1 00:00:00 --> 00:00:00,869 2 00:00:00,869 --> 00:00:08,509 We see last time that using Biot and Savart's formula that 3 00:00:08,509 --> 00:00:15,881 if you have a current going straight into the blackboard 4 00:00:15,881 --> 00:00:24,325 perpendicular to the blackboards that we get a magnetic field at 5 00:00:24,325 --> 00:00:30,223 a distance R. The magnetic field tangentially 6 00:00:30,223 --> 00:00:34,429 to the circle, B here, 7 00:00:34,429 --> 00:00:43,198 B here, and then the strength of that magnetic field equals mu 8 00:00:43,198 --> 00:00:47,798 zero times I divided by two pi R. 9 00:00:47,798 --> 00:00:54,699 If you walk around this circle, just walk around, 10 00:00:54,699 --> 00:01:03,18 and you carve up this circle in little elements DL, 11 00:01:03,18 --> 00:01:08,705 and you calculate the closed circle integral, 12 00:01:08,705 --> 00:01:15,986 so the closed circle of B dot DL, so everywhere locally you 13 00:01:15,986 --> 00:01:21,636 dot B with DL, the B and DL are in exactly the 14 00:01:21,636 --> 00:01:28,541 same direction everywhere, then you would find that this 15 00:01:28,541 --> 00:01:36,327 obviously is B times two pi R. But B times two pi R equals 16 00:01:36,327 --> 00:01:41,784 also mu zero times I. This DL here has nothing to do 17 00:01:41,784 --> 00:01:46,063 with this DL here. Don't confuse the two. 18 00:01:46,063 --> 00:01:52,056 This DL is a small amount of length in the wire that goes 19 00:01:52,056 --> 00:01:56,657 into the blackboard which carries a current. 20 00:01:56,657 --> 00:02:02,969 This DL is simply your DL when you walk around this current 21 00:02:02,969 --> 00:02:07,731 wire. It doesn't matter at what 22 00:02:07,731 --> 00:02:12,645 distance you walk around. You always get mu zero times I. 23 00:02:12,645 --> 00:02:17,91 You see it right in front of your eyes because B is inversely 24 00:02:17,91 --> 00:02:21,859 proportional to R. And it was Ampere who first 25 00:02:21,859 --> 00:02:27,036 recognized that you don't have to walk around in a circle to 26 00:02:27,036 --> 00:02:31,862 get the answer mu zero I, but that you could walk around 27 00:02:31,862 --> 00:02:36,25 in any crooked path as long as it is a closed path, 28 00:02:36,25 --> 00:02:40,725 something like this. And now you have here the local 29 00:02:40,725 --> 00:02:44,359 B, which of course is 30 00:02:44,359 --> 00:02:51,551 perpendicular to this radius and here you have your local DL and 31 00:02:51,551 --> 00:02:56,688 if now you go around, closed circled any path, 32 00:02:56,688 --> 00:03:03,31 it doesn't have to be a circle, dot DL that now becomes mu 33 00:03:03,31 --> 00:03:08,333 zero times I, which is known as Ampere's Law, 34 00:03:08,333 --> 00:03:15,525 and I then is often given an index and closed. 35 00:03:15,525 --> 00:03:19,268 It is the current which is enclosed by that path. 36 00:03:19,268 --> 00:03:23,636 It is actually easy to prove this using Biot and Savart's 37 00:03:23,636 --> 00:03:26,132 formalism. This is almost a third 38 00:03:26,132 --> 00:03:30,031 Maxwell's equation. We already had two out of four. 39 00:03:30,031 --> 00:03:32,995 This is almost number three, not quite. 40 00:03:32,995 --> 00:03:35,881 We're going to amend it in the future. 41 00:03:35,881 --> 00:03:40,482 What is ill-defined a little bit in this equation is what we 42 00:03:40,482 --> 00:03:43,992 mean by enclosed, and I'm going to define that 43 00:03:43,992 --> 00:03:48,36 now so uniquely that there is never any 44 00:03:48,36 --> 00:03:52,036 misunderstanding. If I have a very strange 45 00:03:52,036 --> 00:03:57,596 looking closed path that I have chosen, that's the path I walk, 46 00:03:57,596 --> 00:04:01,721 I have to attach to that closed loop a surface, 47 00:04:01,721 --> 00:04:04,68 an open surface. That's mandatory. 48 00:04:04,68 --> 00:04:07,639 You can make it flat. That's fine. 49 00:04:07,639 --> 00:04:12,571 You're free to choose it. You can also make it sort of a 50 00:04:12,571 --> 00:04:19,297 plastic bag so it's open here. You can put your hands in here, 51 00:04:19,297 --> 00:04:22,372 and here, like a hat. Any surface is fine, 52 00:04:22,372 --> 00:04:25,522 but you must attach to that loop a surface, 53 00:04:25,522 --> 00:04:29,347 so here I have some paths that you could be walking, 54 00:04:29,347 --> 00:04:33,172 and this would be perfectly fine open- open surface. 55 00:04:33,172 --> 00:04:36,173 Could be flat, but it could also be open, 56 00:04:36,173 --> 00:04:39,773 so it's like a hat. And now I can define uniquely 57 00:04:39,773 --> 00:04:43,523 what it means by- what it means by this I enclosed, 58 00:04:43,523 --> 00:04:48,098 because if now I have a current that goes through this surface 59 00:04:48,098 --> 00:04:52,844 and pokes out here, then I have a current 60 00:04:52,844 --> 00:04:57,909 penetrating the surface and that is uniquely defined, 61 00:04:57,909 --> 00:05:03,266 and if I have another one coming in through the surface, 62 00:05:03,266 --> 00:05:07,454 for I two, this is penetrating that surface. 63 00:05:07,454 --> 00:05:11,447 By convention, if you go clockwise around, 64 00:05:11,447 --> 00:05:15,928 we follow the same notation that we had before, 65 00:05:15,928 --> 00:05:20,701 in the right-hand corkscrew notation, 66 00:05:20,701 --> 00:05:24,932 the connection between magnetic field and current. 67 00:05:24,932 --> 00:05:28,905 If you go around clockwise seen from this side, 68 00:05:28,905 --> 00:05:33,136 so you go clockwise, then I one as I have it here, 69 00:05:33,136 --> 00:05:37,454 the new equation would have to be larger than zero. 70 00:05:37,454 --> 00:05:40,132 I two is then smaller than zero. 71 00:05:40,132 --> 00:05:43,672 But if you decided to go counterclockwise, 72 00:05:43,672 --> 00:05:48,077 which is perfectly fine, Ampere's law doesn't at all 73 00:05:48,077 --> 00:05:52,481 dictate in which direction you have to march around, 74 00:05:52,481 --> 00:05:58,258 then I one would be negative and then I two would be 75 00:05:58,258 --> 00:06:01,217 positive. So we follow the right-hand 76 00:06:01,217 --> 00:06:05,326 corkscrew notation. And so if you want to amend now 77 00:06:05,326 --> 00:06:10,258 Ampere's Law to do me a favor, but you don't do books a favor 78 00:06:10,258 --> 00:06:13,792 because all the books use the word enclosed. 79 00:06:13,792 --> 00:06:17,737 I would like to see this replaced by penetration. 80 00:06:17,737 --> 00:06:22,505 It is the penetration of the surface of the current that is 81 00:06:22,505 --> 00:06:26,121 uniquely defined. But a current enclosed by a 82 00:06:26,121 --> 00:06:31,052 loop is ill-defined. Because where possible, 83 00:06:31,052 --> 00:06:35,219 when we apply Ampere's Law, we will try to find easy passes 84 00:06:35,219 --> 00:06:38,524 around circles sometimes, sometimes rectangles, 85 00:06:38,524 --> 00:06:42,26 and since you are free to choose the surface that you 86 00:06:42,26 --> 00:06:46,571 attach to the loop if you can get away with it you use a flat 87 00:06:46,571 --> 00:06:50,881 surface, but you can not always get away with a flat surface. 88 00:06:50,881 --> 00:06:54,904 So the recipe is as follows. You choose your closed loop. 89 00:06:54,904 --> 00:06:58,425 Any loop is allowed. It may not help you very much 90 00:06:58,425 --> 00:07:03,095 if you choose the wrong loop. Any loop is allowed. 91 00:07:03,095 --> 00:07:06,855 You then attach an open surface to that loop. 92 00:07:06,855 --> 00:07:11,726 And I penetrate is now the current that penetrates through 93 00:07:11,726 --> 00:07:15,315 that surface, according to this convention. 94 00:07:15,315 --> 00:07:19,075 And the direction of rotation is free to you. 95 00:07:19,075 --> 00:07:23,946 How you go around to pass is your choice, but that defines 96 00:07:23,946 --> 00:07:27,792 then the sign of the penetrating of the curve, 97 00:07:27,792 --> 00:07:33,262 of the- of the current, according to the right-hand 98 00:07:33,262 --> 00:07:35,567 corkscrew. So now we can, 99 00:07:35,567 --> 00:07:40,082 for the first time, calculate the magnetic field 100 00:07:40,082 --> 00:07:45,174 inside a wire that draws a current using Ampere's Law. 101 00:07:45,174 --> 00:07:50,842 I have here a wire that has a radius capital R and a current 102 00:07:50,842 --> 00:07:55,069 is coming to me, I, and let's assume that the 103 00:07:55,069 --> 00:08:00,833 current is uniformly throughout the wire, so it has a uniform 104 00:08:00,833 --> 00:08:05,935 current density. And I would like to know what 105 00:08:05,935 --> 00:08:08,489 the magnetic field is everywhere. 106 00:08:08,489 --> 00:08:12,96 The cylindrical symmetry, I want to know outside the wire 107 00:08:12,96 --> 00:08:15,674 and I want to know inside the wire. 108 00:08:15,674 --> 00:08:19,586 Let's first look at radius which is larger than R, 109 00:08:19,586 --> 00:08:23,577 and so here we have the cross-section of that wire, 110 00:08:23,577 --> 00:08:26,691 radius R. The current I is going through 111 00:08:26,691 --> 00:08:30,043 this surface. I now have to choose a closed 112 00:08:30,043 --> 00:08:32,438 path. Since we have cylindrical 113 00:08:32,438 --> 00:08:36,59 symmetry it is clear that we would 114 00:08:36,59 --> 00:08:39,586 choose the circle, with radius little R, 115 00:08:39,586 --> 00:08:43,888 so we can be sure that the magnetic field strength is the 116 00:08:43,888 --> 00:08:47,421 same everywhere because of reasons of symmetry. 117 00:08:47,421 --> 00:08:51,57 Since the current is coming towards me and I am free to 118 00:08:51,57 --> 00:08:54,95 choose in which direction I'm going to march, 119 00:08:54,95 --> 00:08:58,868 I know that the magnetic field is in this direction, 120 00:08:58,868 --> 00:09:03,554 so I might as well also march in this direction so that my DLs 121 00:09:03,554 --> 00:09:08,605 are all in this direction. I don't have to do that. 122 00:09:08,605 --> 00:09:12,486 I could march the other way around, but if I march 123 00:09:12,486 --> 00:09:17,397 counterclockwise then both terms left and right of Ampere's Law 124 00:09:17,397 --> 00:09:20,961 will be positive. I now have to attach an open 125 00:09:20,961 --> 00:09:23,971 surface to my path. Well, this will be, 126 00:09:23,971 --> 00:09:27,219 the blackboard will be, that open surface. 127 00:09:27,219 --> 00:09:31,576 And so now I apply Ampere's Law, so I get B times two pi 128 00:09:31,576 --> 00:09:36,408 little R, because DL and B are in the same direction so it's a 129 00:09:36,408 --> 00:09:40,051 trivial integral. That now equals mu zero times 130 00:09:40,051 --> 00:09:43,607 I, which now penetrates my 131 00:09:43,607 --> 00:09:46,008 surface. Uniquely determined, 132 00:09:46,008 --> 00:09:51,152 all these currents from this wire that comes to me penetrates 133 00:09:51,152 --> 00:09:55,781 my surface, so times I, and so B equals mu zero times I 134 00:09:55,781 --> 00:10:00,153 divided by two pi R, and that's the same result that 135 00:10:00,153 --> 00:10:03,84 we found last time, when we applied Biot and 136 00:10:03,84 --> 00:10:07,012 Savart. So that's no surprise that you 137 00:10:07,012 --> 00:10:11,47 see this, because now we have a way of 138 00:10:11,47 --> 00:10:15,303 finding the magnetic field also inside the wire, 139 00:10:15,303 --> 00:10:19,299 so here we have the wire again, the cross-section, 140 00:10:19,299 --> 00:10:23,622 current coming out of the blackboard, and now I want a 141 00:10:23,622 --> 00:10:28,027 radius which is smaller than capital R and of course my 142 00:10:28,027 --> 00:10:32,757 closed pass again for reasons for symmetry is going to be a 143 00:10:32,757 --> 00:10:36,999 circle with radius R. And my surface that I attach is 144 00:10:36,999 --> 00:10:39,609 a flat surface, and so here I go, 145 00:10:39,609 --> 00:10:43,524 B times two pi little R equals mu 146 00:10:43,524 --> 00:10:46,791 zero times- ah, now I have to be careful, 147 00:10:46,791 --> 00:10:51,285 because now not the full current I is now penetrating my 148 00:10:51,285 --> 00:10:55,615 surface, but it is only a fraction that penetrates the 149 00:10:55,615 --> 00:11:00,435 surface, and the fraction that penetrates the surface is now 150 00:11:00,435 --> 00:11:04,765 little R squared divided by capital R squared times I. 151 00:11:04,765 --> 00:11:09,503 You see, because the total current comes through the radius 152 00:11:09,503 --> 00:11:15,548 capital R, but I only have now a circle with radius little R. 153 00:11:15,548 --> 00:11:21,004 And so I lose one R here and so we get a very different result. 154 00:11:21,004 --> 00:11:26,284 You get now that the magnetic field equals mu zero times I is 155 00:11:26,284 --> 00:11:31,388 now linear in little R divided by two pi capital R squared. 156 00:11:31,388 --> 00:11:36,668 And this grows linearly with R, whereas this falls off as one 157 00:11:36,668 --> 00:11:39,836 over R. And if you substitute in this 158 00:11:39,836 --> 00:11:44,324 equation R equals capital R, which then would be the 159 00:11:44,324 --> 00:11:48,543 magnetic field right at the surface of 160 00:11:48,543 --> 00:11:52,388 the wire, you find exactly the same result here. 161 00:11:52,388 --> 00:11:57,132 Little R becomes a capital R. If little R becomes a capital 162 00:11:57,132 --> 00:12:01,303 R, you lose one capital R, you get the same result. 163 00:12:01,303 --> 00:12:06,211 And so if you make a plot of the magnetic field as a function 164 00:12:06,211 --> 00:12:11,2 of little R, then it looks like- like so, so this is little R, 165 00:12:11,2 --> 00:12:15,126 this is capital R, and this is the magnetic field 166 00:12:15,126 --> 00:12:20,769 strength because we know that it is tangentially 167 00:12:20,769 --> 00:12:25,347 to the circles. It would be straight line and 168 00:12:25,347 --> 00:12:31,381 then here it falls off as one over R, and the maximum value 169 00:12:31,381 --> 00:12:37,935 here is the value that you find there if you substitute little R 170 00:12:37,935 --> 00:12:42,513 equals capital R. I will now show you that we 171 00:12:42,513 --> 00:12:47,402 can, using Ampere's Law, also come very close to 172 00:12:47,402 --> 00:12:53,051 calculating the magnetic field inside what we call 173 00:12:53,051 --> 00:12:55,943 solenoids. Solenoids is like a slinky 174 00:12:55,943 --> 00:13:00,762 current that goes around in a spiral, one loop after another. 175 00:13:00,762 --> 00:13:05,741 I want to remind you that if we had a loop, a nice current loop 176 00:13:05,741 --> 00:13:10,56 coming out of the blackboard here, and the current going into 177 00:13:10,56 --> 00:13:15,058 the blackboard so there's a circular wire but I only show 178 00:13:15,058 --> 00:13:19,154 you the cross-section. I want to remind you that the 179 00:13:19,154 --> 00:13:23,09 magnetic field as we discussed last 180 00:13:23,09 --> 00:13:28,069 time, would be clockwise here, would be counterclockwise here. 181 00:13:28,069 --> 00:13:31,416 In the middle, remember, it was like this. 182 00:13:31,416 --> 00:13:34,191 And then in-between it was like so. 183 00:13:34,191 --> 00:13:38,681 That was sort of the magnetic field configuration in the 184 00:13:38,681 --> 00:13:43,252 vicinity of a loop through which we have a current going. 185 00:13:43,252 --> 00:13:47,007 But now imagine that you put another loop here, 186 00:13:47,007 --> 00:13:51,578 current again coming out of the blackboard going into the 187 00:13:51,578 --> 00:13:56,721 blackboard, and another one, and so on, several. 188 00:13:56,721 --> 00:14:01,811 What do you think is going to happen with these magnetic field 189 00:14:01,811 --> 00:14:06,233 lines which now diverge? They're going to be sucked in 190 00:14:06,233 --> 00:14:09,154 here. This loop also wants the field 191 00:14:09,154 --> 00:14:12,909 lines to come through its circle, so to speak, 192 00:14:12,909 --> 00:14:16,831 and this one too, and so you're beginning to get 193 00:14:16,831 --> 00:14:22,004 a near-constant magnetic field and the more tightly these loops 194 00:14:22,004 --> 00:14:26,76 are wound, the more accurately will your magnetic field be 195 00:14:26,76 --> 00:14:31,267 approximately constant, and I have some 196 00:14:31,267 --> 00:14:35,727 transparencies which will show that in more detail. 197 00:14:35,727 --> 00:14:38,938 Here we have a figure from your book. 198 00:14:38,938 --> 00:14:41,704 You see five windings, a spiral. 199 00:14:41,704 --> 00:14:46,075 If you look from the left, the current is going in 200 00:14:46,075 --> 00:14:50,357 clockwise direction, and so the magnetic field is 201 00:14:50,357 --> 00:14:53,747 going from this side to that direction. 202 00:14:53,747 --> 00:14:58,743 And when you look here you see that the magnetic field is 203 00:14:58,743 --> 00:15:02,474 approximately constant inside, 204 00:15:02,474 --> 00:15:06,789 and outside these current loops, outside the solenoids -- 205 00:15:06,789 --> 00:15:11,182 we call them solenoids -- magnetic field is extremely low. 206 00:15:11,182 --> 00:15:14,959 And if you start winding these loops very tightly, 207 00:15:14,959 --> 00:15:18,349 then you get a configuration looks like this. 208 00:15:18,349 --> 00:15:22,588 You get an almost perfect constant magnetic field inside 209 00:15:22,588 --> 00:15:27,212 the solenoids and the magnetic field outside the solenoids is 210 00:15:27,212 --> 00:15:30,141 extremely weak. And now I would like to 211 00:15:30,141 --> 00:15:35,664 calculate with you using Ampere's Law 212 00:15:35,664 --> 00:15:43,123 what that magnetic field inside such a solenoid would be. 213 00:15:43,123 --> 00:15:48,052 And we have to make a few assumptions. 214 00:15:48,052 --> 00:15:55,245 Let this be my solenoid, and the length of the solenoid 215 00:15:55,245 --> 00:16:00,706 is capital L. A current I is going through 216 00:16:00,706 --> 00:16:05,838 like so. I, and I assume that if I look 217 00:16:05,838 --> 00:16:10,944 from the left side that the windings are wound clockwise, 218 00:16:10,944 --> 00:16:16,322 so I know that the magnetic field is then in this direction. 219 00:16:16,322 --> 00:16:21,428 I make the assumption that the magnetic field outside the 220 00:16:21,428 --> 00:16:26,806 solenoid is approximately zero. I will show you later with a 221 00:16:26,806 --> 00:16:31,638 demonstration that that's a pretty good approximation. 222 00:16:31,638 --> 00:16:37,886 And so the question now is, what is the magnetic field 223 00:16:37,886 --> 00:16:41,407 there. And I assume I have N loops, 224 00:16:41,407 --> 00:16:46,896 N windings, capital N. So now I have to choose a path. 225 00:16:46,896 --> 00:16:51,556 I have to apply Ampere's Law. I choose a pass, 226 00:16:51,556 --> 00:16:56,838 and you may be surprised the path I'm going to take. 227 00:16:56,838 --> 00:17:01,291 This is the path I choose. It's a rectangle. 228 00:17:01,291 --> 00:17:08,022 And the length of this side inside the solenoid is L. 229 00:17:08,022 --> 00:17:11,647 And I think of this as four different passes. 230 00:17:11,647 --> 00:17:14,613 Number one, number two, number three, 231 00:17:14,613 --> 00:17:18,484 and number four. Let's first look at number two. 232 00:17:18,484 --> 00:17:22,85 We have assumed that the magnetic field is practically 233 00:17:22,85 --> 00:17:27,463 zero, so clearly if you go to integrals, you'd go around, 234 00:17:27,463 --> 00:17:30,676 then the contribution here must be zero. 235 00:17:30,676 --> 00:17:35,536 If the magnetic field is zero, then the integral B dot DL is 236 00:17:35,536 --> 00:17:40,321 zero, so that's easy. But if you look at one and 237 00:17:40,321 --> 00:17:44,449 three, there is no magnetic field, very small magnetic field 238 00:17:44,449 --> 00:17:47,178 outside. The magnetic field inside is in 239 00:17:47,178 --> 00:17:50,327 this direction. But DL is like this if I march 240 00:17:50,327 --> 00:17:54,806 like this, and B is like this so there's ninety degree angles and 241 00:17:54,806 --> 00:17:58,514 so the dot product is zero. And so the only paths that 242 00:17:58,514 --> 00:18:02,713 contribute to my closed-loop integral of Ampere's Law is only 243 00:18:02,713 --> 00:18:06,701 path four, and that tells me then that B times little L -- 244 00:18:06,701 --> 00:18:11,35 because B is constant, I have assumed that it is 245 00:18:11,35 --> 00:18:15,409 constant, and I integrate it over a length little L. 246 00:18:15,409 --> 00:18:18,035 Now I have to agree on my surface. 247 00:18:18,035 --> 00:18:22,571 What surface am I going to choose to attach to that closed 248 00:18:22,571 --> 00:18:25,038 loop? Well, why not using a flat 249 00:18:25,038 --> 00:18:27,585 surface just like the blackboard? 250 00:18:27,585 --> 00:18:32,041 Now, I have to calculate the current that penetrates that 251 00:18:32,041 --> 00:18:34,826 surface. The current that penetrates 252 00:18:34,826 --> 00:18:38,169 that surface, I have to know how many times 253 00:18:38,169 --> 00:18:42,785 this winding pokes through that surface. 254 00:18:42,785 --> 00:18:47,161 If the length of my rectangle is little L and is if the length 255 00:18:47,161 --> 00:18:51,393 of the solenoid is capital L, and if there are N windings on 256 00:18:51,393 --> 00:18:55,698 capital L, this is the number of times that the current pokes 257 00:18:55,698 --> 00:18:58,424 through that surface, uniquely defined. 258 00:18:58,424 --> 00:19:01,867 I have a surface now. There is no such thing as I 259 00:19:01,867 --> 00:19:04,163 enclosed. There is I penetrating, 260 00:19:04,163 --> 00:19:06,889 through that surface. It's a soap film, 261 00:19:06,889 --> 00:19:11,265 and I poke straight through it, and I do it so many times that 262 00:19:11,265 --> 00:19:14,129 I poke through it, 263 00:19:14,129 --> 00:19:18,356 and then I have to multiply this by mu zero, 264 00:19:18,356 --> 00:19:23,074 and then I have my I, but each time that it pokes 265 00:19:23,074 --> 00:19:28,578 through I have current I. And so what you see now is that 266 00:19:28,578 --> 00:19:33,001 B equals mu zero times I times N divided by L, 267 00:19:33,001 --> 00:19:38,801 and so that is our prediction for approximating the constant 268 00:19:38,801 --> 00:19:44,207 magnetic field inside a solenoid, and this actually is a 269 00:19:44,207 --> 00:19:49,514 very good approximation as long as L, 270 00:19:49,514 --> 00:19:55,719 the length of the solenoid, is substantially larger than 271 00:19:55,719 --> 00:20:02,149 the radius of the solenoid. The radius would be the radius 272 00:20:02,149 --> 00:20:06,662 of these loops. I'll work out a numerical 273 00:20:06,662 --> 00:20:12,416 example which is aimed at a demonstration that comes 274 00:20:12,416 --> 00:20:16,815 shortly. We have here a solenoid whereby 275 00:20:16,815 --> 00:20:20,659 N is about twenty-eight hundred and 276 00:20:20,659 --> 00:20:24,533 L is about sixty centimeters, that is oh point six meters, 277 00:20:24,533 --> 00:20:28,475 and I'm going to run through there a current which I really 278 00:20:28,475 --> 00:20:32,349 don't know yet but is going to be close to four and a half 279 00:20:32,349 --> 00:20:35,679 amperes, we will see when we do the demonstration. 280 00:20:35,679 --> 00:20:39,825 And so I can calculate now what the magnetic field is going to 281 00:20:39,825 --> 00:20:42,067 be. So the magnetic field strength 282 00:20:42,067 --> 00:20:45,534 is going to be four pi times ten to the minus seven, 283 00:20:45,534 --> 00:20:49,679 because that's what mu zero is, and then I have to multiply it 284 00:20:49,679 --> 00:20:52,73 by twenty-eight hundred. 285 00:20:52,73 --> 00:20:56,356 I have to multiply it, divide it by point six, 286 00:20:56,356 --> 00:21:00,707 and then I multiply it by the current, four point five, 287 00:21:00,707 --> 00:21:05,058 and when I do that I find about point oh two six Tesla. 288 00:21:05,058 --> 00:21:09,247 Point oh two six Tesla, that is about two hundred and 289 00:21:09,247 --> 00:21:12,631 sixty Gauss. And when we do the experiment, 290 00:21:12,631 --> 00:21:17,385 the current will be a little different but you will see that 291 00:21:17,385 --> 00:21:21,333 indeed the field will be very close 292 00:21:21,333 --> 00:21:25,516 to two hundred and sixty Gauss. Why is it that the magnetic 293 00:21:25,516 --> 00:21:28,978 field is not proportional to the number of loops, 294 00:21:28,978 --> 00:21:32,945 but proportional to the number of loops per unit length? 295 00:21:32,945 --> 00:21:36,119 You may say well, if I have one loop I have a 296 00:21:36,119 --> 00:21:39,725 certain magnetic field, two loops I have twice that 297 00:21:39,725 --> 00:21:43,043 magnetic field, ten loops I have ten times that 298 00:21:43,043 --> 00:21:46,217 magnetic field. Well, imagine that we start a 299 00:21:46,217 --> 00:21:50,04 solenoid [inaudible] seven. And so here is [inaudible] 300 00:21:50,04 --> 00:21:53,694 seven, and here is that solenoid. 301 00:21:53,694 --> 00:21:55,69 There it goes, all the way, 302 00:21:55,69 --> 00:21:58,683 all the way, thousands and thousands and 303 00:21:58,683 --> 00:22:02,828 thousands and thousands of loops, and we end up here in 304 00:22:02,828 --> 00:22:05,975 twenty-six one hundred. Look at this loop. 305 00:22:05,975 --> 00:22:10,196 Think of it at the first loop. Creates a magnetic field. 306 00:22:10,196 --> 00:22:13,266 What is the shape of that magnetic field? 307 00:22:13,266 --> 00:22:17,564 Well, it is a current loop and as we discussed last time, 308 00:22:17,564 --> 00:22:21,939 the magnetic field that one loop produces is like a dipole 309 00:22:21,939 --> 00:22:25,526 field. So do you really think that 310 00:22:25,526 --> 00:22:29,466 here in twenty-six one hundred we can sense the magnetic field 311 00:22:29,466 --> 00:22:32,243 that is produced by this one dinky toy loop? 312 00:22:32,243 --> 00:22:35,086 Practically nothing! It falls off so rapidly, 313 00:22:35,086 --> 00:22:38,315 the magnetic field, that we don't notice it- notice 314 00:22:38,315 --> 00:22:40,576 it here. So it's immediately obvious 315 00:22:40,576 --> 00:22:44,452 that the magnetic field is not proportional to how many loops 316 00:22:44,452 --> 00:22:45,808 you have. If, however, 317 00:22:45,808 --> 00:22:48,651 you put all those loops on top of each other, 318 00:22:48,651 --> 00:22:51,622 then of course you can add the magnetic fields. 319 00:22:51,622 --> 00:22:55,046 And so it is natural that you get 320 00:22:55,046 --> 00:22:59,275 how many windings you have pre unit length. 321 00:22:59,275 --> 00:23:05,619 So now I want to first show you the magnetic field configuration 322 00:23:05,619 --> 00:23:10,05 of a very loosely wound loop, seven windings, 323 00:23:10,05 --> 00:23:14,381 and I will do that by sprinkling magnetites, 324 00:23:14,381 --> 00:23:17,502 this iron file, in the vicinity. 325 00:23:17,502 --> 00:23:22,94 We've done this before for other current configuration. 326 00:23:22,94 --> 00:23:29,688 Now we'll do it for this solenoid with seven windings, 327 00:23:29,688 --> 00:23:33,962 and I'm going to run a few hundred amperes through there, 328 00:23:33,962 --> 00:23:36,634 have to first get this car battery . 329 00:23:36,634 --> 00:23:39,61 All right. And so we put some iron files 330 00:23:39,61 --> 00:23:44,038 on here and what I want you to see now is that the magnetic 331 00:23:44,038 --> 00:23:47,243 field inside, even though it's very loosely 332 00:23:47,243 --> 00:23:51,747 wound, begins to look nicely uniform and that there's almost 333 00:23:51,747 --> 00:23:54,724 no electric- er, magnetic field outside. 334 00:23:54,724 --> 00:23:59,075 Look at this, isn't that wonderful? 335 00:23:59,075 --> 00:24:02,805 Isn't that incredible? You see how these iron files 336 00:24:02,805 --> 00:24:07,206 line themselves up very nicely horizontally inside the loops 337 00:24:07,206 --> 00:24:10,787 and when you look outside the loop here or there, 338 00:24:10,787 --> 00:24:14,443 where we assume the magnetic field was about zero, 339 00:24:14,443 --> 00:24:18,471 you don't see the iron file being where we ended in any 340 00:24:18,471 --> 00:24:21,754 preferred direction, which indicates that the 341 00:24:21,754 --> 00:24:25,857 magnetic field is very low. Now, I want to show you what 342 00:24:25,857 --> 00:24:30,482 magnetic field we can get with this baby, which is exactly what 343 00:24:30,482 --> 00:24:34,014 I had here on the blackboards. 344 00:24:34,014 --> 00:24:38,661 It has twenty-eight hundred windings, and we're going to run 345 00:24:38,661 --> 00:24:43,15 a current which is something like four point five amperes, 346 00:24:43,15 --> 00:24:46,773 but I'm going to tell you what that current is, 347 00:24:46,773 --> 00:24:51,657 because I have a current meter there for you and I also have a- 348 00:24:51,657 --> 00:24:55,122 a meter which indicates the magnetic fields. 349 00:24:55,122 --> 00:24:59,69 The lower one is the current meter, and the maximum current 350 00:24:59,69 --> 00:25:04,259 that you see there at the three would 351 00:25:04,259 --> 00:25:07,486 be six amperes. And the upper one is calibrated 352 00:25:07,486 --> 00:25:11,625 in such a way that if it is full scale, you would have three 353 00:25:11,625 --> 00:25:13,59 hundred Gauss, so it's three, 354 00:25:13,59 --> 00:25:17,308 it's three hundred Gauss. And I can -- I have a probe, 355 00:25:17,308 --> 00:25:21,027 a magnetic probe -- we never discussed how that works. 356 00:25:21,027 --> 00:25:24,745 We call it a Hall probe, and this Hall probe allows me 357 00:25:24,745 --> 00:25:29,095 to measure the magnetic field in the vicinity of this solenoid. 358 00:25:29,095 --> 00:25:32,884 It's even sign sensitive. If the magnetic field is like 359 00:25:32,884 --> 00:25:38,212 this, it would go to the right. If the magnetic field is like 360 00:25:38,212 --> 00:25:41,728 this, it would go to the left. And so this allows us, 361 00:25:41,728 --> 00:25:45,447 then, to be actually quite quantitative and evaluate the 362 00:25:45,447 --> 00:25:48,693 magnetic field near the opening of the solenoids. 363 00:25:48,693 --> 00:25:52,547 Then we can go in there and we can also probe the outside. 364 00:25:52,547 --> 00:25:55,657 So I'm running now a current. Let's look at it, 365 00:25:55,657 --> 00:25:59,106 that's the bottom meter. So that is about four point 366 00:25:59,106 --> 00:26:01,878 eight amperes. I assumed it was four point 367 00:26:01,878 --> 00:26:03,636 five. It's a little higher. 368 00:26:03,636 --> 00:26:07,355 And here comes this probe, and I'm now about a foot away 369 00:26:07,355 --> 00:26:10,032 from the entrance, 370 00:26:10,032 --> 00:26:13,603 and you see nothing. And I come closer to the 371 00:26:13,603 --> 00:26:17,336 entrance and the magnetic field begins to show. 372 00:26:17,336 --> 00:26:21,88 Nowhere nearly constant yet. I'm now entering one hundred 373 00:26:21,88 --> 00:26:23,99 Gauss. I'm going in deeper. 374 00:26:23,99 --> 00:26:26,425 Two hundred Gauss. Even deeper. 375 00:26:26,425 --> 00:26:30,726 And deeper, and now I have about two hundred and forty 376 00:26:30,726 --> 00:26:33,647 Gauss and notice, as I go in farther, 377 00:26:33,647 --> 00:26:38,84 it doesn't increase. It's more or less constant. 378 00:26:38,84 --> 00:26:41,45 Amazing, that it's more or less constant. 379 00:26:41,45 --> 00:26:45,038 And when I come out here, I move it back and forth about 380 00:26:45,038 --> 00:26:48,038 twenty centimeters. If I came in from the other 381 00:26:48,038 --> 00:26:51,235 side, you would simply see a reversal in the sign, 382 00:26:51,235 --> 00:26:54,888 which is not so interesting, so you see two hundred forty 383 00:26:54,888 --> 00:26:58,215 Gauss with the other direction because this probe is 384 00:26:58,215 --> 00:27:01,216 sign-sensitive. I can now also show you that if 385 00:27:01,216 --> 00:27:04,738 I come on the outside of the solenoid, you see nothing. 386 00:27:04,738 --> 00:27:08,652 So indeed, our assumption that the magnetic field is very low 387 00:27:08,652 --> 00:27:14,12 outside a tightly wound solenoid was a very good 388 00:27:14,12 --> 00:27:16,303 assumption. Very well. 389 00:27:16,303 --> 00:27:21,398 You've been asked, and the deadline is Friday four 390 00:27:21,398 --> 00:27:24,621 p. ., to explain the behavior of 391 00:27:24,621 --> 00:27:30,028 the Kelvin water dropper. And I decided to give you a 392 00:27:30,028 --> 00:27:35,747 little bit of help on that. Most of you may already have 393 00:27:35,747 --> 00:27:40,426 figured it out, but those who haven't probably 394 00:27:40,426 --> 00:27:46,727 won't figure it out between now and Friday anyhow, 395 00:27:46,727 --> 00:27:51,083 so I might as well tell you. That water dropper, 396 00:27:51,083 --> 00:27:56,088 called the Kelvin water dropper, is an amazing battery. 397 00:27:56,088 --> 00:28:00,259 We've seen it before. We know what it's doing, 398 00:28:00,259 --> 00:28:05,727 but I will go over that again. We have here buckets A and B. 399 00:28:05,727 --> 00:28:10,083 Water comes down from above, water runs through. 400 00:28:10,083 --> 00:28:13,419 You see the water there, it runs out. 401 00:28:13,419 --> 00:28:17,682 And we collect these water drops 402 00:28:17,682 --> 00:28:20,303 here in bucket D, it's a conductor, 403 00:28:20,303 --> 00:28:24,928 and this water is collected in bucket C, is also a conductor, 404 00:28:24,928 --> 00:28:27,779 and the paint can A is connected to C. 405 00:28:27,779 --> 00:28:30,631 That's crucial. And the paint can B is 406 00:28:30,631 --> 00:28:34,177 connected with D. And here there are two bowls, 407 00:28:34,177 --> 00:28:36,643 which I can bring close together. 408 00:28:36,643 --> 00:28:39,957 I run water, and after a while I see a spark 409 00:28:39,957 --> 00:28:42,732 here. I can even see a spark when the 410 00:28:42,732 --> 00:28:47,356 distance is something like six millimeters, 411 00:28:47,356 --> 00:28:52,721 which would be about potential difference of about twenty 412 00:28:52,721 --> 00:28:55,307 kilovolts. How does it work? 413 00:28:55,307 --> 00:29:00,864 Well, water has a pH of seven. And that means one in ten to 414 00:29:00,864 --> 00:29:05,653 the seven molecules is ionized. So I have OH minus, 415 00:29:05,653 --> 00:29:10,251 and I have H plus. And the- Those are going to be 416 00:29:10,251 --> 00:29:14,85 the current carriers. The ions are doing the work 417 00:29:14,85 --> 00:29:20,98 here, are doing the job. Let us make an enlargement 418 00:29:20,98 --> 00:29:24,104 here of can A. And can A, let us assume that 419 00:29:24,104 --> 00:29:27,59 purely by chance, it has a little bit of positive 420 00:29:27,59 --> 00:29:30,06 charge on it. It could be negative, 421 00:29:30,06 --> 00:29:33,11 but I'll just assume it's positive for now. 422 00:29:33,11 --> 00:29:36,088 In either case it will work, you will see. 423 00:29:36,088 --> 00:29:39,284 Just by chance, like you have a little bit of 424 00:29:39,284 --> 00:29:42,262 net charge. You're not completely neutral. 425 00:29:42,262 --> 00:29:46,402 And so this can has a little bit of positive extra charge. 426 00:29:46,402 --> 00:29:50,251 Now here is the drop from the spout. 427 00:29:50,251 --> 00:29:53,06 What's going to happen? Through induction, 428 00:29:53,06 --> 00:29:56,623 through polarization, you get a little bit of excess- 429 00:29:56,623 --> 00:30:00,87 excess negative charge here and a little bit of excess positive 430 00:30:00,87 --> 00:30:04,432 there, because the positive repels each other and the 431 00:30:04,432 --> 00:30:08,474 negative is being attracted. So the H plus goes a little bit 432 00:30:08,474 --> 00:30:11,42 up and the OH minus comes a little bit down. 433 00:30:11,42 --> 00:30:14,708 But now the drop breaks, and there goes the drop. 434 00:30:14,708 --> 00:30:18,887 So it's a little bit negative. So now a little bit of negative 435 00:30:18,887 --> 00:30:23,134 drops come down and so this becomes negative. 436 00:30:23,134 --> 00:30:26,678 But this is connected with B, so B becomes negative. 437 00:30:26,678 --> 00:30:30,707 But what do you think is going to happen now with the drops 438 00:30:30,707 --> 00:30:33,764 that fall through B? They are going to become 439 00:30:33,764 --> 00:30:37,446 positive, because if B is negative then of course this 440 00:30:37,446 --> 00:30:40,572 will be reversed, the bottom will be positive, 441 00:30:40,572 --> 00:30:44,462 the top will be negative, and so those drops now that are 442 00:30:44,462 --> 00:30:47,658 going to fall through are going to be positive. 443 00:30:47,658 --> 00:30:50,993 So C becomes positive. But C is connected with A, 444 00:30:50,993 --> 00:30:56,114 so A becomes more positive, and so A can do even a better 445 00:30:56,114 --> 00:31:00,173 job now on these water drops, and polarize them even more, 446 00:31:00,173 --> 00:31:02,452 and so you get a runaway process. 447 00:31:02,452 --> 00:31:06,368 And the whole system feeds on itself until the potential 448 00:31:06,368 --> 00:31:10,356 difference here becomes so high that you exceed the three 449 00:31:10,356 --> 00:31:14,272 million volts per meter, and there you get the breakdown 450 00:31:14,272 --> 00:31:17,334 and you see a spark. Now, you can think of a 451 00:31:17,334 --> 00:31:21,464 continuous stream of water as a stream of individual drops, 452 00:31:21,464 --> 00:31:25,096 so it also works if you just have a 453 00:31:25,096 --> 00:31:28,064 regular stream of water going down. 454 00:31:28,064 --> 00:31:32,78 Who is doing the work here? Someone has to do the work. 455 00:31:32,78 --> 00:31:36,884 You have a battery. The battery's being charged, 456 00:31:36,884 --> 00:31:40,202 and then it is discharged to the spark. 457 00:31:40,202 --> 00:31:42,909 Who is doing the work? Any idea? 458 00:31:42,909 --> 00:31:45,791 Have you thought about that? Yeah? 459 00:31:45,791 --> 00:31:47,363 Gravity. Very good. 460 00:31:47,363 --> 00:31:50,419 It's gravity that is doing the work. 461 00:31:50,419 --> 00:31:55,745 We can see that very easily by identifying the current that is 462 00:31:55,745 --> 00:32:02,174 flowing and the electric field. How is the current flowing? 463 00:32:02,174 --> 00:32:06,451 If negative charge is going down, would we all agree that 464 00:32:06,451 --> 00:32:10,346 the current is going up? If positive charge is going 465 00:32:10,346 --> 00:32:14,012 down, do we agree that the current is going down? 466 00:32:14,012 --> 00:32:18,136 This side of the spout, here, will be slightly positive 467 00:32:18,136 --> 00:32:22,413 and this is slightly negative, because the H plus is more 468 00:32:22,413 --> 00:32:26,384 abundant here than there, and so we're going to get a 469 00:32:26,384 --> 00:32:29,745 current through the water, in this direction. 470 00:32:29,745 --> 00:32:33,622 Current has a reasonable conductivity, 471 00:32:33,622 --> 00:32:37,289 because it's ionized one out of ten to the seven molecules, 472 00:32:37,289 --> 00:32:40,198 and so once in a while if you see a spark here, 473 00:32:40,198 --> 00:32:43,677 then you get a current there, but that's intermittent of 474 00:32:43,677 --> 00:32:46,016 course. How about the electric fields? 475 00:32:46,016 --> 00:32:49,242 Well, electric fields we know go from plus to minus, 476 00:32:49,242 --> 00:32:52,087 so that's easy. We can put the electric fields 477 00:32:52,087 --> 00:32:55,123 just in like that. Electric field must here be in 478 00:32:55,123 --> 00:32:57,969 this direction. Electric fields here goes from 479 00:32:57,969 --> 00:33:00,119 plus to minus. C is to plus charge, 480 00:33:00,119 --> 00:33:04,546 B is minus charge, and so the electric field is in 481 00:33:04,546 --> 00:33:07,766 this direction. Electric field is from plus to 482 00:33:07,766 --> 00:33:09,125 minus. This is plus, 483 00:33:09,125 --> 00:33:12,059 this is minus, so the electric field is in 484 00:33:12,059 --> 00:33:15,279 this direction. Electric field is from plus to 485 00:33:15,279 --> 00:33:17,355 minus. The can A was positive, 486 00:33:17,355 --> 00:33:20,074 remember? So the electric field is from 487 00:33:20,074 --> 00:33:23,079 plus to minus. So that's the electric field 488 00:33:23,079 --> 00:33:26,228 configuration. But now look what's happening. 489 00:33:26,228 --> 00:33:29,663 Here, the E field and the current are in the same 490 00:33:29,663 --> 00:33:31,237 direction. That's fine. 491 00:33:31,237 --> 00:33:34,958 Here the E field and the current are also in the same 492 00:33:34,958 --> 00:33:38,173 direction. That's great, 493 00:33:38,173 --> 00:33:40,799 but now look at these poor negative ions. 494 00:33:40,799 --> 00:33:44,607 These negative ions don't want to go in the direction of E. 495 00:33:44,607 --> 00:33:48,153 Negative charge wants to go against the direction of E. 496 00:33:48,153 --> 00:33:50,845 But gravity says, "Sorry, you can't do it. 497 00:33:50,845 --> 00:33:53,996 I force you down. And so these negative drops are 498 00:33:53,996 --> 00:33:57,805 forced by gravity to go down. Look at this positive charge. 499 00:33:57,805 --> 00:34:01,284 These poor water drops which are positively charged go 500 00:34:01,284 --> 00:34:04,436 against the electric field. They don't want that. 501 00:34:04,436 --> 00:34:07,981 Positive charges want to go with the 502 00:34:07,981 --> 00:34:10,014 electric field. Gravity says, 503 00:34:10,014 --> 00:34:12,772 "Sorry, it's too bad. I force you down. 504 00:34:12,772 --> 00:34:16,038 And so gravity is doing the work, so to speak, 505 00:34:16,038 --> 00:34:18,287 against the will of the charges. 506 00:34:18,287 --> 00:34:22,279 And then the battery charges up and charges up until the 507 00:34:22,279 --> 00:34:26,851 potential difference becomes so high there that you see a spark, 508 00:34:26,851 --> 00:34:30,916 and you deal with potential differences of something like 509 00:34:30,916 --> 00:34:33,601 twenty kilovolts. Remember last time, 510 00:34:33,601 --> 00:34:37,811 and you will see that again today, 511 00:34:37,811 --> 00:34:41,662 that as the water goes through and as the system charges up, 512 00:34:41,662 --> 00:34:45,644 that you begin to see that the water which starts running like 513 00:34:45,644 --> 00:34:48,059 so, begins to spread out. It fans out. 514 00:34:48,059 --> 00:34:52,106 You can hear it by changing the sound, but you can also see it, 515 00:34:52,106 --> 00:34:54,456 and I'll make you see it again today. 516 00:34:54,456 --> 00:34:56,806 Why is that? Well, that's immediately 517 00:34:56,806 --> 00:34:58,96 obvious. If this can is positively 518 00:34:58,96 --> 00:35:01,963 charged but if the water is negatively charged, 519 00:35:01,963 --> 00:35:05,618 the negative charge wants to go through the positive can, 520 00:35:05,618 --> 00:35:09,013 and so it spreads out. So it's clear that by the time 521 00:35:09,013 --> 00:35:12,603 that you reach almost a spark, 522 00:35:12,603 --> 00:35:17,537 that that water will spread out quite substantially and you will 523 00:35:17,537 --> 00:35:20,122 see that. And then when there is a 524 00:35:20,122 --> 00:35:24,195 discharge, it will start running again narrow stream, 525 00:35:24,195 --> 00:35:27,72 and then slowly in time the water will spread. 526 00:35:27,72 --> 00:35:32,185 And so now I will do a series of demonstrations which will 527 00:35:32,185 --> 00:35:36,179 support what we know and what we perhaps don't know. 528 00:35:36,179 --> 00:35:40,722 Let's first give a little bit of light here, 529 00:35:40,722 --> 00:35:45,608 because we will need that, and then I'm going to make it 530 00:35:45,608 --> 00:35:49,073 completely dark, so that you get maximum 531 00:35:49,073 --> 00:35:53,87 pleasure for your money. And I will first show you here 532 00:35:53,87 --> 00:35:59,467 the- the gap those two bowls and this time we have a real treat, 533 00:35:59,467 --> 00:36:03,82 which we owe to Marcos, who is standing behind the 534 00:36:03,82 --> 00:36:08,35 instrument very modestly. This time we have a gauge, 535 00:36:08,35 --> 00:36:13,325 a meter, which measures the electric fields very close to 536 00:36:13,325 --> 00:36:17,943 can A, and the reason why that is nice 537 00:36:17,943 --> 00:36:23,27 is that as this system charges up, we just don't have to wait 538 00:36:23,27 --> 00:36:28,064 now just until we see the spark, but we can look at the 539 00:36:28,064 --> 00:36:33,48 galvanometer there and slowly see it being charged up and then 540 00:36:33,48 --> 00:36:38,275 we get a spark and then it discharges, so you get a lot 541 00:36:38,275 --> 00:36:42,448 more for your money. So I propose that the first 542 00:36:42,448 --> 00:36:47,952 thing we do is what we did last time, that we simply let it run 543 00:36:47,952 --> 00:36:54,87 and see whether we get a spark. Uh, there's always air bubbles 544 00:36:54,87 --> 00:36:58,474 in the system which I have to get out. 545 00:36:58,474 --> 00:37:03,248 OK, I think I get that. OK, let's just be patient. 546 00:37:03,248 --> 00:37:07,729 Ah, it starts already. Look at the- look at the 547 00:37:07,729 --> 00:37:08,995 e-field. Bang! 548 00:37:08,995 --> 00:37:12,892 First spark. Can you see the spark on the 549 00:37:12,892 --> 00:37:15,23 screen? Look at it again. 550 00:37:15,23 --> 00:37:19,516 There's a spark. And at the same time you see 551 00:37:19,516 --> 00:37:24,271 how the electric field goes away, 552 00:37:24,271 --> 00:37:27,69 charges up, bang. Charges up, bang. 553 00:37:27,69 --> 00:37:33,422 So it cha- it starts the whole system charged because of a 554 00:37:33,422 --> 00:37:39,255 random positive or negative charge that would be present on 555 00:37:39,255 --> 00:37:43,981 one of the cans. What I want to do now is I want 556 00:37:43,981 --> 00:37:49,814 to increase the gap between the two bowls, and I make it so 557 00:37:49,814 --> 00:37:55,547 large that you will never achieve a magnetic- 558 00:37:55,547 --> 00:37:59,502 an electric field there of three million volts per meter. 559 00:37:59,502 --> 00:38:03,811 But somewhere else on the unit, it has lots of sharp edges and 560 00:38:03,811 --> 00:38:06,637 sharp points, somewhere else the electric 561 00:38:06,637 --> 00:38:10,875 field will reach the breakdown voltage and so the system will 562 00:38:10,875 --> 00:38:14,407 go into dis- into discharge, into corona discharge. 563 00:38:14,407 --> 00:38:18,08 You will never see sparks but it goes into discharge. 564 00:38:18,08 --> 00:38:22,106 And you can see that because now, I will open the gap now. 565 00:38:22,106 --> 00:38:27,28 If you now look at the electric field it will reach a maximum 566 00:38:27,28 --> 00:38:30,267 value and now it goes into discharge, you see. 567 00:38:30,267 --> 00:38:33,984 It begins to sort of sputter a little bit back and forth, 568 00:38:33,984 --> 00:38:37,104 so now there is no longer the spark on the bowl, 569 00:38:37,104 --> 00:38:39,958 so you don't see anything between the bowls, 570 00:38:39,958 --> 00:38:42,878 but it is somewhere else. I don't know where, 571 00:38:42,878 --> 00:38:46,197 where there is a continuous stream now of charging, 572 00:38:46,197 --> 00:38:49,184 leaving the system, and so it's discharging to 573 00:38:49,184 --> 00:38:51,64 corona discharge. And so in this mode, 574 00:38:51,64 --> 00:38:54,693 you expect the water to be spread all the time. 575 00:38:54,693 --> 00:39:00,239 And I will show that to you by switching now to the water. 576 00:39:00,239 --> 00:39:03,869 Maybe Marcos, you can improve on the- on the, 577 00:39:03,869 --> 00:39:06,839 on the lights. I could turn this off, 578 00:39:06,839 --> 00:39:09,397 maybe then you'll see it better. 579 00:39:09,397 --> 00:39:14,347 But you see that the water is spread and I will now bring the 580 00:39:14,347 --> 00:39:19,462 two bowls closer together -- ah, you also want to see of course 581 00:39:19,462 --> 00:39:22,844 the electric fields, to see the discharge. 582 00:39:22,844 --> 00:39:28,949 I bring them closer together, stopping the corona discharge. 583 00:39:28,949 --> 00:39:32,282 There's a spark. And now watch the water. 584 00:39:32,282 --> 00:39:36,948 See, the water is now just not interesting, and there it 585 00:39:36,948 --> 00:39:39,614 spreads. I'll turn the light off. 586 00:39:39,614 --> 00:39:43,446 You look at the water. And slowly the system is 587 00:39:43,446 --> 00:39:45,946 charging up. You see the water? 588 00:39:45,946 --> 00:39:48,945 Bingo. You can even tell by the water 589 00:39:48,945 --> 00:39:51,361 when it sparks. There it goes. 590 00:39:51,361 --> 00:39:54,361 Now I want to do something real mean. 591 00:39:54,361 --> 00:39:59,11 What I want to do now is to raise 592 00:39:59,11 --> 00:40:05,002 the spout so high that A can not reach out all the way to the 593 00:40:05,002 --> 00:40:07,359 spout. It's too far away, 594 00:40:07,359 --> 00:40:13,055 and can not polarize the water. So the poor battery can not 595 00:40:13,055 --> 00:40:16,493 start. That's a pretty mean thing to 596 00:40:16,493 --> 00:40:20,224 do to a battery. But on the other hand, 597 00:40:20,224 --> 00:40:24,546 I'm not all bad. What I can do is I can start 598 00:40:24,546 --> 00:40:29,161 the system, I can help the system. 599 00:40:29,161 --> 00:40:33,652 I use my extrophorus disk and I'm going to hold my extrophorus 600 00:40:33,652 --> 00:40:37,7 disk very close to one spout, temporarily allowing it to 601 00:40:37,7 --> 00:40:42,264 polarize the water and once it starts, chances are that it will 602 00:40:42,264 --> 00:40:45,061 feed on itself and go into the runaway. 603 00:40:45,061 --> 00:40:48,963 It's not very predictable, but I will make an attempt. 604 00:40:48,963 --> 00:40:53,527 So the first thing that I will have to do is maybe you can zero 605 00:40:53,527 --> 00:40:55,588 the E field. Yeah, thank you. 606 00:40:55,588 --> 00:40:59,195 So the first thing I want to do is 607 00:40:59,195 --> 00:41:03,037 to make sure that if we start running water now, 608 00:41:03,037 --> 00:41:07,943 that the system doesn't start by itself, because then I can't 609 00:41:07,943 --> 00:41:12,031 make -- then I can't be nice to the system anymore. 610 00:41:12,031 --> 00:41:16,774 So let's just run some water. I hope that Marcos brought it 611 00:41:16,774 --> 00:41:21,271 high enough, and let's see -- and you can really tell by 612 00:41:21,271 --> 00:41:25,277 looking at the Oh, there's the air bubbles in the 613 00:41:25,277 --> 00:41:28,139 system. I have to get rid of the air 614 00:41:28,139 --> 00:41:31,521 bubbles. There we go. 615 00:41:31,521 --> 00:41:34 OK. So look at the electric field 616 00:41:34 --> 00:41:36,866 doing nothing. The system can't start. 617 00:41:36,866 --> 00:41:40,584 A is desperately reaching out through this water, 618 00:41:40,584 --> 00:41:44,457 but it's too far away. It can't polarize it and the 619 00:41:44,457 --> 00:41:48,64 battery can't get going. Ah, ay, ay, it does get going. 620 00:41:48,64 --> 00:41:51,816 Oh, Marcos, we didn't bring it far enough! 621 00:41:51,816 --> 00:41:55,146 You have to bring it higher! Oh, by the way, 622 00:41:55,146 --> 00:41:59,019 this is interesting. Let's see where it actually -- 623 00:41:59,019 --> 00:42:04,837 oh, boy, this is incredible. This is a distance of about 624 00:42:04,837 --> 00:42:07,593 fifty centimeters, and look at it! 625 00:42:07,593 --> 00:42:10,432 That is amazing! The little sucker, 626 00:42:10,432 --> 00:42:14,941 I had never expected that. Let's give it a fair chance. 627 00:42:14,941 --> 00:42:18,615 Let's give it a chance. It's only reasonable. 628 00:42:18,615 --> 00:42:22,54 Goes very slowly now. You can see why it goes so 629 00:42:22,54 --> 00:42:26,381 slowly, because A very far away from the spout. 630 00:42:26,381 --> 00:42:29,638 But boy, and- and you can see the water. 631 00:42:29,638 --> 00:42:32,31 The water is still pretty normal. 632 00:42:32,31 --> 00:42:36,667 Oh, man, it's almost cheating on me! 633 00:42:36,667 --> 00:42:40,139 Uh-oh, uh-oh, we'll have to raise it a little 634 00:42:40,139 --> 00:42:44,399 further, er, aft- but I- I want to give it a chance to, 635 00:42:44,399 --> 00:42:47,713 uh, to spark. Yeah, the two balls are close 636 00:42:47,713 --> 00:42:50,553 enough, so I will probably get there. 637 00:42:50,553 --> 00:42:53,236 Boy, this is almost torture for me. 638 00:42:53,236 --> 00:42:55,603 Aw, look at that, look at that. 639 00:42:55,603 --> 00:42:58,128 I begin to see the water already. 640 00:42:58,128 --> 00:43:01,757 Look at the water, it's already spreading it -- 641 00:43:01,757 --> 00:43:05,15 ah, there it is. Marcos, can you run it even 642 00:43:05,15 --> 00:43:11,605 higher and then we'll see whether we 643 00:43:11,605 --> 00:43:21,019 can actually stop it altogether, bring it a lot higher and then 644 00:43:21,019 --> 00:43:30,737 we will make an attempt to start it with some help from a friend. 645 00:43:30,737 --> 00:43:36,507 You ready? Oh, man, I can hardly -- OK. 646 00:43:36,507 --> 00:43:44,099 Don't tell me that it going to- it 647 00:43:44,099 --> 00:43:49,237 can go to the other direction, of course, because it's a 648 00:43:49,237 --> 00:43:52,787 random choice that it has at the start. 649 00:43:52,787 --> 00:43:58,205 Ah, ah, it's letting me down! Let me see whether I can help 650 00:43:58,205 --> 00:44:02,128 it a little. My electr- electrophorus disk. 651 00:44:02,128 --> 00:44:07,266 I'm going to hold it here. You know why I held it there? 652 00:44:07,266 --> 00:44:12,03 Because I was hoping it would reverse the direction. 653 00:44:12,03 --> 00:44:16,233 It doesn't even want to do that. 654 00:44:16,233 --> 00:44:20,253 It's really recalcitrant today, isn't it? 655 00:44:20,253 --> 00:44:23,168 Hold it here, negative charge. 656 00:44:23,168 --> 00:44:28,695 The reason why you see the sudden change in the electric 657 00:44:28,695 --> 00:44:34,122 field is because of the e-field probe, which senses the 658 00:44:34,122 --> 00:44:39,75 electrophorus disk when I held it near the spout above B. 659 00:44:39,75 --> 00:44:43,569 It has decided, no matter what -- well, 660 00:44:43,569 --> 00:44:47,915 has it really? Ah, ah, ah, ah. 661 00:44:47,915 --> 00:44:51,288 Has it really made any decision? 662 00:44:51,288 --> 00:44:54,553 Ah! It's thinking now what it's 663 00:44:54,553 --> 00:44:56,73 going to do. Oh, man. 664 00:44:56,73 --> 00:45:02,715 Yeah, it's going in the direction that I wanted it to go 665 00:45:02,715 --> 00:45:09,462 because I held negative charge close to B and I know that would 666 00:45:09,462 --> 00:45:14,576 force it into the direction that it's going now. 667 00:45:14,576 --> 00:45:17,623 Oh, man. Yeah. 668 00:45:17,623 --> 00:45:21,021 Well, look, the distance is -- now, what is it, 669 00:45:21,021 --> 00:45:24,788 now, something like eighty, eighty-five centimeters? 670 00:45:24,788 --> 00:45:27,669 The system is desperate, but it's, it's, 671 00:45:27,669 --> 00:45:30,254 it's doing what it's supposed to do. 672 00:45:30,254 --> 00:45:34,02 Physics works again. And we will get a spark because 673 00:45:34,02 --> 00:45:38,009 -- is this close enough? Ah, boy you got a lot for your 674 00:45:38,009 --> 00:45:40,299 money this time. You really did, 675 00:45:40,299 --> 00:45:43,327 didn't you? You saw for one thing that the 676 00:45:43,327 --> 00:45:47,242 system first started up going in one 677 00:45:47,242 --> 00:45:50,788 direction and later in the other because there was a random 678 00:45:50,788 --> 00:45:54,456 charge which changed polarity, which is something that we can 679 00:45:54,456 --> 00:45:57,452 not always control, but by holding this negatively 680 00:45:57,452 --> 00:46:00,631 charged disk close to the spout above B, I forced the 681 00:46:00,631 --> 00:46:04,055 polarization in the way that I wanted it, and that's what 682 00:46:04,055 --> 00:46:06,806 you're seeing now. We've got to give it a fair 683 00:46:06,806 --> 00:46:10,352 chance, and then I'll give you light and then you have four 684 00:46:10,352 --> 00:46:13,042 more minutes left to fill out the evaluation. 685 00:46:13,042 --> 00:46:16,099 But let's at least give this battery a charge now, 686 00:46:16,099 --> 00:46:21,329 to lay its egg. The water, it still doesn't 687 00:46:21,329 --> 00:46:25,466 show much of a sign of spreading, but I expect that 688 00:46:25,466 --> 00:46:30,1 that will happen very shortly because we've seen this now 689 00:46:30,1 --> 00:46:32,831 before. It's slowly increasing the 690 00:46:32,831 --> 00:46:35,065 charge on the cans, A and B. 691 00:46:35,065 --> 00:46:40,03 It's creeping so slowly that if we wait you may never able to 692 00:46:40,03 --> 00:46:45,243 fill out your -- I'll give you a little light so that you can s- 693 00:46:45,243 --> 00:46:51,119 fill out the evaluation and then we can still [inaudible] 694 00:46:51,119 --> 00:46:55,437 and see what happens. So please leave the evaluations 695 00:46:55,437 --> 00:46:59,423 here as you leave, and I will keep that going for 696 00:46:59,423 --> 00:47:03,492 some of you who have the patience to see what will 697 00:47:03,492 --> 47:08 happen.