1 00:00:00 --> 00:00:09,842 2 00:00:09,842 --> 00:00:14,166 Last time I mentioned to you that charge resides at the 3 00:00:14,166 --> 00:00:18,491 surface of solid conductors but that it's not uniformly 4 00:00:18,491 --> 00:00:21,534 distributed. Perhaps you remember that, 5 00:00:21,534 --> 00:00:24,097 unless it happens to be a sphere. 6 00:00:24,097 --> 00:00:26,58 And I want to pursue that today. 7 00:00:26,58 --> 00:00:31,225 If I had a solid conductor which say had this shape and I'm 8 00:00:31,225 --> 00:00:36,11 going to convince you today that right here the surface charge 9 00:00:36,11 --> 00:00:40,035 density will be higher than there. 10 00:00:40,035 --> 00:00:44,666 Because the curvature is stronger than it is here. 11 00:00:44,666 --> 00:00:49,297 And the way I want to approach that is as follows. 12 00:00:49,297 --> 00:00:54,684 Suppose I have here a solid conductor A which has radius R 13 00:00:54,684 --> 00:00:59,788 of A and very very far away, maybe tens of meters away, 14 00:00:59,788 --> 00:01:05,175 I have a solid conductor B with radius R of B and they are 15 00:01:05,175 --> 00:01:08,483 connected through a conducting wire. 16 00:01:08,483 --> 00:01:12,453 That's essential. If they are 17 00:01:12,453 --> 00:01:18,554 connected through a conducting wire, then it's equipotential. 18 00:01:18,554 --> 00:01:21,808 They all have the same potential. 19 00:01:21,808 --> 00:01:26,588 I'm going to charge them up until I get a charge 20 00:01:26,588 --> 00:01:30,554 distribution QA here and I get QB there. 21 00:01:30,554 --> 00:01:36,859 The potential of A is about the same that it would be if B were 22 00:01:36,859 --> 00:01:40,825 not there. Because B is so far away that 23 00:01:40,825 --> 00:01:44,391 if I come with some charge from 24 00:01:44,391 --> 00:01:48,703 infinity in my pocket that the work that I have to do to reach 25 00:01:48,703 --> 00:01:53,015 A per unit charge is independent of whether B is there or not, 26 00:01:53,015 --> 00:01:55,631 because B is far away, tens of meters, 27 00:01:55,631 --> 00:01:58,458 if you can make it a mile if you want to. 28 00:01:58,458 --> 00:02:02,629 And so the potential of A is then the charge on A divided by 29 00:02:02,629 --> 00:02:05,174 four pi epsilon zero the radius of A. 30 00:02:05,174 --> 00:02:08,567 But since it is an equipotential because it's all 31 00:02:08,567 --> 00:02:12,949 conducting, this must be also the potential of 32 00:02:12,949 --> 00:02:17,153 the sphere B, and that is the charge on B 33 00:02:17,153 --> 00:02:21,147 divided by four pi epsilon zero R of B. 34 00:02:21,147 --> 00:02:26,822 And so you see immediately that the Q, the charge on B, 35 00:02:26,822 --> 00:02:32,707 divided by the radius of B, is the charge on A divided by 36 00:02:32,707 --> 00:02:37,647 the radius on A. And if the radius of B were for 37 00:02:37,647 --> 00:02:42,586 instance five times larger than the radius of A, 38 00:02:42,586 --> 00:02:50,301 there would be five times more charge on B than there would be 39 00:02:50,301 --> 00:02:53,393 on A. But if B has a five times 40 00:02:53,393 --> 00:02:59,784 larger radius then its surface area is twenty-five times larger 41 00:02:59,784 --> 00:03:06,278 and since surface charge density sigma is the charge on a sphere 42 00:03:06,278 --> 00:03:12,668 divided by the surface area of the sphere, it is now clear that 43 00:03:12,668 --> 00:03:17,41 if the radius of B is five times larger than A, 44 00:03:17,41 --> 00:03:21,519 it's true that the charge on B is five 45 00:03:21,519 --> 00:03:25,129 times the charge on A, but the surface charge density 46 00:03:25,129 --> 00:03:29,295 on B is now only one-fifth of the surface charge density of A 47 00:03:29,295 --> 00:03:33,392 because its area is twenty-five times larger and so you have 48 00:03:33,392 --> 00:03:37,211 this -- the highest surface charge density at A than you 49 00:03:37,211 --> 00:03:39,641 have at B. Five times higher surface 50 00:03:39,641 --> 00:03:43,807 charge density here than there. And I hope that convinces you 51 00:03:43,807 --> 00:03:46,792 that if we have a solid conductor like this, 52 00:03:46,792 --> 00:03:50,681 even though it's not ideal as we have here with these two 53 00:03:50,681 --> 00:03:54,86 spheres far apart, that the surface 54 00:03:54,86 --> 00:04:00,199 charge density here will be larger than there because it has 55 00:04:00,199 --> 00:04:04,361 a smaller radius. It's basically the same idea. 56 00:04:04,361 --> 00:04:09,881 And so you expect the highest surface charge density where the 57 00:04:09,881 --> 00:04:13,591 curvature is the highest, smallest radius, 58 00:04:13,591 --> 00:04:18,93 and that means that also the electric field will be stronger 59 00:04:18,93 --> 00:04:22,097 there. That follows immediately from 60 00:04:22,097 --> 00:04:26,62 Gauss's law. If this is the surface of a 61 00:04:26,62 --> 00:04:30,076 conductor, any conductor, a solid conductor, 62 00:04:30,076 --> 00:04:34,015 where the E field is zero inside of the conductor, 63 00:04:34,015 --> 00:04:38,517 and there is surface charge here, what I'm going to do is 64 00:04:38,517 --> 00:04:42,697 I'm going to make a Gaussian pillbox, this surface is 65 00:04:42,697 --> 00:04:46,555 parallel to the conductor, I go in the conductor, 66 00:04:46,555 --> 00:04:50,735 and this now is my Gaussian surface, let this area be 67 00:04:50,735 --> 00:04:55,639 capital A, and let's assume that it is positive charge so that 68 00:04:55,639 --> 00:05:00,115 the electric field lines come out of the 69 00:05:00,115 --> 00:05:03,824 surface like so, perpendicular to the surface. 70 00:05:03,824 --> 00:05:06,873 Always perpendicular to equipotential, 71 00:05:06,873 --> 00:05:11,819 so now if I apply Gauss's law which tells me that the surface 72 00:05:11,819 --> 00:05:16,681 integral of the electric flux throughout this whole surface, 73 00:05:16,681 --> 00:05:21,214 well, there's only flux coming out of this surface here, 74 00:05:21,214 --> 00:05:25,912 I can bring that surface as close to the surface as I want 75 00:05:25,912 --> 00:05:29,339 to. I can almost make it touch the 76 00:05:29,339 --> 00:05:31,906 conductor. So everything comes out only 77 00:05:31,906 --> 00:05:35,214 through this surface, and so what comes out is the 78 00:05:35,214 --> 00:05:37,983 surface area A times the electric field E. 79 00:05:37,983 --> 00:05:41,9 The A and E are in the same direction because remember E is 80 00:05:41,9 --> 00:05:45,276 perpendicular to the surface of the equipotentials. 81 00:05:45,276 --> 00:05:48,788 And so this is all there is for the surface integral, 82 00:05:48,788 --> 00:05:52,57 and that is all the charge inside, well the charge inside 83 00:05:52,57 --> 00:05:56,351 is of course the surface charge density times the area A, 84 00:05:56,351 --> 00:06:00,715 divided by epsilon zero, this is Gauss's law. 85 00:06:00,715 --> 00:06:05,22 And so you find immediately that the electric field is sigma 86 00:06:05,22 --> 00:06:08,733 divided by epsilon zero. So whenever you have a 87 00:06:08,733 --> 00:06:13,086 conductor if you know the local surface charge density you 88 00:06:13,086 --> 00:06:15,835 always know the local electric field. 89 00:06:15,835 --> 00:06:19,959 And since the surface charge density is going to be the 90 00:06:19,959 --> 00:06:23,243 highest here, even though the whole thing is 91 00:06:23,243 --> 00:06:26,908 an equipotential, the electric field will also be 92 00:06:26,908 --> 00:06:29,428 higher here than it will be there. 93 00:06:29,428 --> 00:06:33,399 I can demonstrate this to you in a 94 00:06:33,399 --> 00:06:36,842 uh very simple way. I have here a cooking pan and 95 00:06:36,842 --> 00:06:40,285 the cooking pan I used to boil lobsters in there, 96 00:06:40,285 --> 00:06:43,513 it's a large pan. The cooking pan I'm going to 97 00:06:43,513 --> 00:06:47,673 charge up and the cooking pan here has a radius whatever it 98 00:06:47,673 --> 00:06:51,761 is, maybe twenty centimeters, but look here at the handle, 99 00:06:51,761 --> 00:06:55,778 how very small this radius is, so you could put charge on 100 00:06:55,778 --> 00:07:00,081 there and I'm going to convince you that I can scoop off more 101 00:07:00,081 --> 00:07:05,747 charge here where the radius is small than I can scoop off here. 102 00:07:05,747 --> 00:07:10,546 I have here a small flat spoon and I'm going to put the spoon 103 00:07:10,546 --> 00:07:15,184 here on the surface here and on the surface there and we're 104 00:07:15,184 --> 00:07:19,662 going to see from where we can scoop off the most charge. 105 00:07:19,662 --> 00:07:22,781 Still charged from the previous lecture. 106 00:07:22,781 --> 00:07:26,7 So here, we see the electroscope that we have seen 107 00:07:26,7 --> 00:07:29,179 before. I'm going to charge this 108 00:07:29,179 --> 00:07:33,177 cooking pan with my favorite technique which is the 109 00:07:33,177 --> 00:07:36,616 electrophorus. So we have the cat fur and we 110 00:07:36,616 --> 00:07:39,664 have the glass plate. 111 00:07:39,664 --> 00:07:43,429 I'm going to rub this first with the cat fur, 112 00:07:43,429 --> 00:07:47,45 put it on, put my finger on, get a little shock, 113 00:07:47,45 --> 00:07:50,445 charge up the pan, put my finger on, 114 00:07:50,445 --> 00:07:53,525 get another shock, charge up the pan, 115 00:07:53,525 --> 00:07:56,434 and another one, charge up the pan, 116 00:07:56,434 --> 00:08:00,113 make sure that I get enough charge on there, 117 00:08:00,113 --> 00:08:03,022 rub the glass again, put it on top, 118 00:08:03,022 --> 00:08:06,017 put my finger on, charge, once more, 119 00:08:06,017 --> 00:08:09,525 and once more. Let's assume we have enough 120 00:08:09,525 --> 00:08:12,865 charge on there now. 121 00:08:12,865 --> 00:08:17,411 Here is my little spoon. I touch here the outside here 122 00:08:17,411 --> 00:08:22,128 of the can -- of the pan. And go to the electroscope and 123 00:08:22,128 --> 00:08:25,559 you see a little charge. It's very clear. 124 00:08:25,559 --> 00:08:30,363 What I want to show you now it's very qualitative is that 125 00:08:30,363 --> 00:08:34,995 when I touch here the handle, it's a very small radius, 126 00:08:34,995 --> 00:08:37,654 that I can take off more charge. 127 00:08:37,654 --> 00:08:41,6 There we go. Substantially more. 128 00:08:41,6 --> 00:08:43,644 That's all I wanted to show you. 129 00:08:43,644 --> 00:08:47,734 So you've seen now in front of your own eyes for the first time 130 00:08:47,734 --> 00:08:51,494 that even though this is a conductor that means that it is 131 00:08:51,494 --> 00:08:54,661 an equipotential, that the surface charge density 132 00:08:54,661 --> 00:08:58,619 right -- right here is higher than the surface charge density 133 00:08:58,619 --> 00:09:00,598 here. Only if it is a sphere of 134 00:09:00,598 --> 00:09:04,226 course for s- circle symmetry reasons will the charge be 135 00:09:04,226 --> 00:09:07,59 uniformly distributed. If the electric field becomes 136 00:09:07,59 --> 00:09:10,69 too high we get what we call electric breakdown. 137 00:09:10,69 --> 00:09:14,054 We get a discharge into the air. 138 00:09:14,054 --> 00:09:18,265 And the reason for that is actually quite simple. 139 00:09:18,265 --> 00:09:23,178 If I have an electron here and this is an electric field, 140 00:09:23,178 --> 00:09:28,003 the electron will start to accelerate in this direction. 141 00:09:28,003 --> 00:09:33,442 The electron will collide with nitrogen and oxygen molecules in 142 00:09:33,442 --> 00:09:38,882 the air and if the electron has enough kinetic energy to ionize 143 00:09:38,882 --> 00:09:43,882 that molecule then one electron will become two electrons. 144 00:09:43,882 --> 00:09:49,31 The original electron plus the electron from the ion. 145 00:09:49,31 --> 00:09:53,222 And if these now start to accelerate in this electric 146 00:09:53,222 --> 00:09:56,607 field, and if they collide with the molecules, 147 00:09:56,607 --> 00:10:00,594 and if they make an ion, then each one will become two 148 00:10:00,594 --> 00:10:03,453 electrons, and so you get an avalanche. 149 00:10:03,453 --> 00:10:07,666 And this avalanche is an electric breakdown and you get a 150 00:10:07,666 --> 00:10:10,299 spark. When the ions that are formed 151 00:10:10,299 --> 00:10:14,361 become neutral again they produce light and that's what 152 00:10:14,361 --> 00:10:17,145 you see. That's the light that you see 153 00:10:17,145 --> 00:10:19,571 in the spark. 154 00:10:19,571 --> 00:10:24,362 And so sparks will occur typically at the -- at sharp 155 00:10:24,362 --> 00:10:28,785 points -- at areas where the curvature is strong, 156 00:10:28,785 --> 00:10:34,128 whereby the radius is very small, that's where the electric 157 00:10:34,128 --> 00:10:39,012 fields are the highest. How strong should the electric 158 00:10:39,012 --> 00:10:42,697 field be? Well, we can make a back of the 159 00:10:42,697 --> 00:10:46,659 envelope calculation. If you take air of one 160 00:10:46,659 --> 00:10:51,312 atmosphere, dry air, at room temperature, 161 00:10:51,312 --> 00:10:55,12 then the -- the electron on average, on average, 162 00:10:55,12 --> 00:10:59,657 will have to travel about one micron, which is ten to the 163 00:10:59,657 --> 00:11:03,546 minus six meters, between the collisions with the 164 00:11:03,546 --> 00:11:06,787 molecules, it's just a given. On average. 165 00:11:06,787 --> 00:11:10,676 Sometimes a little more, sometimes a little less. 166 00:11:10,676 --> 00:11:13,835 Because it's a random process of course. 167 00:11:13,835 --> 00:11:16,752 To ionize nitrogen, to ionize oxygen, 168 00:11:16,752 --> 00:11:21,251 takes energy. To ionize an oxygen molecule 169 00:11:21,251 --> 00:11:24,169 takes twelve-and-a-half electron volts. 170 00:11:24,169 --> 00:11:28,546 And to ionize nitrogen takes about fifteen electron volts. 171 00:11:28,546 --> 00:11:32,539 What is an electron volt? Well, an electron volt is a 172 00:11:32,539 --> 00:11:35,226 teeny weeny little amount of energy. 173 00:11:35,226 --> 00:11:39,603 It's one point six times ten to the minus nineteen joules. 174 00:11:39,603 --> 00:11:43,595 Electron volt is actually a very nice unit of energy. 175 00:11:43,595 --> 00:11:47,588 Because once you have an electron and it moves over a 176 00:11:47,588 --> 00:11:51,351 potential difference of one volt, 177 00:11:51,351 --> 00:11:54,989 it gains in kinetic energy, that's the definition of an 178 00:11:54,989 --> 00:11:57,752 electron volt, it gains one electron volt. 179 00:11:57,752 --> 00:12:01,39 It's the charge of the electron, which is one point six 180 00:12:01,39 --> 00:12:05,298 times ten to the minus nineteen coulombs, multiplied by one 181 00:12:05,298 --> 00:12:07,454 volt. And that gives you then the 182 00:12:07,454 --> 00:12:11,093 energy, one electron volt. And so what it means then -- 183 00:12:11,093 --> 00:12:14,529 let's assume that this number is ten electron volts. 184 00:12:14,529 --> 00:12:18,303 Do we -- we only want a back of the envelope calculation. 185 00:12:18,303 --> 00:12:23,423 So we want the electron to move over a potential difference 186 00:12:23,423 --> 00:12:28,315 delta V which is roughly ten volts and we want it to do that 187 00:12:28,315 --> 00:12:33,29 over a distance delta X which is ten to the minus six meters, 188 00:12:33,29 --> 00:12:37,684 that's your one micron. And if that happens you'll get 189 00:12:37,684 --> 00:12:42,493 this enough kinetic energy in the electron to cause an ion. 190 00:12:42,493 --> 00:12:46,058 So what electric field is required for that, 191 00:12:46,058 --> 00:12:49,458 that is delta V, the potential difference, 192 00:12:49,458 --> 00:12:53,769 divided by the delta X, so that is ten divided by ten 193 00:12:53,769 --> 00:12:58,388 to the minus six, so that's about ten to the 194 00:12:58,388 --> 00:13:02,242 seven volts per meter. That's a very strong electric 195 00:13:02,242 --> 00:13:04,963 field. In reality when we measure the 196 00:13:04,963 --> 00:13:09,498 electric fields near breakdown, it is more like three million 197 00:13:09,498 --> 00:13:12,672 volts per meter. But it's still very close. 198 00:13:12,672 --> 00:13:16,3 This was only a back of the envelope calculation. 199 00:13:16,3 --> 00:13:20,305 So very roughly at one atmosphere air room temperature 200 00:13:20,305 --> 00:13:24,311 when the air is dry we get electric breakdown at about 201 00:13:24,311 --> 00:13:28,694 three million volts per meter. When the ions neutralize you 202 00:13:28,694 --> 00:13:32,621 see light, that's why sparks can be 203 00:13:32,621 --> 00:13:34,357 seen. They heat the air, 204 00:13:34,357 --> 00:13:38,583 they produce a little pressure wave, so you can also hear 205 00:13:38,583 --> 00:13:41,3 noise. If you had two parallel plates 206 00:13:41,3 --> 00:13:45,828 and you would bring those plates closely together and suppose 207 00:13:45,828 --> 00:13:49,904 they had a potential difference of three hundred volts, 208 00:13:49,904 --> 00:13:53,979 then you would reach an electric field of three million 209 00:13:53,979 --> 00:13:58,206 volts per meter when the distance D is about one tenth of 210 00:13:58,206 --> 00:14:02,356 a millimeter. So that's when you expect 211 00:14:02,356 --> 00:14:05,455 spontaneous discharge between these two plates. 212 00:14:05,455 --> 00:14:09,632 In practice however it probably will happen when the plates are 213 00:14:09,632 --> 00:14:12,596 further apart than one tenth of a millimeter. 214 00:14:12,596 --> 00:14:16,368 And the reason for that is that there is no such thing as 215 00:14:16,368 --> 00:14:19,4 perfect plates. The plates have imperfections. 216 00:14:19,4 --> 00:14:23,374 That means there are always areas on the plate which are not 217 00:14:23,374 --> 00:14:26,877 flat, which are a little bit like what you see there, 218 00:14:26,877 --> 00:14:29,774 small radius, and that's of course where the 219 00:14:29,774 --> 00:14:33,411 electric field then will be larger and that's where the 220 00:14:33,411 --> 00:14:36,403 discharge will occur first. 221 00:14:36,403 --> 00:14:39,859 However, if you touch the doorknob and you get a spark, 222 00:14:39,859 --> 00:14:42,803 you feel a spark, and you look at the spark and 223 00:14:42,803 --> 00:14:46,324 you see that when you're three millimeters away from the 224 00:14:46,324 --> 00:14:49,844 doorknob that the spark develops, you can s- pretty sure 225 00:14:49,844 --> 00:14:53,685 that the potential difference between you and the door was of 226 00:14:53,685 --> 00:14:57,205 the order of ten thousand volts, several thousand volts, 227 00:14:57,205 --> 00:14:59,702 at least. Because over three millimeters 228 00:14:59,702 --> 00:15:03,542 it requires ten thousand volts to get the three million volts 229 00:15:03,542 --> 00:15:06,166 per meter. When you comb your hair or when 230 00:15:06,166 --> 00:15:09,511 you take your shirt off you get 231 00:15:09,511 --> 00:15:12,492 little sparks, you can hear them and if it's 232 00:15:12,492 --> 00:15:16,167 dark you can see them, and you can be sure that at the 233 00:15:16,167 --> 00:15:18,802 sharp ends of this hair, of the fabric, 234 00:15:18,802 --> 00:15:22,546 that you have developed electric fields of the order of 235 00:15:22,546 --> 00:15:26,706 three million volts per meter. And then you get the automatic 236 00:15:26,706 --> 00:15:29,203 breakdown. Now of course high voltage 237 00:15:29,203 --> 00:15:31,56 alone doesn't necessarily kill you. 238 00:15:31,56 --> 00:15:35,79 What -- what -- what matters is not so much the voltage to get 239 00:15:35,79 --> 00:15:40,878 killed but it's the current that goes through you. 240 00:15:40,878 --> 00:15:44,217 And current is charge per unit time. 241 00:15:44,217 --> 00:15:48,987 And so in SI units it would be coulombs per second. 242 00:15:48,987 --> 00:15:54,138 For which we write a capital A which stands for Ampere, 243 00:15:54,138 --> 00:15:59,861 the man who did a tremendous amount of research in this area, 244 00:15:59,861 --> 00:16:03,009 Frenchman. And so if you touch the 245 00:16:03,009 --> 00:16:08,256 doorknob the instantaneous current may actually be quite 246 00:16:08,256 --> 00:16:11,726 high. It may be an ampere even, 247 00:16:11,726 --> 00:16:14,379 but it may only last for one millisecond. 248 00:16:14,379 --> 00:16:16,7 And so that's not going to kill you. 249 00:16:16,7 --> 00:16:20,811 We all know that when you comb your hair that you don't die and 250 00:16:20,811 --> 00:16:24,922 you also know that when you take your shirt off even though you 251 00:16:24,922 --> 00:16:27,708 may hear the sparks that that's not lethal. 252 00:16:27,708 --> 00:16:31,885 So maybe in a future lecture we can discuss in some more details 253 00:16:31,885 --> 00:16:35,665 what it does take to actually execute someone electrically 254 00:16:35,665 --> 00:16:39,445 which is very unpleasant but nevertheless we would have to 255 00:16:39,445 --> 00:16:43,423 evaluate how long the current should last, 256 00:16:43,423 --> 00:16:47,807 how strong the current should be and then also during which 257 00:16:47,807 --> 00:16:52,19 parts of the body the current would cause lethal reactions. 258 00:16:52,19 --> 00:16:56,422 So I want to be a little bit more quantitative now uh and 259 00:16:56,422 --> 00:16:59,369 deepen our knowledge of the VandeGraaff. 260 00:16:59,369 --> 00:17:03,224 Slowly we're going to understand how the VandeGraaff 261 00:17:03,224 --> 00:17:05,869 works. And today I want to calculate 262 00:17:05,869 --> 00:17:10,554 with you how much charge we can put on the VandeGraaff and what 263 00:17:10,554 --> 00:17:13,501 the maximum potential is at the surface. 264 00:17:13,501 --> 00:17:17,204 If we charge up the VandeGraaff, 265 00:17:17,204 --> 00:17:21,023 with charge Q, then the potential of the 266 00:17:21,023 --> 00:17:26,799 surface is an equipotential, is Q divided by four pi epsilon 267 00:17:26,799 --> 00:17:30,226 zero R. And the electric field right 268 00:17:30,226 --> 00:17:36,198 here at the surface would be Q divided by four pi epsilon zero 269 00:17:36,198 --> 00:17:39,919 R squared. So in this case of spherical 270 00:17:39,919 --> 00:17:45,206 symmetry we have that the potential V equals E times R. 271 00:17:45,206 --> 00:17:49,612 But we know that E cannot exceed 272 00:17:49,612 --> 00:17:53,97 three million volts per meter. And so that gives you now a 273 00:17:53,97 --> 00:17:58,175 limit on the potential that we can give the VandeGraaff. 274 00:17:58,175 --> 00:18:02,533 So if you substitute in here three million volts per meter 275 00:18:02,533 --> 00:18:07,198 you can calculate what potential you can maximally reach for a 276 00:18:07,198 --> 00:18:09,644 given sphere with a given radius. 277 00:18:09,644 --> 00:18:14,156 And if we here have the radius and we here have the voltage, 278 00:18:14,156 --> 00:18:18,284 then if the radius of the sphere were three millimeters 279 00:18:18,284 --> 00:18:22,107 then you could not exceed a voltage 280 00:18:22,107 --> 00:18:25,093 of ten kilovolts. If you did you would get this 281 00:18:25,093 --> 00:18:28,404 automatic electric breakdown. You would get a spark. 282 00:18:28,404 --> 00:18:32,039 If you have a sphere of three centimeters that would be a 283 00:18:32,039 --> 00:18:35,674 hundred kilovolts and our VandeGraaff, which has a radius 284 00:18:35,674 --> 00:18:39,049 of thirty centimeters, would therefore be one million 285 00:18:39,049 --> 00:18:41,386 volts. And you could not exceed that. 286 00:18:41,386 --> 00:18:45,215 And in practice in fact this one doesn't even make it to one 287 00:18:45,215 --> 00:18:47,812 million volts. The sphere is not perfect. 288 00:18:47,812 --> 00:18:50,214 There are imperfections of the sphere. 289 00:18:50,214 --> 00:18:55,171 There are areas which have so-to-speak sharp points and so 290 00:18:55,171 --> 00:18:57,602 we won't make it to one million volts. 291 00:18:57,602 --> 00:19:00,887 We get a breakdown maybe at a few hundred thousand, 292 00:19:00,887 --> 00:19:03,121 maybe three hundred thousand volts. 293 00:19:03,121 --> 00:19:06,997 You can now also calculate what the maximum charge is on the 294 00:19:06,997 --> 00:19:09,231 VandeGraaff. Because if the maximum 295 00:19:09,231 --> 00:19:11,925 potential is three hundred thousand volts, 296 00:19:11,925 --> 00:19:14,619 you know the radius is point three meters, 297 00:19:14,619 --> 00:19:18,495 so you can calculate now what the maximum charge is that you 298 00:19:18,495 --> 00:19:21,517 can put on the VandeGraaff using that equation, 299 00:19:21,517 --> 00:19:23,554 will give you ten microcoulombs. 300 00:19:23,554 --> 00:19:27,365 And so the maximum potential for our 301 00:19:27,365 --> 00:19:31,63 VandeGraaff is of the order of three hundred thousand volts. 302 00:19:31,63 --> 00:19:35,607 So this gives you now a feeling, a quantitative feeling, 303 00:19:35,607 --> 00:19:38,644 for numbers, for what the -- can I put this 304 00:19:38,644 --> 00:19:43,271 down, haha, so that gives you an idea of what our VandeGraaff can 305 00:19:43,271 --> 00:19:47,465 do, and later we will understand how the charge gets there. 306 00:19:47,465 --> 00:19:51,297 But at least you have some feeling now for potentials, 307 00:19:51,297 --> 00:19:53,972 and for the charges that are involved. 308 00:19:53,972 --> 00:19:59,539 If here's my VandeGraaff and I approach the VandeGraaff with a 309 00:19:59,539 --> 00:20:03,059 sphere which is connected to the earth and if this 310 00:20:03,059 --> 00:20:07,152 VandeGraaff had positive charge on it then the sphere will 311 00:20:07,152 --> 00:20:11,246 become negatively charged through induction and so you get 312 00:20:11,246 --> 00:20:15,268 field lines which go from the VandeGraaff to this object, 313 00:20:15,268 --> 00:20:18,284 always perpendicular to the equipotentials, 314 00:20:18,284 --> 00:20:21,947 so they go like this, and so the electric field here 315 00:20:21,947 --> 00:20:26,04 will probably be the strongest, and so the spark will then 316 00:20:26,04 --> 00:20:30,35 develop between this sphere and the VandeGraaff provided that 317 00:20:30,35 --> 00:20:34,671 you were close enough. So that you do achieve a 318 00:20:34,671 --> 00:20:38,28 electric field close to this sphere of about three million 319 00:20:38,28 --> 00:20:41,257 volts per meter. And I will show you that later, 320 00:20:41,257 --> 00:20:45,121 you will see more sparks today than you've ever seen before in 321 00:20:45,121 --> 00:20:48,667 your life, but I want you to appreciate a little bit more 322 00:20:48,667 --> 00:20:52,53 about the sparks about lightning before uh I demonstrate that. 323 00:20:52,53 --> 00:20:54,937 So you get a little bit more out of it. 324 00:20:54,937 --> 00:20:58,737 If I approach the VandeGraaff not with the sphere but I would 325 00:20:58,737 --> 00:21:02,221 walk to the VandeGraaff being very courageous like this, 326 00:21:02,221 --> 00:21:05,451 I'm also a pretty good conductor, 327 00:21:05,451 --> 00:21:09,007 I'm also connected with the earth, then the chances are that 328 00:21:09,007 --> 00:21:12,142 the spark would develop first between my nose and the 329 00:21:12,142 --> 00:21:15,88 VandeGraaff, because that is the smallest curve -- the sha- the 330 00:21:15,88 --> 00:21:18,231 sharpest curvature, the smallest radius, 331 00:21:18,231 --> 00:21:21,245 or certainly my head, would be a good candidate for 332 00:21:21,245 --> 00:21:23,958 being hit first. If I approach the VandeGraaff 333 00:21:23,958 --> 00:21:27,093 like this with my hand stretched, then chances are of 334 00:21:27,093 --> 00:21:30,167 course that the sparks will first develop between my 335 00:21:30,167 --> 00:21:32,337 fingertips. Because it's a very small 336 00:21:32,337 --> 00:21:35,231 radius and they're very close to the VandeGraaff, 337 00:21:35,231 --> 00:21:38,487 and so that's where the discharge 338 00:21:38,487 --> 00:21:41,931 will occur. So before we will enjoy some of 339 00:21:41,931 --> 00:21:45,621 this, you will enjoy it, I will enjoy it less, 340 00:21:45,621 --> 00:21:50,623 um I want to talk a little bit about lightning with you first. 341 00:21:50,623 --> 00:21:54,969 Because what you're going to see in a way is a form of 342 00:21:54,969 --> 00:21:58,33 lightning. There are four hundred thousand 343 00:21:58,33 --> 00:22:01,856 thunderstorms every day on average on earth. 344 00:22:01,856 --> 00:22:04,727 Four hundred thousand thunderstorms. 345 00:22:04,727 --> 00:22:08,826 There are about a hundred lightning 346 00:22:08,826 --> 00:22:12,201 flashes every second. The top of a thundercloud 347 00:22:12,201 --> 00:22:15,722 becomes positive and the bottom becomes negative. 348 00:22:15,722 --> 00:22:20,05 The physics of that is not so easy, and probably incomplete, 349 00:22:20,05 --> 00:22:23,645 and I will not go into the details of the physics, 350 00:22:23,645 --> 00:22:27,386 but it does have to do with the flow of water drops. 351 00:22:27,386 --> 00:22:31,274 They become elongated, they can become charged because 352 00:22:31,274 --> 00:22:35,529 of friction, and they can break off, and they can transport 353 00:22:35,529 --> 00:22:38,023 charge. I will simply give you some 354 00:22:38,023 --> 00:22:40,59 facts. And so I will accept the fact 355 00:22:40,59 --> 00:22:44,32 that the cloud is going to be 356 00:22:44,32 --> 00:22:46,533 charged. This is the cloud. 357 00:22:46,533 --> 00:22:50,193 Positive at the top, negative at the bottom. 358 00:22:50,193 --> 00:22:53,853 And here is the earth. Because of induction, 359 00:22:53,853 --> 00:22:58,194 the earth of course will therefore become positively 360 00:22:58,194 --> 00:23:01,939 charged here, and so we're going to see field 361 00:23:01,939 --> 00:23:06,875 lines, electric field lines, which go from the earth to the 362 00:23:06,875 --> 00:23:12,323 cloud, always perpendicular to the equipotentials, 363 00:23:12,323 --> 00:23:16,853 something like this. I'll give you some dimensions, 364 00:23:16,853 --> 00:23:20,93 uh this may be something like five kilometers, 365 00:23:20,93 --> 00:23:25,189 this vertical distance D is about one kilometer. 366 00:23:25,189 --> 00:23:29,538 These are typical numbers, of course, it can vary 367 00:23:29,538 --> 00:23:33,524 enormously from thunderstorm to thunderstorm. 368 00:23:33,524 --> 00:23:38,779 And this height is something typically like ten kilometers. 369 00:23:38,779 --> 00:23:43,128 And this allows us now to make some 370 00:23:43,128 --> 00:23:46,832 very interesting calculations to get some feeling for the 371 00:23:46,832 --> 00:23:50,271 potential difference between the cloud and the earth. 372 00:23:50,271 --> 00:23:52,388 That's the first thing we can do. 373 00:23:52,388 --> 00:23:55,959 If we make the simplifying assumption that the electric 374 00:23:55,959 --> 00:23:59,663 field is more or less constant here, it's like having two 375 00:23:59,663 --> 00:24:02,507 parallel plates, where the electric field is 376 00:24:02,507 --> 00:24:05,88 constant between them, then the potential difference 377 00:24:05,88 --> 00:24:09,385 delta V between the bottom of the cloud and the earth, 378 00:24:09,385 --> 00:24:12,626 is simply the electric field times the distance D. 379 00:24:12,626 --> 00:24:17,422 So this becomes E times D. But if the breakdown occurs at 380 00:24:17,422 --> 00:24:20,939 three million volts per meter -- by the way that's dry air, 381 00:24:20,939 --> 00:24:24,334 when it -- when there is a thunderstorm it's probably not 382 00:24:24,334 --> 00:24:27,73 so dry, but let's take the three million volts per meter, 383 00:24:27,73 --> 00:24:30,823 so we get three times ten to the six, that is for E, 384 00:24:30,823 --> 00:24:34,34 and the distance between the cloud and the earth let's take 385 00:24:34,34 --> 00:24:36,826 one kilometers. So that's ten to the third 386 00:24:36,826 --> 00:24:40,464 meters, so we get of the order of three billion volts between 387 00:24:40,464 --> 00:24:43,375 the earth and the clouds. And the values that are 388 00:24:43,375 --> 00:24:47,256 typically measured are several hundred million 389 00:24:47,256 --> 00:24:49,82 to one billion volts, so it is not all that 390 00:24:49,82 --> 00:24:52,202 different. You expect that the potential 391 00:24:52,202 --> 00:24:55,867 is probably less than what we have calculated because clearly 392 00:24:55,867 --> 00:24:58,737 uh these are not flat surfaces, there are trees, 393 00:24:58,737 --> 00:25:01,485 here on the ground, there are buildings on the 394 00:25:01,485 --> 00:25:05,149 ground, which are like sharp points, where the electric field 395 00:25:05,149 --> 00:25:08,447 will be locally higher, and so you will get a discharge 396 00:25:08,447 --> 00:25:11,867 at these sharp points first. And that means the potential 397 00:25:11,867 --> 00:25:15,531 difference between the cloud and the earth could then be less 398 00:25:15,531 --> 00:25:19,867 than the three billion that we have calculated here. 399 00:25:19,867 --> 00:25:23,082 It's only a back of the envelope calculation. 400 00:25:23,082 --> 00:25:27,466 The details of the physics of the discharge very complicated. 401 00:25:27,466 --> 00:25:31,338 But I want to share with you some facts without giving 402 00:25:31,338 --> 00:25:34,845 detailed explanations. The start of the lightning 403 00:25:34,845 --> 00:25:38,937 begins when electrons begin to flow from the cloud to the 404 00:25:38,937 --> 00:25:40,763 earth. They form a funnel, 405 00:25:40,763 --> 00:25:44,782 which is about one to ten meters in diameter and we call 406 00:25:44,782 --> 00:25:49,458 that the step leader. The step leader moves about 407 00:25:49,458 --> 00:25:53,85 a hundred miles per second and so it comes down in about five 408 00:25:53,85 --> 00:25:56,999 milliseconds. Five milliseconds from here to 409 00:25:56,999 --> 00:26:00,733 here and it takes about half a coulomb to the earth. 410 00:26:00,733 --> 00:26:03,881 Half a coulomb, for about five milliseconds, 411 00:26:03,881 --> 00:26:07,615 that means the current is about one hundred amperes. 412 00:26:07,615 --> 00:26:11,129 The step leader creates a channel of ionized air, 413 00:26:11,129 --> 00:26:15,23 full of ions and full of electrons, which is an extremely 414 00:26:15,23 --> 00:26:18,231 good conductor. And with -- when this step 415 00:26:18,231 --> 00:26:22,332 leader reaches the ground there is this 416 00:26:22,332 --> 00:26:26,183 highly conductive channel and the electrons can now very 417 00:26:26,183 --> 00:26:29,264 quickly flow from this channel to the ground. 418 00:26:29,264 --> 00:26:32,976 And that starts first right here at the surface of the 419 00:26:32,976 --> 00:26:35,567 earth. That's where the electrons will 420 00:26:35,567 --> 00:26:39,278 first go to the earth. And then successively electrons 421 00:26:39,278 --> 00:26:43,34 which are higher up in the channel will make it down to the 422 00:26:43,34 --> 00:26:45,581 earth. And so you're going to see 423 00:26:45,581 --> 00:26:49,573 electrons going through the channel to the earth but first 424 00:26:49,573 --> 00:26:53,984 the electrons are closer to the earth than the 425 00:26:53,984 --> 00:26:57,743 electrons farther away and then even farther away. 426 00:26:57,743 --> 00:27:01,731 And this is actually where most of the action occurs. 427 00:27:01,731 --> 00:27:05,949 The current is now enormously high, ten thousand to some 428 00:27:05,949 --> 00:27:09,477 hundred thousand amperes, and you heat the air, 429 00:27:09,477 --> 00:27:13,696 get a tremendous amount of light, the ions recombine and 430 00:27:13,696 --> 00:27:17,07 you get pressure, heat can produces pressure, 431 00:27:17,07 --> 00:27:21,442 and there comes your thunder. And so most of the action is 432 00:27:21,442 --> 00:27:25,891 not in the step leader but is in the second 433 00:27:25,891 --> 00:27:28,899 phenomenon, which we call the return stroke. 434 00:27:28,899 --> 00:27:31,417 Which is from the earth to the cloud. 435 00:27:31,417 --> 00:27:35,404 And the speed of that return stroke is about ten to twenty 436 00:27:35,404 --> 00:27:39,602 percent of the speed of light. During the return stroke there 437 00:27:39,602 --> 00:27:44,009 is about five coulombs exchange between the cloud and the earth, 438 00:27:44,009 --> 00:27:48,066 and five coulombs is a sizable fraction of the total charge 439 00:27:48,066 --> 00:27:52,333 that was on the cloud -- on the cloud the first place -- t- to 440 00:27:52,333 --> 00:27:55,202 start with. After a return 441 00:27:55,202 --> 00:27:57,496 stroke, maybe twenty milliseconds later, 442 00:27:57,496 --> 00:27:59,497 this whole process can start again. 443 00:27:59,497 --> 00:28:02,557 You can get a step leader. And you can get the return 444 00:28:02,557 --> 00:28:04,675 stroke. However, the step leader will 445 00:28:04,675 --> 00:28:08,206 now follow exactly the same path that was made before because 446 00:28:08,206 --> 00:28:11,913 that's where the air is ionized so that's where the conductivity 447 00:28:11,913 --> 00:28:14,326 is very high, so that's the easiest way to 448 00:28:14,326 --> 00:28:16,032 go. And this process can recur 449 00:28:16,032 --> 00:28:19,504 five, ten, maybe fifteen times. So what a- appears to you as 450 00:28:19,504 --> 00:28:23,094 one lightning bolt in fact could be ten flashes back and forth 451 00:28:23,094 --> 00:28:26,161 between the cloud and the earth. 452 00:28:26,161 --> 00:28:29,225 And the -- the real light is not in the step leader, 453 00:28:29,225 --> 00:28:32,41 that's very little light, but the real light is in the 454 00:28:32,41 --> 00:28:34,813 return strokes. So t- ten return strokes, 455 00:28:34,813 --> 00:28:37,577 which may be twenty, thirty, forty milliseconds 456 00:28:37,577 --> 00:28:40,461 apart, appear to you and to me only as one flash, 457 00:28:40,461 --> 00:28:43,826 which would take place maybe in as little as a tenth of a 458 00:28:43,826 --> 00:28:45,929 second. And during these five or ten 459 00:28:45,929 --> 00:28:49,413 return strokes you exchange between the cloud and the earth 460 00:28:49,413 --> 00:28:52,177 maybe a total of twenty-five to fifty coulombs, 461 00:28:52,177 --> 00:28:56,683 and that of course will lower the potential difference. 462 00:28:56,683 --> 00:29:01,624 And if the potential difference becomes too low then the process 463 00:29:01,624 --> 00:29:04,29 stops. You have to wait now for the 464 00:29:04,29 --> 00:29:08,682 clouds to charge up again. And then lightning will strike 465 00:29:08,682 --> 00:29:11,584 again. And that can take anywhere from 466 00:29:11,584 --> 00:29:14,485 maybe four, five, ten, twenty seconds. 467 00:29:14,485 --> 00:29:17,544 And then you get another lightning bolt. 468 00:29:17,544 --> 00:29:22,249 The study of these -- of this process, of the step leader and 469 00:29:22,249 --> 00:29:27,19 of the return stroke, can be done with a camera, 470 00:29:27,19 --> 00:29:29,665 which is called the Bors camera. 471 00:29:29,665 --> 00:29:34,377 Let me first explain to you in detail -- in principle how it 472 00:29:34,377 --> 00:29:37,333 works. If this is the area on the film 473 00:29:37,333 --> 00:29:42,045 that is exposed by your lens suppose that I move the film at 474 00:29:42,045 --> 00:29:46,517 a very high speed to the left and suppose the step leader 475 00:29:46,517 --> 00:29:50,83 comes down and it sees some light from the step leader, 476 00:29:50,83 --> 00:29:53,306 then I may see on the film this. 477 00:29:53,306 --> 00:29:56,341 Some light. And from here to here would 478 00:29:56,341 --> 00:30:00,178 then be the five milliseconds which it 479 00:30:00,178 --> 00:30:03,699 takes the step leader to go from the cloud to the earth. 480 00:30:03,699 --> 00:30:07,411 Now the return stroke takes place with way higher speed and 481 00:30:07,411 --> 00:30:11,316 so I see a tremendous amount of light because there's a lot of 482 00:30:11,316 --> 00:30:14,709 light in the return stroke. And of course this is very 483 00:30:14,709 --> 00:30:17,077 steep. Because it goes a hundred times 484 00:30:17,077 --> 00:30:19,638 faster up than the step leader came down. 485 00:30:19,638 --> 00:30:23,222 And so you can measure these times and so you can get the 486 00:30:23,222 --> 00:30:26,423 speed of the return stroke. And then later in time, 487 00:30:26,423 --> 00:30:29,751 maybe thirty, forty seconds later, 488 00:30:29,751 --> 00:30:32,417 on the film, you may see another return 489 00:30:32,417 --> 00:30:34,873 stroke. And you may see another one. 490 00:30:34,873 --> 00:30:38,801 And so you can see then how long the time was between the 491 00:30:38,801 --> 00:30:42,589 return strokes and you can also calculate their speeds. 492 00:30:42,589 --> 00:30:46,588 With a real camera it's not really the film that is moving 493 00:30:46,588 --> 00:30:50,656 but it is the -- the lens that is moving, and the way these 494 00:30:50,656 --> 00:30:53,673 pictures are taken, and I will show you one, 495 00:30:53,673 --> 00:30:57,461 is if this is photographic plate, then it is the camera 496 00:30:57,461 --> 00:31:02,301 that moves over the plate with a um very high speed, 497 00:31:02,301 --> 00:31:05,725 about three thousand revolutions per minute, 498 00:31:05,725 --> 00:31:10,024 and so you would get these -- this information then not 499 00:31:10,024 --> 00:31:14,164 horizontally but you get it spread out over the film. 500 00:31:14,164 --> 00:31:18,145 But you get the same information, you can calculate 501 00:31:18,145 --> 00:31:21,33 speeds and times. During the past decade, 502 00:31:21,33 --> 00:31:25,948 new forms of lightning have been discovered which occur way 503 00:31:25,948 --> 00:31:28,416 above the clouds. Way higher up. 504 00:31:28,416 --> 00:31:32,715 Red colors have been seen. Red sprites they are called. 505 00:31:32,715 --> 00:31:36,616 And also blue jets. The light is 506 00:31:36,616 --> 00:31:40,94 very faint and it occurs only for a very short amount of time. 507 00:31:40,94 --> 00:31:43,278 It's very difficult to photograph. 508 00:31:43,278 --> 00:31:46,751 I have not been able to get good slides for today. 509 00:31:46,751 --> 00:31:49,798 However, I did see some pictures on the Web. 510 00:31:49,798 --> 00:31:54,121 And when you log into the Web, when you visit the Web eight oh 511 00:31:54,121 --> 00:31:57,736 two which you should, then I give you directions how 512 00:31:57,736 --> 00:32:01,917 to access slides pictures of the red sprites and of the blue 513 00:32:01,917 --> 00:32:04,468 jets. The physics of that is not very 514 00:32:04,468 --> 00:32:07,445 well understood. It's being researched very 515 00:32:07,445 --> 00:32:11,698 heavily. But it's way above the clouds. 516 00:32:11,698 --> 00:32:15,442 There are also other forms of electric breakdown, 517 00:32:15,442 --> 00:32:18,874 of discharge. They are different in the sense 518 00:32:18,874 --> 00:32:21,448 that it's not an individual spark. 519 00:32:21,448 --> 00:32:25,503 But there is a continuous flow of -- of -- of charge. 520 00:32:25,503 --> 00:32:28,545 It occurs always from very sharp points. 521 00:32:28,545 --> 00:32:32,445 So there is a continuous current actually going on. 522 00:32:32,445 --> 00:32:36,969 And some of that you may have seen but you may not remember 523 00:32:36,969 --> 00:32:42,183 when we used a carbon arc here. We had two carbon arcs, 524 00:32:42,183 --> 00:32:44,742 two carbon rods, and we had a potential 525 00:32:44,742 --> 00:32:48,648 difference between them and we got a discharge between them 526 00:32:48,648 --> 00:32:52,621 which caused a tremendous amount of light, which we used for 527 00:32:52,621 --> 00:32:55,853 projection purposes. So a carbon arc discharge is 528 00:32:55,853 --> 00:33:00,028 such a form of discharge whereby you have a continuous current. 529 00:33:00,028 --> 00:33:03,395 It's not just sparks. If you take grass or trees or 530 00:33:03,395 --> 00:33:06,829 brushes for that matter, with thunderstorm activity, 531 00:33:06,829 --> 00:33:10,263 they can go into this discharge at their sharp tips. 532 00:33:10,263 --> 00:33:13,698 And we call this brush discharge, 533 00:33:13,698 --> 00:33:15,553 we call it St. Elmo's fire, 534 00:33:15,553 --> 00:33:18,908 it's all the same thing, it's also called corona 535 00:33:18,908 --> 00:33:21,407 discharge. I normally call it corona 536 00:33:21,407 --> 00:33:24,191 discharge. It produces light because the 537 00:33:24,191 --> 00:33:26,974 ions when they neutralize produce light. 538 00:33:26,974 --> 00:33:30,258 Heat makes sound, pressure, and so you can hear 539 00:33:30,258 --> 00:33:33,399 this cracking noise of the corona discharges. 540 00:33:33,399 --> 00:33:37,753 An airplane that flies or a car that drives, there is friction 541 00:33:37,753 --> 00:33:40,68 with the air, and any form of friction can 542 00:33:40,68 --> 00:33:45,079 charge things up. And so it's not uncommon at 543 00:33:45,079 --> 00:33:49,078 night that you can see this corona discharge from the tip of 544 00:33:49,078 --> 00:33:52,67 the wings of an airplane. I've also seen it from cars. 545 00:33:52,67 --> 00:33:56,263 Corona discharge from cars. Which charge themselves up 546 00:33:56,263 --> 00:33:58,499 simply by driving through the air. 547 00:33:58,499 --> 00:34:00,736 The air flow would charge them up. 548 00:34:00,736 --> 00:34:03,718 You can hear it, cracking, and you can see it 549 00:34:03,718 --> 00:34:07,039 sometimes if it's dark enough, you see some light. 550 00:34:07,039 --> 00:34:10,834 In general it's bluish light. Something completely on the 551 00:34:10,834 --> 00:34:14,766 side, going back to the lightning bolts, 552 00:34:14,766 --> 00:34:16,787 lightning bolts, the discharge, 553 00:34:16,787 --> 00:34:19,684 the moving electrons, can cause radio waves. 554 00:34:19,684 --> 00:34:23,39 And these radio waves you can receive on your car radio. 555 00:34:23,39 --> 00:34:25,815 And all of you have experienced this. 556 00:34:25,815 --> 00:34:28,443 Driving around, lightning very far away, 557 00:34:28,443 --> 00:34:32,148 you can hear it on the radio. So that's telling you that 558 00:34:32,148 --> 00:34:34,641 there is lightning going on somewhere. 559 00:34:34,641 --> 00:34:38,077 After a thunderstorm, something that many of you may 560 00:34:38,077 --> 00:34:42,12 not have experienced because in the cities there is always -- 561 00:34:42,12 --> 00:34:46,713 always exhaust from cars, that spoils everything, 562 00:34:46,713 --> 00:34:50,537 but when you're out in the country after a thunderstorm 563 00:34:50,537 --> 00:34:53,298 there's a very special smell in the air. 564 00:34:53,298 --> 00:34:55,21 I love it. And that's ozone. 565 00:34:55,21 --> 00:34:59,175 Oxygen two, oxygen two in lightning becomes oxygen three. 566 00:34:59,175 --> 00:35:01,866 And oxygen three has a wonderful smell, 567 00:35:01,866 --> 00:35:05,264 and you can really smell that. It's very typical. 568 00:35:05,264 --> 00:35:09,583 I hope that most of you sooner or later in life will have that 569 00:35:09,583 --> 00:35:12,132 experience. Go to the country after a 570 00:35:12,132 --> 00:35:16,876 thunderstorm and you can really smell this ozone. 571 00:35:16,876 --> 00:35:21,227 Let's now look at some slides. The first slide that you will 572 00:35:21,227 --> 00:35:24,692 see is one very classic slide made by Gary Ladd, 573 00:35:24,692 --> 00:35:28,748 a Kitt Peak Observatory in Arizona, uh what I like about 574 00:35:28,748 --> 00:35:31,919 this is that uh these are the observatories, 575 00:35:31,919 --> 00:35:33,983 the telescopes, in the domes, 576 00:35:33,983 --> 00:35:38,334 and of course when you're an astronomer, this is the kind of 577 00:35:38,334 --> 00:35:42,758 weather that you can do without. But nevertheless it happens. 578 00:35:42,758 --> 00:35:48,391 Uh you see here return strokes, the light is definitely due to 579 00:35:48,391 --> 00:35:51,082 the return strokes, it's very bright. 580 00:35:51,082 --> 00:35:55,342 These are step l- leaders that never made it to the earth, 581 00:35:55,342 --> 00:35:59,676 and if a step leader doesn't make it to the earth you don't 582 00:35:59,676 --> 00:36:04,01 get a return stroke and so the light as you can see here is 583 00:36:04,01 --> 00:36:07,074 much less. And what you think here is only 584 00:36:07,074 --> 00:36:10,512 one bolt is probably at least ten, five to ten, 585 00:36:10,512 --> 00:36:12,156 maybe fifteen, flashes. 586 00:36:12,156 --> 00:36:15,37 Return strokes. All right next slide please. 587 00:36:15,37 --> 00:36:20,452 Here you see the result of a Bors camera exposure. 588 00:36:20,452 --> 00:36:23,273 For those of you who are sitting in front you can 589 00:36:23,273 --> 00:36:25,977 recognize maybe the Empire State Building here. 590 00:36:25,977 --> 00:36:29,503 And the Empire State Building is hit here by lightning at the 591 00:36:29,503 --> 00:36:33,089 very tip, that's the sharp edge, that's where you expect it to 592 00:36:33,089 --> 00:36:35,029 be hit. This is not taken when the 593 00:36:35,029 --> 00:36:37,909 camera was rotating. This is just the exposure the 594 00:36:37,909 --> 00:36:41,259 way you and I would see it. Not moving camera but here you 595 00:36:41,259 --> 00:36:43,728 see the result of the rotating Bors camera. 596 00:36:43,728 --> 00:36:46,843 And this is the same flash. So here you see the return 597 00:36:46,843 --> 00:36:50,193 stroke, the -- the light from the step 598 00:36:50,193 --> 00:36:52,816 leader is too faint. You can't see that. 599 00:36:52,816 --> 00:36:56,649 So here is the return stroke and then this time separation 600 00:36:56,649 --> 00:36:59,003 may be thirty or forty milliseconds, 601 00:36:59,003 --> 00:37:01,625 see another stroke, you see another one, 602 00:37:01,625 --> 00:37:04,046 and another one, so there's six here, 603 00:37:04,046 --> 00:37:06,467 looks like you see a double one here. 604 00:37:06,467 --> 00:37:09,964 And so you have six or seven of these return strokes. 605 00:37:09,964 --> 00:37:13,797 And this is the way that you can study speeds and how much 606 00:37:13,797 --> 00:37:17,563 charge actually is exchanged between these uh between the 607 00:37:17,563 --> 00:37:22,135 cloud and in this case the Empire State Building. 608 00:37:22,135 --> 00:37:25,226 Uh the next slide shows you a corona discharge in the 609 00:37:25,226 --> 00:37:28,614 laboratory this is a high voltage supply with a very sharp 610 00:37:28,614 --> 00:37:31,17 tip -- tip here at the end, the sharp point, 611 00:37:31,17 --> 00:37:34,617 and here you see not individual sparks, you don't call this 612 00:37:34,617 --> 00:37:37,47 lightning but this is what you would call the St. 613 00:37:37,47 --> 00:37:39,966 Elmo's fire, the corona discharge is bluish 614 00:37:39,966 --> 00:37:42,106 light. And in fact when you are close 615 00:37:42,106 --> 00:37:45,018 to this power supply you can also smell the ozone. 616 00:37:45,018 --> 00:37:47,99 It also produces locally ozone. And you can see it. 617 00:37:47,99 --> 00:37:51,14 If you make it dark in the laboratory you can see some 618 00:37:51,14 --> 00:37:54,783 bluish light. Uh when I was a graduate 619 00:37:54,783 --> 00:37:58,567 student I had to build power supplies, high voltage power 620 00:37:58,567 --> 00:38:02,622 supplies, and I remember when my soldering job was not a very 621 00:38:02,622 --> 00:38:06,678 good job that means when I take the solder ironing off then I 622 00:38:06,678 --> 00:38:10,936 could draw a little sharp point, the solder, and that would then 623 00:38:10,936 --> 00:38:13,977 later cause me problems with corona discharge, 624 00:38:13,977 --> 00:38:18,235 that means I would have to redo the soldering so that the radius 625 00:38:18,235 --> 00:38:22,222 of the solder joint would become larger, so no sharp points. 626 00:38:22,222 --> 00:38:25,94 That's enough for the slides right now. 627 00:38:25,94 --> 00:38:29,552 Benjamin Franklin invented the lightning rod. 628 00:38:29,552 --> 00:38:34,314 His idea was that through the lightning rod you would get a 629 00:38:34,314 --> 00:38:37,434 continuous discharge, corona discharge, 630 00:38:37,434 --> 00:38:40,226 between the cloud and the building. 631 00:38:40,226 --> 00:38:44,906 And therefore you would keep the potential difference low. 632 00:38:44,906 --> 00:38:48,518 And so there would be no danger of lightning. 633 00:38:48,518 --> 00:38:53,198 And so he advised King George the third to put these sharp 634 00:38:53,198 --> 00:38:57,96 points on the royal palace and on uh powder 635 00:38:57,96 --> 00:39:01,492 houses, ammunition storage places for ammunition. 636 00:39:01,492 --> 00:39:04,877 There was a lot of opposition against Franklin. 637 00:39:04,877 --> 00:39:08,924 Uh they argued that uh a lightning rod will only attract 638 00:39:08,924 --> 00:39:11,573 lightning. And that the effect of the 639 00:39:11,573 --> 00:39:14,811 discharge, lowering the potential difference, 640 00:39:14,811 --> 00:39:18,343 would be insignificant. But nevertheless the King 641 00:39:18,343 --> 00:39:22,096 followed Franklin's advice and after the sharp rods, 642 00:39:22,096 --> 00:39:24,377 the lightning rods, were placed, 643 00:39:24,377 --> 00:39:29,012 there was a lightning bolt that hit one of the ammunition places 644 00:39:29,012 --> 00:39:31,481 at Pearl Fleet, 645 00:39:31,481 --> 00:39:33,945 but there was very little damage. 646 00:39:33,945 --> 00:39:38,719 And so we now know that on the one hand the discharge is indeed 647 00:39:38,719 --> 00:39:41,721 insignificant. And so the opposition was 648 00:39:41,721 --> 00:39:44,339 correct. And in fact you do attract 649 00:39:44,339 --> 00:39:47,804 lightning, unlike what Franklin had hoped for. 650 00:39:47,804 --> 00:39:52,192 However, if your lightning rod is thick enough that it can 651 00:39:52,192 --> 00:39:56,042 handle the high current, which is ten thousand or a 652 00:39:56,042 --> 00:39:59,815 hundred thousand amperes, then the current will go 653 00:39:59,815 --> 00:40:04,025 through the lightning rod and therefore 654 00:40:04,025 --> 00:40:07,907 there will not be an explosion. So it will not hit the 655 00:40:07,907 --> 00:40:10,69 building. So it will be confined to the 656 00:40:10,69 --> 00:40:13,474 lightning rod. And so it worked but for 657 00:40:13,474 --> 00:40:17,722 different reasons than Franklin had in mind, but he had the 658 00:40:17,722 --> 00:40:20,871 right intuition. Was a very great scientist, 659 00:40:20,871 --> 00:40:24,094 and great statesman. And so his lightning rod 660 00:40:24,094 --> 00:40:27,829 survived up to today. So now I want to return to the 661 00:40:27,829 --> 00:40:31,858 VandeGraaff and show you some of the things that we have 662 00:40:31,858 --> 00:40:35,984 discussed. And the first thing that I 663 00:40:35,984 --> 00:40:39,018 would want to do is create some sparks. 664 00:40:39,018 --> 00:40:41,973 Lightning. I run the VandeGraaff and I 665 00:40:41,973 --> 00:40:46,204 will approach it with this small sphere, small radius, 666 00:40:46,204 --> 00:40:50,596 and as I come closer and closer, the electric field will 667 00:40:50,596 --> 00:40:55,546 build up here and then I would predict that as sparks fly over, 668 00:40:55,546 --> 00:41:00,177 that they would go between the VandeGraaff and this uh this 669 00:41:00,177 --> 00:41:03,849 sphere. This sphere is grounded. 670 00:41:03,849 --> 00:41:07,921 And so any current that will flow will flow not through 671 00:41:07,921 --> 00:41:12,746 Walter Lewin but will go through the ground, so there's no danger 672 00:41:12,746 --> 00:41:16,44 that anything will happen to me. At least not yet. 673 00:41:16,44 --> 00:41:19,154 You already hear some cracking noise. 674 00:41:19,154 --> 00:41:23,3 That means there are already sparks flying around inside 675 00:41:23,3 --> 00:41:25,562 there. It's very hard to avoid, 676 00:41:25,562 --> 00:41:29,784 there are always some sharp edges in there that we cannot 677 00:41:29,784 --> 00:41:31,82 remove. This is not an ideal 678 00:41:31,82 --> 00:41:36,134 instrument. But I still think I will be 679 00:41:36,134 --> 00:41:40,133 able to show you some lightning. By coming closer. 680 00:41:40,133 --> 00:41:43,479 There we go. So what you think is only one 681 00:41:43,479 --> 00:41:47,641 spark may well be several like these return strokes, 682 00:41:47,641 --> 00:41:50,416 the way I described with lightning. 683 00:41:50,416 --> 00:41:54,987 So what you're seeing here now is that the electric field 684 00:41:54,987 --> 00:41:59,802 locally has become larger than three million volts per meter 685 00:41:59,802 --> 00:42:04,454 and then you're going to this discharge phenomenon that we 686 00:42:04,454 --> 00:42:08,919 described, and that gives you then -- that 687 00:42:08,919 --> 00:42:12,926 gives you the lightning. What I will do now is I would 688 00:42:12,926 --> 00:42:16,706 like you to experience -- although it may not be so 689 00:42:16,706 --> 00:42:20,789 fascinating for you -- to experience a corona discharge 690 00:42:20,789 --> 00:42:25,325 between a very sharp point that I have here, extremely sharp, 691 00:42:25,325 --> 00:42:28,878 and the VandeGraaff. And the only way that I can 692 00:42:28,878 --> 00:42:33,112 convince you that there is indeed going to be a discharge 693 00:42:33,112 --> 00:42:37,496 between this point and the VandeGraaff is by 694 00:42:37,496 --> 00:42:41,309 approaching the VandeGraaff and this cracking noise that you 695 00:42:41,309 --> 00:42:44,539 hear now will disappear. And the reason why it will 696 00:42:44,539 --> 00:42:48,416 disappear is that if I get a corona discharge between the tip 697 00:42:48,416 --> 00:42:51,065 and the VandeGraaff it will drain current, 698 00:42:51,065 --> 00:42:54,813 it will lower the potential and so that cracking noise will 699 00:42:54,813 --> 00:42:57,203 disappear. So the sparks which are now 700 00:42:57,203 --> 00:42:59,594 flying over will not fly over anymore. 701 00:42:59,594 --> 00:43:01,985 You will not be able to see the light. 702 00:43:01,985 --> 00:43:04,052 It's -- it's too much light here. 703 00:43:04,052 --> 00:43:09,157 Although I can probably see at the tip here this blue light. 704 00:43:09,157 --> 00:43:12,129 So I'm going to approach the VandeGraaff now. 705 00:43:12,129 --> 00:43:15,507 It's almost as if I had a lightning rod and I'm not 706 00:43:15,507 --> 00:43:19,493 worried at all because if any current starts flowing it goes 707 00:43:19,493 --> 00:43:22,6 through this rod, which is like a lightning rod 708 00:43:22,6 --> 00:43:25,235 to the earth. So I'm not worried at all. 709 00:43:25,235 --> 00:43:27,734 I just am very brave, very courageous, 710 00:43:27,734 --> 00:43:31,247 approaching the V- the VandeGraaff, and I want you to 711 00:43:31,247 --> 00:43:34,895 listen to that cracking noise. That cracking noise will 712 00:43:34,895 --> 00:43:38,949 disappear when I'm going to be -- draw a current through this 713 00:43:38,949 --> 00:43:42,461 sharp point. Oh, boy, there I go. 714 00:43:42,461 --> 00:43:46,91 And the cracking stops. And I can actually see here 715 00:43:46,91 --> 00:43:49,579 some glowing discharge, bluish. 716 00:43:49,579 --> 00:43:52,515 Will be impossible for you to see. 717 00:43:52,515 --> 00:43:55,54 I can come closer, I'm not worried. 718 00:43:55,54 --> 00:44:00,611 And so I'm draining charge now off the VandeGraaff thereby 719 00:44:00,611 --> 00:44:05,861 lowering the potential of the VandeGraaff and so these crazy 720 00:44:05,861 --> 00:44:09,597 sparks that occur here can no longer occur. 721 00:44:09,597 --> 00:44:13,985 But now they will. Can you hear them? 722 00:44:13,985 --> 00:44:17,693 And now you can't. If I were crazy then I would 723 00:44:17,693 --> 00:44:21,966 develop a corona discharge between the VandeGraaff and 724 00:44:21,966 --> 00:44:24,868 myself. One way I could do that is by 725 00:44:24,868 --> 00:44:29,14 approach it with my fingertips as I mentioned earlier, 726 00:44:29,14 --> 00:44:33,977 but that may be a little bit too dangerous because I may draw 727 00:44:33,977 --> 00:44:38,169 a spark, I may be hit by lightning, which is the last 728 00:44:38,169 --> 00:44:42,765 thing that I would want today. However, a corona discharge 729 00:44:42,765 --> 00:44:46,663 using these tinsels may be less 730 00:44:46,663 --> 00:44:50,105 dangerous. So I get a continuous flow of 731 00:44:50,105 --> 00:44:55,663 current which now unfortunately doesn't go through the lightning 732 00:44:55,663 --> 00:44:59,546 rod but now it goes straight through my body. 733 00:44:59,546 --> 00:45:03,163 And I can assure you that I can feel that. 734 00:45:03,163 --> 00:45:05,987 It's probably a very low current. 735 00:45:05,987 --> 00:45:08,899 It may be only a few microamperes. 736 00:45:08,899 --> 00:45:12,163 But it's not funny. It's not pleasant. 737 00:45:12,163 --> 00:45:17,458 But anything for my students, what the hell. 738 00:45:17,458 --> 00:45:20,282 There we go. Ya ya ya ya ya. 739 00:45:20,282 --> 00:45:24,99 You see tinsels, I'm now in a corona discharge 740 00:45:24,99 --> 00:45:31,163 and I feel the current through my fingers, it's a continuous 741 00:45:31,163 --> 00:45:33,779 discharge now. This is St. 742 00:45:33,779 --> 00:45:36,708 Elmo's fire. You can't h- ah, 743 00:45:36,708 --> 00:45:42,044 there was lightning. Boy, you got something for your 744 00:45:42,044 --> 00:45:46,019 twenty-seven thousand dollars. Oh, man. 745 00:45:46,019 --> 00:45:48,635 OK. So you saw both corona 746 00:45:48,635 --> 00:45:56,561 discharge and you saw lightning. Boy, you were luckier than the 747 00:45:56,561 --> 00:45:59,733 -- than the first class by the way. 748 00:45:59,733 --> 00:46:04,958 Clearly lightning can be dangerous, lightning can cause a 749 00:46:04,958 --> 00:46:08,784 fire, it can excite, it can explode fumes, 750 00:46:08,784 --> 00:46:14,196 if you gas your car just the flow of gasoline can charge up 751 00:46:14,196 --> 00:46:20,074 the nozzle, friction can charge things up, that's why the nozzle 752 00:46:20,074 --> 00:46:25,019 is always grounded, because a spark could 753 00:46:25,019 --> 00:46:28,943 cause a major explosion. If you fill a balloon with 754 00:46:28,943 --> 00:46:33,338 hydrogen then the flow of hydrogen is friction can charge 755 00:46:33,338 --> 00:46:37,654 up the balloon and a spark can then ignite the hydrogen. 756 00:46:37,654 --> 00:46:41,185 And this has led to a classic tragic accident, 757 00:46:41,185 --> 00:46:44,874 it's a long time ago. But it's so classic that I 758 00:46:44,874 --> 00:46:49,582 really have to show this to you. Hitler was very proud of his 759 00:46:49,582 --> 00:46:52,564 large airships. They're named after Gar 760 00:46:52,564 --> 00:46:56,567 Zeppelin the Germans called them the 761 00:46:56,567 --> 00:47:00,12 Zeppelins, we call them dirigibles or bl- blimps. 762 00:47:00,12 --> 00:47:04,487 And one of the largest ones that Hitler's Germany ever built 763 00:47:04,487 --> 00:47:08,04 was the Hindenburg, eight hundred three feet long 764 00:47:08,04 --> 00:47:11,001 and seven million cubic feet of hydrogen. 765 00:47:11,001 --> 00:47:15,147 And the Germans couldn't fill their Zeppelins with helium 766 00:47:15,147 --> 00:47:19,44 because they didn't have helium. And the Americans were not 767 00:47:19,44 --> 00:47:22,919 going to sell them helium, for very good reason. 768 00:47:22,919 --> 00:47:26,472 And so they had to fill them with 769 00:47:26,472 --> 00:47:29,922 hydrogen. And so the Hindenburg which was 770 00:47:29,922 --> 00:47:34,234 the name of this Zeppelin came over in May nineteen 771 00:47:34,234 --> 00:47:39,495 thirty-seven and when it arrived at Lakehurst in New Jersey it 772 00:47:39,495 --> 00:47:43,894 started a gigantic fire. It came over in thirty-five 773 00:47:43,894 --> 00:47:48,292 hours trans-Atlantic and you see here the explosion. 774 00:47:48,292 --> 00:47:52,173 May six at seven twenty-five in the afternoon. 775 00:47:52,173 --> 00:47:56,313 There were forty-five passengers on 776 00:47:56,313 --> 00:47:59,676 board and thirty-five died in this fire. 777 00:47:59,676 --> 00:48:04,16 The speculation was that this may have been sabotage. 778 00:48:04,16 --> 00:48:08,903 It's still quite possible. Although the official inquiry 779 00:48:08,903 --> 00:48:12,612 board concluded that it was St. Elmo's fire, 780 00:48:12,612 --> 00:48:16,406 that as the uh ship moored on this mast here, 781 00:48:16,406 --> 00:48:20,977 that a spark flew over and that that caused the uh the 782 00:48:20,977 --> 00:48:24,857 explosion, the fire. And it was the end of the 783 00:48:24,857 --> 00:48:29,342 dirigibles for Germany. Napoleon, also not the nicest 784 00:48:29,342 --> 00:48:33,876 man on earth, uh had the suspicion 785 00:48:33,876 --> 00:48:39,495 when many of his soldiers got sick in Egypt that this was the 786 00:48:39,495 --> 00:48:43,99 result of marsh gas. And they suspected that this 787 00:48:43,99 --> 00:48:49,703 bad air that they could smell when they were near marshes that 788 00:48:49,703 --> 00:48:54,76 that was the cause of the disease, bad air in French is 789 00:48:54,76 --> 00:48:59,161 mal air, and so they called the disease malaria. 790 00:48:59,161 --> 00:49:03,563 And so the way that they tested the 791 00:49:03,563 --> 00:49:09,014 air to make sure that the soldiers wouldn't get malaria 792 00:49:09,014 --> 00:49:14,364 was to build a small gun which was like so, this was a 793 00:49:14,364 --> 00:49:19,311 conducting barrel. And they would let some of this 794 00:49:19,311 --> 00:49:23,651 marsh gas in the gun and put a cork on here, 795 00:49:23,651 --> 00:49:27,488 close it off, and here was a sharp pin, 796 00:49:27,488 --> 00:49:33,646 this pin was completely insulated from the barrel, 797 00:49:33,646 --> 00:49:37,211 the conducting barrel, and then they would put some 798 00:49:37,211 --> 00:49:40,206 charge on here, so that the spark would fly 799 00:49:40,206 --> 00:49:43,201 over there. This is really the precursor of 800 00:49:43,201 --> 00:49:45,982 the spark plug that we have in our cars. 801 00:49:45,982 --> 00:49:49,476 It's no different. And so if indeed there was then 802 00:49:49,476 --> 00:49:53,398 this marsh gas in there, there might be an explosion and 803 00:49:53,398 --> 00:49:57,534 that was a warning then that um there may be danger for the 804 00:49:57,534 --> 00:49:59,887 soldiers. Well, this morning I was 805 00:49:59,887 --> 00:50:04,023 walking through the building and I was in Lobby seven and I 806 00:50:04,023 --> 00:50:08,822 smelled some funny, it was a funny smell, 807 00:50:08,822 --> 00:50:12,803 and I was just wondering whether perhaps, 808 00:50:12,803 --> 00:50:18,575 who knows, at MIT anything can happen, whether uh there was 809 00:50:18,575 --> 00:50:23,451 some uh some uh gas there that shouldn't be there. 810 00:50:23,451 --> 00:50:28,527 And so I brought my uh my special gun which is here, 811 00:50:28,527 --> 00:50:33,602 which is uh built after Napoleon and uh you see here 812 00:50:33,602 --> 00:50:38,745 this uh little sphere and I opened up the cork 813 00:50:38,745 --> 00:50:42,867 here and I let some of that air in, Building seven, 814 00:50:42,867 --> 00:50:47,649 and then I decided that we, you and I would do the test and 815 00:50:47,649 --> 00:50:52,513 see whether perhaps there was some uh some gas there that uh 816 00:50:52,513 --> 00:50:56,47 may cause some danger. So I would have to cause a 817 00:50:56,47 --> 00:51:00,098 discharge then inside the -- the barrel here. 818 00:51:00,098 --> 00:51:05,126 I can try to do that by combing my hair uh but that may not be 819 00:51:05,126 --> 00:51:09,248 sufficient amount of charge so I can 820 00:51:09,248 --> 00:51:13,459 always make sure that there will be a spark inside that gun 821 00:51:13,459 --> 00:51:17,307 and use this -- this disk. Which has a little bit more 822 00:51:17,307 --> 00:51:20,356 charge on it. So here is then this uh Lobby 823 00:51:20,356 --> 00:51:23,405 seven gas inside. Now of course there's one 824 00:51:23,405 --> 00:51:27,253 possibility that there was nothing wrong with the air, 825 00:51:27,253 --> 00:51:29,721 in which case you will see nothing. 826 00:51:29,721 --> 00:51:33,424 And there is another possibility that the air wasn't 827 00:51:33,424 --> 00:51:37,779 kosher enough and that you may see here small bloop and since 828 00:51:37,779 --> 00:51:42,111 it's going to be very small at best you 829 00:51:42,111 --> 00:51:46,769 have to be very quiet otherwise you won't hear anything. 830 00:51:46,769 --> 00:51:50,071 And so let's first try now with my comb. 831 00:51:50,071 --> 00:51:54,39 I have my comb here. To see whether I can generate a 832 00:51:54,39 --> 00:51:59,218 spark inside this barrel and that may not work because I'm 833 00:51:59,218 --> 00:52:03,113 not sure that I get enough charge on this comb. 834 00:52:03,113 --> 00:52:08,11 No, that doesn't work at all. Well, let's see whether we can 835 00:52:08,11 --> 00:52:10,915 use this instrument. 836 00:52:10,915 --> 00:52:14,073 I sure hope that we won't get malaria. 837 00:52:14,073 --> 52:19 See you tomorrow.