 --> 00:19:15,342 have on the blackboard, similar to what you have here. 269 00:19:15,342 --> 00:19:19,998 Oh, not, not this one. Similar to this. 270 00:19:19,998 --> 00:19:25,021 Yeah, actually, it was also the one that I 271 00:19:25,021 --> 00:19:30,045 have, but this is nicer way to look at it. 272 00:19:30,045 --> 00:19:37,152 So we have one wire going in and one wire coming out of the 273 00:19:37,152 --> 00:19:41,563 plane. All right, so let's first put 274 00:19:41,563 --> 00:19:48,303 some iron file on. All right, 275 00:19:48,303 --> 00:19:52,382 and now a few hundred amperes through it, tap it, 276 00:19:52,382 --> 00:19:57,057 and you can see close to the wire that goes in here and 277 00:19:57,057 --> 00:20:00,966 here, you see circles. Those are the one over R 278 00:20:00,966 --> 00:20:04,281 relationship. They dominate the magnetic 279 00:20:04,281 --> 00:20:07,001 fields, but look in between here. 280 00:20:07,001 --> 00:20:11,165 With a little bit of imagination you can see these 281 00:20:11,165 --> 00:20:16,01 field lines going like this, just like I have today on the 282 00:20:16,01 --> 00:20:19,75 blackboard. All right. 283 00:20:19,75 --> 00:20:24,702 We don't need it anymore, and we don't need that anymore. 284 00:20:24,702 --> 00:20:29,832 So this gives you a little bit of insight into the magnetic 285 00:20:29,832 --> 00:20:34,961 field configurations that we have about these wires when we 286 00:20:34,961 --> 00:20:39,118 run a current through. I will return to magnetic 287 00:20:39,118 --> 00:20:43,01 fields next lecture and we will expand on it. 288 00:20:43,01 --> 00:20:48,051 We will learn techniques to calculate magnetic fields in a 289 00:20:48,051 --> 00:20:53,623 way which is highly superior to Biot-Savart's law. 290 00:20:53,623 --> 00:20:58,01 In fact, that wil get us to the third Maxwell equation, 291 00:20:58,01 --> 00:21:00,934 almost. But I now want you to relax a 292 00:21:00,934 --> 00:21:05,728 little bit because this may already have been a little rough 293 00:21:05,728 --> 00:21:10,684 on you, so now I want to discuss something entirely different, 294 00:21:10,684 --> 00:21:14,746 something very practical, and it has to do with the 295 00:21:14,746 --> 00:21:19,377 transport of electrical energy. So we have a power station 296 00:21:19,377 --> 00:21:23,358 somewhere at location A, and they deliver electric 297 00:21:23,358 --> 00:21:27,258 power, electric energy to Boston. 298 00:21:27,258 --> 00:21:29,38 Here is Boston, location B. 299 00:21:29,38 --> 00:21:32,809 And A is the location of the power station. 300 00:21:32,809 --> 00:21:36,402 This could be a thousand miles, the distance. 301 00:21:36,402 --> 00:21:40,484 There's a cable going from the power station to us, 302 00:21:40,484 --> 00:21:44,239 and the potential here in this line, say, is B, 303 00:21:44,239 --> 00:21:47,424 a field B. Here's a cable for the return 304 00:21:47,424 --> 00:21:51,751 current, so the current goes like this, and the return 305 00:21:51,751 --> 00:21:56,241 current is in this direction, and, and here you use this 306 00:21:56,241 --> 00:22:01,054 energy. You hook up your computer, 307 00:22:01,054 --> 00:22:05,443 you hook up your hairdryer, your heaters, 308 00:22:05,443 --> 00:22:11,369 electric toothbrush and what have you, your TV station, 309 00:22:11,369 --> 00:22:15,54 everything. And so you are the consumer 310 00:22:15,54 --> 00:22:19,051 here. You take the energy that is 311 00:22:19,051 --> 00:22:25,526 provided by this power station. I will call the potential of 312 00:22:25,526 --> 00:22:33,866 this line zero and so this is V of A higher than this line here. 313 00:22:33,866 --> 00:22:40,586 Well, according to Ohm's Law, VA minus VB is the current 314 00:22:40,586 --> 00:22:48,161 times capital R which is now not radius, but that is resistance 315 00:22:48,161 --> 00:22:54,392 in the wire, this wire. This cable, however thick it 316 00:22:54,392 --> 00:23:00,989 may be, has a finite resistance. And so VB, that is the 317 00:23:00,989 --> 00:23:06,104 potential that we receive in Boston, 318 00:23:06,104 --> 00:23:11,38 equals VA minus IR. So if there's no current going 319 00:23:11,38 --> 00:23:16,226 through the wire, no one is using any electric 320 00:23:16,226 --> 00:23:19,779 energy, then VB is the same as VA. 321 00:23:19,779 --> 00:23:23,979 Now I want to know if we consume energy, 322 00:23:23,979 --> 00:23:30,117 so we're dealing now with power, so the power that we take 323 00:23:30,117 --> 00:23:38,37 off at Boston is I times V of B. That's the number of joules per 324 00:23:38,37 --> 00:23:45,061 second that we are consuming. So that then equals VA times I 325 00:23:45,061 --> 00:23:48,35 minus I square R. That's fine. 326 00:23:48,35 --> 00:23:53,113 What is this? This is the energy per second 327 00:23:53,113 --> 00:23:57,082 that we are consuming. What is this? 328 00:23:57,082 --> 00:24:03,206 This is the energy per second that the power station is 329 00:24:03,206 --> 00:24:07,749 delivering to us. What is this? 330 00:24:07,749 --> 00:24:12,573 That's lost energy. It's the I square R that is the 331 00:24:12,573 --> 00:24:17,88 heat produced in this cable that goes into the universe. 332 00:24:17,88 --> 00:24:21,739 It's gone. So the economy demands that we 333 00:24:21,739 --> 00:24:25,309 try to make this as small as possible. 334 00:24:25,309 --> 00:24:31,099 Uh, this is the power that is available but you get a loss of 335 00:24:31,099 --> 00:24:35,344 power in terms of heats, the minus sign here, 336 00:24:35,344 --> 00:24:42,377 so you get less in Boston. And so how can you make this I 337 00:24:42,377 --> 00:24:45,898 square R low? Well, what is the resistance of 338 00:24:45,898 --> 00:24:49,42 a wire that is rho, which is the resistivity, 339 00:24:49,42 --> 00:24:54,142 times the length of the wire divided by the cross-section of 340 00:24:54,142 --> 00:24:57,023 the wire. So we have several options. 341 00:24:57,023 --> 00:25:01,265 You could make A very large, a very thick copper wire, 342 00:25:01,265 --> 00:25:05,267 and that's expensive. You could also make the wires 343 00:25:05,267 --> 00:25:10,789 out of gold, which has a lower resistivity than copper. 344 00:25:10,789 --> 00:25:15,545 That's also expensive. People are thinking of making 345 00:25:15,545 --> 00:25:20,393 these transmission wires of superconducting material. 346 00:25:20,393 --> 00:25:24,776 They have to cool them at very low temperatures. 347 00:25:24,776 --> 00:25:30,277 That's outrageously expensive but that's a way you could get 348 00:25:30,277 --> 00:25:34,939 the resistance down. Let's now look at the current. 349 00:25:34,939 --> 00:25:37,83 What can we do with the current? 350 00:25:37,83 --> 00:25:42,788 Suppose we consume a hundred megawatts. 351 00:25:42,788 --> 00:25:49,145 Not an unreasonable number, so we are consuming a hundred 352 00:25:49,145 --> 00:25:54,594 megawatts, and just for the sake of the argument, 353 00:25:54,594 --> 00:25:59,589 suppose at VB the potential is hundred volts, 354 00:25:59,589 --> 00:26:05,606 so V of B is a hundred volts. What now is the current? 355 00:26:05,606 --> 00:26:10,601 Well, current times potential gives me power, 356 00:26:10,601 --> 00:26:16,845 and so my current is now a million amperes. 357 00:26:16,845 --> 00:26:21,09 Alternatively, suppose that the potential at B 358 00:26:21,09 --> 00:26:24,769 in the wire is a hundred thousand volts, 359 00:26:24,769 --> 00:26:29,391 a thousand times higher. Now the current is only a 360 00:26:29,391 --> 00:26:33,259 thousand amperes, gives me the same power. 361 00:26:33,259 --> 00:26:37,315 In both cases, am I consuming at a rate of a 362 00:26:37,315 --> 00:26:40,429 hundred million joules per second. 363 00:26:40,429 --> 00:26:44,579 But I square R, the heat loss on the way from 364 00:26:44,579 --> 00:26:50,265 the power station to me, is a million times lower in 365 00:26:50,265 --> 00:26:54,501 this case than in that case, because I is a thousand times 366 00:26:54,501 --> 00:26:57,771 lower, and the heat loss goes with I squared, 367 00:26:57,771 --> 00:27:01,635 and so now you understand why electricity, when it is 368 00:27:01,635 --> 00:27:06,168 transported from one place to another, why this is done at the 369 00:27:06,168 --> 00:27:09,735 highest voltage possible. When you get to Boston, 370 00:27:09,735 --> 00:27:13,823 you've obviously got to do something about this enormous 371 00:27:13,823 --> 00:27:18,058 potential, because if you were to deliver a 372 00:27:18,058 --> 00:27:20,841 hundred thousand potential difference there, 373 00:27:20,841 --> 00:27:24,658 then half the population in Boston would electrocute itself, 374 00:27:24,658 --> 00:27:28,475 so now you've got to come down in voltage, which you do with 375 00:27:28,475 --> 00:27:31,192 transformers. We will talk about that later 376 00:27:31,192 --> 00:27:33,974 in the course. And so you bring it down to a 377 00:27:33,974 --> 00:27:37,145 comfortable voltage, which is in the United States 378 00:27:37,145 --> 00:27:40,768 about a hundred and ten volts. In Europe it's two twenty. 379 00:27:40,768 --> 00:27:44,132 Now comes the question, how high can you make V of A. 380 00:27:44,132 --> 00:27:47,82 The higher you could make it, the less loss there would be 381 00:27:47,82 --> 00:27:49,96 along the way. 382 00:27:49,96 --> 00:27:54,076 Well, you've got to stay away from the breakdown electric 383 00:27:54,076 --> 00:27:57,677 field, which is the three million volts per meter. 384 00:27:57,677 --> 00:28:01,646 If at the surface of these cables you get three million 385 00:28:01,646 --> 00:28:04,659 volts per meter, you get corona discharge. 386 00:28:04,659 --> 00:28:08,555 That's a big loss and you want to stay away from that, 387 00:28:08,555 --> 00:28:11,715 and so typical cables have about a radius R. 388 00:28:11,715 --> 00:28:14,875 This is now, R is the radius of the cable of 389 00:28:14,875 --> 00:28:19,285 about two centimeters that gives him a cross-sectional area I 390 00:28:19,285 --> 00:28:24,449 think of about ten to the minus three 391 00:28:24,449 --> 00:28:27,306 meters squared, that's correct. 392 00:28:27,306 --> 00:28:32,923 And the potential V at A is roughly three hundred kilovolts, 393 00:28:32,923 --> 00:28:38,351 and with that configuration you stay comfortably below the 394 00:28:38,351 --> 00:28:42,826 electric field of three million volts per meter, 395 00:28:42,826 --> 00:28:46,444 but you don't get the corona discharge. 396 00:28:46,444 --> 00:28:51,966 If the length of that cable, L, if that were something like 397 00:28:51,966 --> 00:28:57,816 thousand kilometers, not an unreasonable number, 398 00:28:57,816 --> 00:29:03,332 thousand kilometer distance from if we get our electricity 399 00:29:03,332 --> 00:29:08,752 from Niagara Falls to Boston, not an unreasonable number, 400 00:29:08,752 --> 00:29:14,558 you can calculate now what the resistance of that cable would 401 00:29:14,558 --> 00:29:20,461 be, because that resistance R equals rho times L divided by A. 402 00:29:20,461 --> 00:29:25,106 If you take copper, that has a resistivity of two 403 00:29:25,106 --> 00:29:29,944 times ten to the minus eight SI units. 404 00:29:29,944 --> 00:29:35,698 We have a length of ten to the sixth meters of the cable and we 405 00:29:35,698 --> 00:29:41,172 have a cross-sectional area of ten to the minus three square 406 00:29:41,172 --> 00:29:46,183 meters so that thousand kilometer cable would only have 407 00:29:46,183 --> 00:29:51,101 a resistance of twenty ohms. And to make the numbers a 408 00:29:51,101 --> 00:29:56,019 little easy, if we have a current say of three hundred 409 00:29:56,019 --> 00:30:00,566 amperes, then the power that the power 410 00:30:00,566 --> 00:30:05,627 station produces, if you take the three hundred 411 00:30:05,627 --> 00:30:10,798 kilovolts for now, that power would be the three 412 00:30:10,798 --> 00:30:17,069 hundred kilovolts times the three hundred amperes and that 413 00:30:17,069 --> 00:30:23,34 is about ninety megawatts. That's close to my hundred that 414 00:30:23,34 --> 00:30:28,951 I had in mind earlier. So you can calculate now what 415 00:30:28,951 --> 00:30:34,232 the loss is. The loss is I squared R. 416 00:30:34,232 --> 00:30:38,33 You know R is twenty ohms, you know I, three hundred 417 00:30:38,33 --> 00:30:43,393 amperes, and so you'll find now that you have about two megawatt 418 00:30:43,393 --> 00:30:45 loss. That's not bad. 419 00:30:45 --> 00:30:48,696 Two out of ninety. So we have about two percent 420 00:30:48,696 --> 00:30:53,597 energy loss in transportation. You can also calculate now what 421 00:30:53,597 --> 00:30:58,338 the difference is in potential between the power station and 422 00:30:58,338 --> 00:31:02,356 Boston, VA minus VB is IR. You know that I is three 423 00:31:02,356 --> 00:31:06,615 hundred amperes and you know that R is 424 00:31:06,615 --> 00:31:10,312 twenty ohms, so VA minus VB is about six 425 00:31:10,312 --> 00:31:12,623 kilovolts. In other words, 426 00:31:12,623 --> 00:31:17,8 if the power station puts it on the line at three hundred 427 00:31:17,8 --> 00:31:22,884 kilovolts, then you would get it here with only four six 428 00:31:22,884 --> 00:31:27,136 kilovolts less. So it's not a very unreasonable 429 00:31:27,136 --> 00:31:30,556 situation. I told you that these power 430 00:31:30,556 --> 00:31:36,657 lines have to stay away from the three 431 00:31:36,657 --> 00:31:40,435 million volts per meter electric field because then you 432 00:31:40,435 --> 00:31:44,492 get corona discharge and when there is thunderstorms in the 433 00:31:44,492 --> 00:31:48,828 area it can actually push up the electric field on the wire and 434 00:31:48,828 --> 00:31:53,025 you can get corona discharge. I have seen that several times, 435 00:31:53,025 --> 00:31:57,012 not only seen it at night, with my naked eyes that you see 436 00:31:57,012 --> 00:32:00,09 the power lines glow, but I've also heard it, 437 00:32:00,09 --> 00:32:03,518 because you can here this cracking noise of corona 438 00:32:03,518 --> 00:32:05,756 discharge. It's very fascinating, 439 00:32:05,756 --> 00:32:08,973 actually. I have a slide here 440 00:32:08,973 --> 00:32:12,787 which shows that. So here you see a high voltage 441 00:32:12,787 --> 00:32:17,735 power line, transmission line, and you clearly see the glowing 442 00:32:17,735 --> 00:32:22,035 of the corona discharge. They compare that with what's 443 00:32:22,035 --> 00:32:24,631 called a [inaudible] kite string. 444 00:32:24,631 --> 00:32:29,58 Kite strings at night when you fly them near thunderstorms can 445 00:32:29,58 --> 00:32:32,744 also produce corona discharge and light. 446 00:32:32,744 --> 00:32:36,882 That's why the call [inaudible] kite string candles. 447 00:32:36,882 --> 00:32:41,019 Benjamin Franklin did quite a bit of 448 00:32:41,019 --> 00:32:47,155 experiments at night with, uh, kites near thunderstorms. 449 00:32:47,155 --> 00:32:52,843 Dangerous business by the way. So you see that these 450 00:32:52,843 --> 00:32:58,978 high-voltage power lines can go into a corona discharge. 451 00:32:58,978 --> 00:33:02,994 I now want to revisit our Leyden jar. 452 00:33:02,994 --> 00:33:09,575 We had a truly absurd situation whereby we did an experiment 453 00:33:09,575 --> 00:33:13,87 with a jar which you still see here, 454 00:33:13,87 --> 00:33:16,599 and I will redo the demonstration, 455 00:33:16,599 --> 00:33:20,818 but it's crying for an explanation because it looked 456 00:33:20,818 --> 00:33:24,374 like there was something wrong with physics, 457 00:33:24,374 --> 00:33:28,758 and I want to refresh your memory of what we have seen 458 00:33:28,758 --> 00:33:32,397 before and what this Leyden jar is all about. 459 00:33:32,397 --> 00:33:37,608 The Leyden jar is nothing but a capacitor, which is a dielectric 460 00:33:37,608 --> 00:33:41,661 between two conductors in the form, 461 00:33:41,661 --> 00:33:46,128 in the shape of a- of a bottle, the jar. 462 00:33:46,128 --> 00:33:50,711 And so the inner portion, which is glass, 463 00:33:50,711 --> 00:33:54,835 say has this shape. You see it there, 464 00:33:54,835 --> 00:34:01,021 you're going to see it shortly there, and then we have 465 00:34:01,021 --> 00:34:06,52 conductors, the conducting beaker around it here, 466 00:34:06,52 --> 00:34:14,513 and we have a conducting beaker on the inside. 467 00:34:14,513 --> 00:34:18,935 And we charge these up with the Wimshurst. 468 00:34:18,935 --> 00:34:24,327 This is the Wimshurst machine. And when we do that, 469 00:34:24,327 --> 00:34:30,366 we get free charge on the conductor, and so you get sigma 470 00:34:30,366 --> 00:34:37,052 free right here and you get it here, opposite signs of course, 471 00:34:37,052 --> 00:34:41,689 and you get sigma induced on the dielectric. 472 00:34:41,689 --> 00:34:48,315 Why do you get it? Because the dielectric sees an 473 00:34:48,315 --> 00:34:53,848 external field due to this sigma free, so it begins to polarize, 474 00:34:53,848 --> 00:34:59,03 and so you get here induced charge and you get there induced 475 00:34:59,03 --> 00:35:01,841 charge. If this side is positive, 476 00:35:01,841 --> 00:35:05,793 then the induced charge here will be negative, 477 00:35:05,793 --> 00:35:09,482 and vice-versa. We have here a metal hook, 478 00:35:09,482 --> 00:35:13,083 so that we can lift out the inner portion. 479 00:35:13,083 --> 00:35:19,167 And so what we did, we charged it up with the 480 00:35:19,167 --> 00:35:23,276 Wimshurst, and then there is a certain amount of energy. 481 00:35:23,276 --> 00:35:27,609 The electrostatic potential energy of this configuration is 482 00:35:27,609 --> 00:35:31,045 one-half Q free times the potential difference, 483 00:35:31,045 --> 00:35:35,528 and the Q free is the charge which is on the outer conductor. 484 00:35:35,528 --> 00:35:38,666 And what I then did, I disassembled it very 485 00:35:38,666 --> 00:35:43,073 carefully after we had charged it up, took the inner portion 486 00:35:43,073 --> 00:35:47,331 out, took the glass out, the outer portion, 487 00:35:47,331 --> 00:35:50,534 and I took all the free charge off. 488 00:35:50,534 --> 00:35:54,679 I touched the conductors and discharged them, 489 00:35:54,679 --> 00:35:58,164 so there is no Q free left. It's gone. 490 00:35:58,164 --> 00:36:03,816 The moment that that is gone, the induced charge must also go 491 00:36:03,816 --> 00:36:09,374 away because the induced charge is only there because of the 492 00:36:09,374 --> 00:36:13,048 free charge. Remember the induced charge 493 00:36:13,048 --> 00:36:17,946 density is one minus one over kappa times sigma free. 494 00:36:17,946 --> 00:36:22,373 So if glass has a kappa of five, 495 00:36:22,373 --> 00:36:26,73 then the induced surface charge density is about oh point eight 496 00:36:26,73 --> 00:36:29,329 times the free surface charge density. 497 00:36:29,329 --> 00:36:33,194 The moment that the free one goes, the induced one goes. 498 00:36:33,194 --> 00:36:37,48 And then I assembled it again, and much to our surprise when I 499 00:36:37,48 --> 00:36:40,993 short out the inner portion with the outer portion, 500 00:36:40,993 --> 00:36:44,295 we saw a huge spark. That means there was energy 501 00:36:44,295 --> 00:36:48,37 left and that is very puzzling. There can not be any energy 502 00:36:48,37 --> 00:36:52,938 left unless there is something wrong with physics. 503 00:36:52,938 --> 00:37:00,053 So I first want to show that again, to remind you of what you 504 00:37:00,053 --> 00:37:05,745 have seen before, and then I will make a proposal 505 00:37:05,745 --> 00:37:11,792 for a- for an explanation. Let me check my- my light 506 00:37:11,792 --> 00:37:17,01 configuration. Ah, we're going to make it all 507 00:37:17,01 --> 00:37:21,279 dark. I can charge it up while you're 508 00:37:21,279 --> 00:37:24,244 seeing it, actually. Yeah. 509 00:37:24,244 --> 00:37:26,615 510 00:37:26,615 --> 00:37:35,195 Make it dark now. And now I will disassemble it. 511 00:37:35,195 --> 00:37:45,965 I take the inner portion out. The glass is a good insulator, 512 00:37:45,965 --> 00:37:56,188 so I don't mind touching that with my hand. 513 00:37:56,188 --> 00:38:00,919 OK, and so now I take the inner conductor, touch it, 514 00:38:00,919 --> 00:38:04,722 lick it, kiss it, take all the charge off. 515 00:38:04,722 --> 00:38:08,247 There it is. Do the same with the outer 516 00:38:08,247 --> 00:38:13,627 conductor, have it in my hand. For sure, there is no Q free 517 00:38:13,627 --> 00:38:16,596 left on anymore, on that anymore. 518 00:38:16,596 --> 00:38:21,605 I put the glass back in again, and then I put the inner 519 00:38:21,605 --> 00:38:27,356 [inaudible], and now I'll make it a little darker 520 00:38:27,356 --> 00:38:31,326 for you because I want you to see that when I short this out 521 00:38:31,326 --> 00:38:35,161 that you're going to see a spark, so I'm going to turn the 522 00:38:35,161 --> 00:38:37,382 lights down, so look very closely. 523 00:38:37,382 --> 00:38:40,409 I'm going to tell you when I'm going to do it. 524 00:38:40,409 --> 00:38:43,033 Three, two, one, I'm approaching it now, 525 00:38:43,033 --> 00:38:45,052 zero. And there's a huge spark. 526 00:38:45,052 --> 00:38:47,407 That means energy, and that's crazy. 527 00:38:47,407 --> 00:38:50,838 There shouldn't be any. And so some of you must have 528 00:38:50,838 --> 00:38:54,269 had sleepless nights not being able to explain this. 529 00:38:54,269 --> 00:38:58,844 Some of uh- some of you actually wrote me e-mail. 530 00:38:58,844 --> 00:39:03,898 Uh, you didn't have sleepless nights, I can tell that. 531 00:39:03,898 --> 00:39:08,378 So what's going on? There's only one possibility 532 00:39:08,378 --> 00:39:13,145 and that is there must be free charge on the glass. 533 00:39:13,145 --> 00:39:17,34 How did it get there? Well, corona discharge. 534 00:39:17,34 --> 00:39:20,773 That's the only way it can get there. 535 00:39:20,773 --> 00:39:24,872 Keep in mind that the electric field in air, 536 00:39:24,872 --> 00:39:30,688 in air, can be no larger than three times ten to the six volts 537 00:39:30,688 --> 00:39:34,735 per meter. If it gets larger, 538 00:39:34,735 --> 00:39:38,987 you get corona discharge. In glass, by the way, 539 00:39:38,987 --> 00:39:43,332 it's a bit higher. It's ten to the seventh volts 540 00:39:43,332 --> 00:39:46,105 per meter. I will now make some 541 00:39:46,105 --> 00:39:49,895 calculations based on certain assumptions. 542 00:39:49,895 --> 00:39:55,256 And those assumptions may not be exactly accurate because I 543 00:39:55,256 --> 00:39:59,508 don't know the exact dimensions of this system, 544 00:39:59,508 --> 00:40:04,072 but the exact dimensions don't matter. 545 00:40:04,072 --> 00:40:08,682 What matters is the idea behind it, why it does such crazy 546 00:40:08,682 --> 00:40:10,542 things. So first of all, 547 00:40:10,542 --> 00:40:14,828 I will assume that this capacitor is just two parallel 548 00:40:14,828 --> 00:40:18,305 plain plates. That's a simplifying situation 549 00:40:18,305 --> 00:40:21,217 because it has the shape of a bottle. 550 00:40:21,217 --> 00:40:25,503 I will assume that the Wimshurst produces about thirty 551 00:40:25,503 --> 00:40:28,738 kilovolts. I know that it's approximately 552 00:40:28,738 --> 00:40:31,326 right, but it may be twenty-five. 553 00:40:31,326 --> 00:40:37,753 It may be thirty-five. I will assume that the air gap 554 00:40:37,753 --> 00:40:44,031 between the outer conductor and the glass is one millimeter, 555 00:40:44,031 --> 00:40:49,989 that both are one millimeter, and I would assume that the 556 00:40:49,989 --> 00:40:55,629 glass thickness is three millimeters, and I take kappa 557 00:40:55,629 --> 00:41:01,055 equal five for the glass. So that is the basis of my 558 00:41:01,055 --> 00:41:04,78 calculations. So now I have here the 559 00:41:04,78 --> 00:41:09,983 conductor on the outside. This is the glass, 560 00:41:09,983 --> 00:41:13,78 and this is the conductor on the inside, so this is one 561 00:41:13,78 --> 00:41:17,016 millimeter thick. This is the glass and this is 562 00:41:17,016 --> 00:41:20,744 the conductor on the inside, so this is one millimeter 563 00:41:20,744 --> 00:41:24,541 thick, this is three millimeters thick, and this is one 564 00:41:24,541 --> 00:41:27,706 millimeter thick, and the potential difference 565 00:41:27,706 --> 00:41:31,364 over the whole thing is going to be thirty kilovolts. 566 00:41:31,364 --> 00:41:35,584 But I know that the potential difference is always E times D. 567 00:41:35,584 --> 00:41:40,155 That holds for this gap the local E times this D, 568 00:41:40,155 --> 00:41:44,766 the local E times this D, and the local E times that D. 569 00:41:44,766 --> 00:41:50,059 I also know that E glass is the same as E in the air divided by 570 00:41:50,059 --> 00:41:54,413 that kappa, which is five. And I know that the total 571 00:41:54,413 --> 00:41:59,193 potential difference between here and here must be thirty 572 00:41:59,193 --> 00:42:02,864 thousand volts. And so this allows me now to 573 00:42:02,864 --> 00:42:07,218 calculate in a very straightforward way the electric 574 00:42:07,218 --> 00:42:11,829 field here in the air, the electric field 575 00:42:11,829 --> 00:42:15,91 here in the air, and the electric field in the 576 00:42:15,91 --> 00:42:20,899 glass because I get simple equation with one unknown and 577 00:42:20,899 --> 00:42:25,616 that's the following. I first go over this gap and so 578 00:42:25,616 --> 00:42:30,333 I get E in the air times the distance D, which is one 579 00:42:30,333 --> 00:42:33,961 millimeter. But of course later on I have 580 00:42:33,961 --> 00:42:39,313 to go through this gap again so I'll multiply it by two now. 581 00:42:39,313 --> 00:42:43,577 And now I have to add the electric 582 00:42:43,577 --> 00:42:47,087 field in the glass, which is the same as air 583 00:42:47,087 --> 00:42:50,597 divided by five, times its distance which is 584 00:42:50,597 --> 00:42:54,271 three millimeters, and that must now be thirty 585 00:42:54,271 --> 00:42:58,843 thousand, because that's the potential difference between 586 00:42:58,843 --> 00:43:02,353 here and there. That's one equation with one 587 00:43:02,353 --> 00:43:04,884 unknown. And I can calculate the 588 00:43:04,884 --> 00:43:09,7 electric field in the air gap. And the electric field in the 589 00:43:09,7 --> 00:43:16,639 air gap turns out to be eleven point five times ten to the six 590 00:43:16,639 --> 00:43:19,479 volts per meter. It's here the same, 591 00:43:19,479 --> 00:43:23,616 of course, eleven point five times ten to the sixth, 592 00:43:23,616 --> 00:43:27,834 and here it is five times smaller, so I find here two 593 00:43:27,834 --> 00:43:30,592 point three times ten to the sixth. 594 00:43:30,592 --> 00:43:34,162 To show you that I did my homework correctly, 595 00:43:34,162 --> 00:43:38,461 the potential difference here is now eleven point five 596 00:43:38,461 --> 00:43:41,463 kilovolts. I put it here in kilovolts. 597 00:43:41,463 --> 00:43:46,411 The potential difference here is now about seven kilovolts and 598 00:43:46,411 --> 00:43:50,367 the potential difference here is 599 00:43:50,367 --> 00:43:53,701 the same, is eleven point five kilovolts. 600 00:43:53,701 --> 00:43:56,868 And if you add them up, you get thirty. 601 00:43:56,868 --> 00:43:59,869 If you look at this, this can not be, 602 00:43:59,869 --> 00:44:04,953 because a field of eleven point five times ten to the sixth is 603 00:44:04,953 --> 00:44:08,12 way above the breakdown electric field. 604 00:44:08,12 --> 00:44:12,455 And so what are you going to- what's going to happen, 605 00:44:12,455 --> 00:44:17,205 you're going to get corona discharge from the conductor to 606 00:44:17,205 --> 00:44:21,099 the glass, and so what you're doing is 607 00:44:21,099 --> 00:44:24,998 you're spraying charge on the glass, and that's the key to the 608 00:44:24,998 --> 00:44:27,108 solution of this bizarre behavior. 609 00:44:27,108 --> 00:44:30,432 And so when you later disassemble it and you take the 610 00:44:30,432 --> 00:44:34,332 free charge of the conductors. There is still this free charge 611 00:44:34,332 --> 00:44:36,57 which you have sprayed on the glass. 612 00:44:36,57 --> 00:44:39,383 I never remove that. It's very hard to remove 613 00:44:39,383 --> 00:44:41,492 because the glass is an insulator. 614 00:44:41,492 --> 00:44:44,753 It's very difficult to take charge off an insulator. 615 00:44:44,753 --> 00:44:48,269 It's easy to take it off a conductor but I've never even 616 00:44:48,269 --> 00:44:52,233 attempted that because I made you believe, 617 00:44:52,233 --> 00:44:58,085 as I believed myself for years, that once you take the Q free 618 00:44:58,085 --> 00:45:03,645 of the conductor that there can be no charge on the glass. 619 00:45:03,645 --> 00:45:07,156 That is wrong, because there's corona 620 00:45:07,156 --> 00:45:10,668 discharge. So now comes the question, 621 00:45:10,668 --> 00:45:15,642 before we disassemble, what now is the configuration 622 00:45:15,642 --> 00:45:19,641 of the electric fields and the potentials. 623 00:45:19,641 --> 00:45:27,054 I'll make a drawing here and so now I draw again the conductor, 624 00:45:27,054 --> 00:45:31,252 the glass, and the conductor. I resume now that after the 625 00:45:31,252 --> 00:45:36,049 corona discharge this field here is three times ten to the sixth. 626 00:45:36,049 --> 00:45:39,872 Maybe a little lower, but that's the maximum that it 627 00:45:39,872 --> 00:45:44,669 can be, and so the field here in the air will be also three times 628 00:45:44,669 --> 00:45:47,068 ten to the sixth volts per meter. 629 00:45:47,068 --> 00:45:51,04 But since I know that the potential difference between 630 00:45:51,04 --> 00:45:55,537 here and here must be thirty kilovolts, I can now immediately 631 00:45:55,537 --> 00:46:00,409 conclude that the electric field here is now eight 632 00:46:00,409 --> 00:46:03,228 times ten to the sixth volts per meter. 633 00:46:03,228 --> 00:46:07,381 That is the only way that it adds up to thirty kilovolts, 634 00:46:07,381 --> 00:46:11,83 because the three million volts per meter gives me here three 635 00:46:11,83 --> 00:46:14,352 kilovolts. This here gives me three 636 00:46:14,352 --> 00:46:16,948 kilovolts. So now I need a potential 637 00:46:16,948 --> 00:46:21,397 difference here of twenty-four kilovolts, and that over three 638 00:46:21,397 --> 00:46:25,847 millimeters requires this field. Look, this field is stronger 639 00:46:25,847 --> 00:46:30,222 than that field, whereas earlier we made the 640 00:46:30,222 --> 00:46:34,407 assumption that this field was five times lower than that 641 00:46:34,407 --> 00:46:36,798 field. Yah, why is it now higher? 642 00:46:36,798 --> 00:46:40,534 Because we have sprayed right here on this surface, 643 00:46:40,534 --> 00:46:44,793 we have sprayed free charge. It's no longer the field that 644 00:46:44,793 --> 00:46:48,753 is dictated by the external field and then the induced 645 00:46:48,753 --> 00:46:51,293 charges. That's no longer the case. 646 00:46:51,293 --> 00:46:53,759 It carries now itself free charge. 647 00:46:53,759 --> 00:46:57,42 You now have all the tools, maybe not the courage, 648 00:46:57,42 --> 00:47:02,277 to calculate how much free charge there is right 649 00:47:02,277 --> 00:47:05,312 here on the glass to get these fields. 650 00:47:05,312 --> 00:47:08,512 It's a very straightforward calculation. 651 00:47:08,512 --> 00:47:13,435 And you will find that there is twelve times more free charge 652 00:47:13,435 --> 00:47:17,783 here on the glass than there is here on the conductor, 653 00:47:17,783 --> 00:47:21,475 twelve times more, and so if I disassemble and 654 00:47:21,475 --> 00:47:26,316 remove the free charge on the conductors, I have almost done 655 00:47:26,316 --> 00:47:30,828 nothing because most of the free charge is on the glass, 656 00:47:30,828 --> 00:47:35,094 and I have not touched that. So now, if I reassemble, 657 00:47:35,094 --> 00:47:40,515 I have almost all energy left. I have not lost much. 658 00:47:40,515 --> 00:47:44,538 Lost some, but not lost much. And so what I should have 659 00:47:44,538 --> 00:47:47,965 really have done, I should also have discharged 660 00:47:47,965 --> 00:47:50,349 the inner glass. That's not easy, 661 00:47:50,349 --> 00:47:54,596 but I will try that today. It's not easy because it's very 662 00:47:54,596 --> 00:47:58,247 hard to take that charge off, but I will try that. 663 00:47:58,247 --> 00:48:01,897 And then there shouldn't be much energy left if we 664 00:48:01,897 --> 00:48:05,771 reassemble it again and try to get a spark out of it. 665 00:48:05,771 --> 00:48:09,646 So I go through the same routine and 666 00:48:09,646 --> 00:48:15,899 I'm going to charge it up now. OK, take this cable off, 667 00:48:15,899 --> 00:48:20,069 take that cable off. I take it apart, 668 00:48:20,069 --> 00:48:25,164 do everything that I did before the same way, 669 00:48:25,164 --> 00:48:30,144 gone, whole charge gone, whatever there was. 670 00:48:30,144 --> 00:48:35,472 Whole charge gone. Now, this is more difficult. 671 00:48:35,472 --> 00:48:42,304 This is not enough if I do this. 672 00:48:42,304 --> 00:48:46,152 I have to get in there. Ooh, I could actually feel it. 673 00:48:46,152 --> 00:48:48,548 It's really, it's a great feeling. 674 00:48:48,548 --> 00:48:52,687 I can feel a sort of corona discharge with my -- I have to 675 00:48:52,687 --> 00:48:55,954 really get everything out and that's not easy. 676 00:48:55,954 --> 00:48:58,785 It's not. In fact, when I rub in with my 677 00:48:58,785 --> 00:49:03,359 shirt, I may even make it worse. I may be charging it up through 678 00:49:03,359 --> 00:49:05,973 friction. But I'll do the best I can. 679 00:49:05,973 --> 00:49:08,441 It's very indecent, what I'm doing. 680 00:49:08,441 --> 00:49:12,072 OK. So I try to get a charge now, 681 00:49:12,072 --> 00:49:15,567 something that we ignored completely before. 682 00:49:15,567 --> 00:49:20,688 This is really where the energy was, and I'm trying to kill that 683 00:49:20,688 --> 00:49:24,102 now, and so now I'm going to reassemble it, 684 00:49:24,102 --> 00:49:28,329 and I'll go through the same routine [clink] [whoop]. 685 00:49:28,329 --> 00:49:32,394 Good thing I didn't break it. Put it back in again. 686 00:49:32,394 --> 00:49:36,295 I'll make it dark, so that you can see where the- 687 00:49:36,295 --> 00:49:39,71 perhaps there may be a little bit of spark, 688 00:49:39,71 --> 00:49:45,887 if I didn't succeed to remove all the charges from the glass. 689 00:49:45,887 --> 00:49:49,224 So I'm going to short it out again, three, 690 00:49:49,224 --> 00:49:52,887 two, one, zero, and I saw a teeny-weeny little 691 00:49:52,887 --> 00:49:55,817 spark. You may not even have seen it, 692 00:49:55,817 --> 00:50:00,862 so we have to conclude now that the physics behind this lies in 693 00:50:00,862 --> 00:50:05,99 the glass and physics works even when it sometimes surprises us. 694 00:50:05,99 --> 50:11 See you Wednesday.