1 00:00:00 --> 00:00:00,27 2 00:00:00,27 --> 00:00:03,768 Electric fields can induce dipoles in insulators. 3 00:00:03,768 --> 00:00:07,923 Electrons and insulators are bound to the atoms and to the 4 00:00:07,923 --> 00:00:12,005 molecules, unlike conductors, where they can freely move, 5 00:00:12,005 --> 00:00:15,649 and when I apply an external field -- for instance, 6 00:00:15,649 --> 00:00:19,731 a field in this direction, then even though the molecules 7 00:00:19,731 --> 00:00:24,031 or the atoms may be completely spherical, they will become a 8 00:00:24,031 --> 00:00:28,113 little bit elongated in the sense that the electrons will 9 00:00:28,113 --> 00:00:33,07 spend a little bit more time there than they used to, 10 00:00:33,07 --> 00:00:36,507 and so this part become negatively charged and this part 11 00:00:36,507 --> 00:00:39,82 becomes positively charged, and that creates a dipole. 12 00:00:39,82 --> 00:00:43,007 I discussed that with you, already, during the first 13 00:00:43,007 --> 00:00:46,508 lecture, because there's something quite remarkable about 14 00:00:46,508 --> 00:00:49,945 this, that if you have an insulator -- notice the pluses 15 00:00:49,945 --> 00:00:53,195 and the minuses indicate neutral atoms -- and if now, 16 00:00:53,195 --> 00:00:56,696 I apply an electric field, which comes down from the top, 17 00:00:56,696 --> 00:00:59,508 then, you see a slight shift of the electrons, 18 00:00:59,508 --> 00:01:02,383 they spend a little bit more time up than down, 19 00:01:02,383 --> 00:01:05,571 and what you see now is, you see a layer of negative 20 00:01:05,571 --> 00:01:09,055 charge being created at the top, 21 00:01:09,055 --> 00:01:13,223 and a layer of positive charge being created at the bottom. 22 00:01:13,223 --> 00:01:16,744 That's the result of induction, we call that also, 23 00:01:16,744 --> 00:01:19,834 sometimes, polarization. You are polarizing, 24 00:01:19,834 --> 00:01:24,002 in a way, the electric charge. Uh, substances that do this, 25 00:01:24,002 --> 00:01:28,027 we call them dielectrics, and today, we will talk quite a 26 00:01:28,027 --> 00:01:31,835 bit about dielectrics. The first part of my lecture is 27 00:01:31,835 --> 00:01:34,854 on the web, uh, if you go eight oh two web, 28 00:01:34,854 --> 00:01:38,519 you will see there a document which 29 00:01:38,519 --> 00:01:43,484 describes, in great detail, what I'm going to tell you 30 00:01:43,484 --> 00:01:46,576 right now. Suppose we have a plane 31 00:01:46,576 --> 00:01:52,572 capacitor -- two -- planes which I charge with certain potential, 32 00:01:52,572 --> 00:01:56,975 and I have on here, say, a charge plus sigma and 33 00:01:56,975 --> 00:01:59,973 here I have a charge minus sigma. 34 00:01:59,973 --> 00:02:04,001 I'm going to call this free -- you will see, 35 00:02:04,001 --> 00:02:10,841 very shortly why I call this free -- and this is minus free. 36 00:02:10,841 --> 00:02:14,774 So there's a potential difference between the plate, 37 00:02:14,774 --> 00:02:17,782 charge flows on there, it has an area A, 38 00:02:17,782 --> 00:02:22,101 and sigma free is the charge density, how much charge per 39 00:02:22,101 --> 00:02:24,724 unit area. So we're going to get an 40 00:02:24,724 --> 00:02:28,117 electric field, which runs in this direction, 41 00:02:28,117 --> 00:02:32,051 and I call that E free. And the distance between the 42 00:02:32,051 --> 00:02:34,904 plates, say, is D. So this is a given. 43 00:02:34,904 --> 00:02:39,609 I now remove the power supply that I used to give it a certain 44 00:02:39,609 --> 00:02:44,622 potential difference. I completely take it away. 45 00:02:44,622 --> 00:02:48,323 So that means that this charge here is trapped, 46 00:02:48,323 --> 00:02:52,024 can not change. But now I move in a dielectric. 47 00:02:52,024 --> 00:02:54,679 I move in one of those substances. 48 00:02:54,679 --> 00:02:58,702 And what you're going to see here, now, at the top, 49 00:02:58,702 --> 00:03:02,242 you're going to see a negative-induced layer, 50 00:03:02,242 --> 00:03:05,379 and at the bottom, you're going to see a 51 00:03:05,379 --> 00:03:09,724 positive-induced layer. I called it plus-sigma-induced, 52 00:03:09,724 --> 00:03:12,539 and I call this minus-sigma-induced. 53 00:03:12,539 --> 00:03:16,643 And the only reason why I call the 54 00:03:16,643 --> 00:03:22,081 other free, is to distinguish them from the induced charge. 55 00:03:22,081 --> 00:03:25,953 This induced charge, which I have in green, 56 00:03:25,953 --> 00:03:31,208 will produce an electric field which is in the opposite I- 57 00:03:31,208 --> 00:03:34,526 direction, and I call that E-induced. 58 00:03:34,526 --> 00:03:37,568 And clearly, E free is, of course, 59 00:03:37,568 --> 00:03:42,178 the surface charge density divided by epsilon zero, 60 00:03:42,178 --> 00:03:46,879 and E-induced is the induced surface charge density, 61 00:03:46,879 --> 00:03:51,55 divided by epsilon zero. 62 00:03:51,55 --> 00:03:58,29 And so the net E field is the vectorial sum of the two, 63 00:03:58,29 --> 00:04:05,53 so E net -- I gave it a vector -- is E free plus E induced, 64 00:04:05,53 --> 00:04:11,521 vectorially added. Since I'm interested -- I know 65 00:04:11,521 --> 00:04:20,009 the direction already -- since I'm interested in magnitudes, 66 00:04:20,009 --> 00:04:24,248 therefore the strength of the net E field is going to be the 67 00:04:24,248 --> 00:04:28,127 strengths of the E fields created by the so-called free 68 00:04:28,127 --> 00:04:32,221 charge, minus the strengths of the E fields created by the 69 00:04:32,221 --> 00:04:35,454 induced charge, minus -- because this E vector 70 00:04:35,454 --> 00:04:38,614 is down, and this one is in the up direction. 71 00:04:38,614 --> 00:04:42,206 And so, if I now make the assumption that a certain 72 00:04:42,206 --> 00:04:45,941 fraction of the free charge is induced, so I make the 73 00:04:45,941 --> 00:04:50,179 assumption that sigma-induced is some fraction B times sigma 74 00:04:50,179 --> 00:04:52,944 free, I just write, 75 00:04:52,944 --> 00:04:56,588 now, and I for induced and an F for free. 76 00:04:56,588 --> 00:05:00,414 B is smaller than one. If B were point one, 77 00:05:00,414 --> 00:05:05,516 it means that sigma-induced would be ten percent of sigma 78 00:05:05,516 --> 00:05:10,618 free, that's the meaning of B. So clearly, if this is the 79 00:05:10,618 --> 00:05:14,808 case, then, also, E of I must also me B times E 80 00:05:14,808 --> 00:05:17,542 of F. You can tell immediately, 81 00:05:17,542 --> 00:05:21,823 they are connected. And so now I can write down, 82 00:05:21,823 --> 00:05:26,379 for E net, I can also write down E 83 00:05:26,379 --> 00:05:30,655 free times one minus B, and that one minus B, 84 00:05:30,655 --> 00:05:35,807 now, we call one over kappa. I call it one over kappa, 85 00:05:35,807 --> 00:05:41,638 our book calls it one over K. But I'm so used to kappa that I 86 00:05:41,638 --> 00:05:44,846 decided to still hold on to kappa. 87 00:05:44,846 --> 00:05:50,289 And that K, or that kappa, whichever you want to call it, 88 00:05:50,289 --> 00:05:53,496 is called the dielectric constant. 89 00:05:53,496 --> 00:05:59,911 It's a dimensionless number. And so I can write down, 90 00:05:59,911 --> 00:06:04,262 now, in general, that E -- and I drop the word 91 00:06:04,262 --> 00:06:08,227 net, now, from now on, whenever I write E, 92 00:06:08,227 --> 00:06:13,254 throughout this lecture, it's always the net electric 93 00:06:13,254 --> 00:06:18,379 field, takes both into account. So you can write down, 94 00:06:18,379 --> 00:06:22,536 now, that E equals the free electric fields, 95 00:06:22,536 --> 00:06:27,177 divided by kappa, because one minus B is one over 96 00:06:27,177 --> 00:06:30,562 kappa. And so you see, 97 00:06:30,562 --> 00:06:34,101 in this experiment that I did in my head, first, 98 00:06:34,101 --> 00:06:38,468 bringing charge on the plate, certain potential difference, 99 00:06:38,468 --> 00:06:42,685 removing the power supply, shoving in the dielectric that 100 00:06:42,685 --> 00:06:45,773 an E field will go down by a factor kappa. 101 00:06:45,773 --> 00:06:48,107 Kappa, for glass, is about five. 102 00:06:48,107 --> 00:06:52,475 That will be a major reduction, I will show you that later. 103 00:06:52,475 --> 00:06:56,24 If the electric field goes down, in this particular 104 00:06:56,24 --> 00:07:01,06 experiment, it is clear that the potential difference between the 105 00:07:01,06 --> 00:07:05,835 plates will also go down, because the potential 106 00:07:05,835 --> 00:07:10,364 difference between the plates V is always the electric field 107 00:07:10,364 --> 00:07:14,739 between the plates times D. And so, if this one goes down, 108 00:07:14,739 --> 00:07:18,04 by a factor of kappa, if I just shove in the 109 00:07:18,04 --> 00:07:21,341 dielectric, not changing D, then, of course, 110 00:07:21,341 --> 00:07:25,256 the potential between the plates is also going down. 111 00:07:25,256 --> 00:07:29,554 None of this is so intuitive, but I will demonstrate that 112 00:07:29,554 --> 00:07:31,857 later. The question now arises, 113 00:07:31,857 --> 00:07:36,617 does Gauss' Law still hold? And the answer is, 114 00:07:36,617 --> 00:07:40,443 yes, of course, Gauss' Law will still hold. 115 00:07:40,443 --> 00:07:45,728 Gauss' Law tells me that the closed loop -- closed surface, 116 00:07:45,728 --> 00:07:49,555 I should say, not closed loop -- the closed 117 00:07:49,555 --> 00:07:55,204 surface integral of E dot D A is one over epsilon times the sum 118 00:07:55,204 --> 00:07:58,119 of all the charges inside my box. 119 00:07:58,119 --> 00:08:01,035 All the charges! The net charges, 120 00:08:01,035 --> 00:08:05,682 that must take into account both the induced charge, 121 00:08:05,682 --> 00:08:09,514 as well as the free charge. 122 00:08:09,514 --> 00:08:14,709 And so let me write down here, net, to remind you that. 123 00:08:14,709 --> 00:08:18,268 But Q net is, of course, Q free plus Q 124 00:08:18,268 --> 00:08:21,827 induced. And I want to remind you that 125 00:08:21,827 --> 00:08:24,906 this is minus, and this was plus. 126 00:08:24,906 --> 00:08:27,888 The free charge, positive there, 127 00:08:27,888 --> 00:08:33,371 is plus, and at that same plate, if you have your Gaussian 128 00:08:33,371 --> 00:08:39,624 surface at the top, you have the negative charged Q 129 00:08:39,624 --> 00:08:41,592 induced. And so therefore, 130 00:08:41,592 --> 00:08:45,843 Gauss' Law simply means that you have to take both into 131 00:08:45,843 --> 00:08:49,386 account, and so, therefore, you can write down 132 00:08:49,386 --> 00:08:53,008 one over epsilon zero, times the sum of Q free, 133 00:08:53,008 --> 00:08:57,81 but now you have to make sure that you take the induced charge 134 00:08:57,81 --> 00:08:59,936 into account, and therefore, 135 00:08:59,936 --> 00:09:02,692 you divide the whole thing by kappa. 136 00:09:02,692 --> 00:09:07,101 Then you have automatically taken the induced charge into 137 00:09:07,101 --> 00:09:09,699 account. So you can amend mex- uh, 138 00:09:09,699 --> 00:09:14,82 Gauss' Law very easily by this factor of kappa. 139 00:09:14,82 --> 00:09:17,662 Dielectric constant is dimensionless, 140 00:09:17,662 --> 00:09:21,136 as I mentioned already, it is one, in vacuum, 141 00:09:21,136 --> 00:09:24,609 by definition. One atmosphere gases typically 142 00:09:24,609 --> 00:09:28,715 have dielectric constant just a hair larger than one. 143 00:09:28,715 --> 00:09:32,504 We will, most of the time, assume that it is one. 144 00:09:32,504 --> 00:09:35,82 Plastic has a dielectric constant of three, 145 00:09:35,82 --> 00:09:39,531 and glass, which is an extremely good insulator, 146 00:09:39,531 --> 00:09:42,136 has a dielectric constant of five. 147 00:09:42,136 --> 00:09:47,747 If you have an external field, that can induce dipoles in 148 00:09:47,747 --> 00:09:50,97 molecules -- but there are substances, however, 149 00:09:50,97 --> 00:09:55,103 which themselves are already dipoles, even in the absence of 150 00:09:55,103 --> 00:09:57,275 an electric field. If you apply, 151 00:09:57,275 --> 00:10:00,778 now, an external field, these dipoles will start to 152 00:10:00,778 --> 00:10:04,771 align along the electric field, we did an experiment once, 153 00:10:04,771 --> 00:10:08,134 with some grass seeds, perhaps you remember that. 154 00:10:08,134 --> 00:10:12,057 And as they align in the direction of the electric field, 155 00:10:12,057 --> 00:10:15,49 they will strengthen the electric 156 00:10:15,49 --> 00:10:17,038 field. On the other hand, 157 00:10:17,038 --> 00:10:19,813 because of the temperature of the substance, 158 00:10:19,813 --> 00:10:22,587 these dipoles, these molecules which are now 159 00:10:22,587 --> 00:10:25,491 dipoles by themselves, through chaotic motion, 160 00:10:25,491 --> 00:10:28,395 will try to disalign, temperature is trying to 161 00:10:28,395 --> 00:10:30,718 disalign them. So it is going to be a 162 00:10:30,718 --> 00:10:34,267 competition, on the one hand, between the electric field 163 00:10:34,267 --> 00:10:38,074 which tries to align them and the temperature which tries to 164 00:10:38,074 --> 00:10:40,784 disalign them. But if the electric field is 165 00:10:40,784 --> 00:10:45,495 strong, you can get a substantial amount of alignment. 166 00:10:45,495 --> 00:10:48,814 Uh, permanent dipoles, as a rule, are way stronger 167 00:10:48,814 --> 00:10:52,676 that any dipole that you can induce by ordinary means in a 168 00:10:52,676 --> 00:10:56,063 laboratory, and so the substances which are natural 169 00:10:56,063 --> 00:10:59,315 dipoles, they have a much higher value for kappa, 170 00:10:59,315 --> 00:11:02,838 a much higher dielectric constant that the substances 171 00:11:02,838 --> 00:11:05,48 that I just discussed, which themselves, 172 00:11:05,48 --> 00:11:08,19 do not have dipoles. Water is an example, 173 00:11:08,19 --> 00:11:11,645 extremely good example. The electrons spend a little 174 00:11:11,645 --> 00:11:15,438 bit more time near the oxygen than near 175 00:11:15,438 --> 00:11:18,631 the hydrogen, and water has a dielectric 176 00:11:18,631 --> 00:11:21,497 constant of eighty. That's enormous. 177 00:11:21,497 --> 00:11:26,245 And if you go down to lower temperature, if you take ice of 178 00:11:26,245 --> 00:11:29,357 minus forty degrees, it is even higher, 179 00:11:29,357 --> 00:11:32,877 then the dielectric constant is one hundred. 180 00:11:32,877 --> 00:11:37,462 I'm now going to massage you through four demonstrations, 181 00:11:37,462 --> 00:11:39,836 four experiments. One of them, 182 00:11:39,836 --> 00:11:43,684 you have already seen. And try to follow them as 183 00:11:43,684 --> 00:11:48,489 closely as you can, because if you miss 184 00:11:48,489 --> 00:11:51,176 one small step, then you miss, 185 00:11:51,176 --> 00:11:54,976 perhaps, a lot. I have two parallel plates 186 00:11:54,976 --> 00:11:59,979 which a- are on this table, as you have seen last time, 187 00:11:59,979 --> 00:12:03,037 and I have, here, a current meter, 188 00:12:03,037 --> 00:12:07,393 I put it -- an A on there, that means amp meter. 189 00:12:07,393 --> 00:12:11,284 And the plates have a certain separation D. 190 00:12:11,284 --> 00:12:16,474 I'm going to charge this capacitor up by connecting these 191 00:12:16,474 --> 00:12:22,095 ends to a power supply, and I'm going to connect them 192 00:12:22,095 --> 00:12:25,972 to fifteen hundred volts. I'm -- I'm already going to set 193 00:12:25,972 --> 00:12:29,919 my light, because that's where you're going to see it very 194 00:12:29,919 --> 00:12:32,48 shortly. I'm going to start off with a 195 00:12:32,48 --> 00:12:36,703 distance D -- so this is going to be my experiment one -- with 196 00:12:36,703 --> 00:12:40,927 a distance D of one millimeter. And the voltage V always means 197 00:12:40,927 --> 00:12:45,15 the voltage the -- the -- the potential difference between the 198 00:12:45,15 --> 00:12:48,127 plates is going to be fifteen hundred volts. 199 00:12:48,127 --> 00:12:52,489 Forgive me for the two Vs, I can't help that. 200 00:12:52,489 --> 00:12:55,884 This means, here, the potential difference, 201 00:12:55,884 --> 00:13:00,329 and this is the unit in volts. Once I have charged them, 202 00:13:00,329 --> 00:13:04,936 I disconnect -- this is very important -- I disconnect the 203 00:13:04,936 --> 00:13:07,764 power supply, for which I write P S. 204 00:13:07,764 --> 00:13:10,916 That's it. So the charge is now trapped. 205 00:13:10,916 --> 00:13:13,826 As I charge it, as you saw last time, 206 00:13:13,826 --> 00:13:18,837 you will see that the amp meter shows a short surge of current, 207 00:13:18,837 --> 00:13:24,574 because, as I put charge on the plates, the charge has to go 208 00:13:24,574 --> 00:13:28,729 from the power supply to the plates, and you will see a short 209 00:13:28,729 --> 00:13:32,953 surge of current which will make the handle -- the hand of the 210 00:13:32,953 --> 00:13:36,761 power su- of the amp meter, as you will see on the -- on 211 00:13:36,761 --> 00:13:40,361 the wall there -- go to the right side, just briefly, 212 00:13:40,361 --> 00:13:43,547 and then come back. This indicates that you are 213 00:13:43,547 --> 00:13:46,939 charging the plates. Now, I'm going to open up the 214 00:13:46,939 --> 00:13:50,401 gap -- so this is my initial condition, there is no 215 00:13:50,401 --> 00:13:54,421 dielectric -- and now I'm going to go D to 216 00:13:54,421 --> 00:13:57,655 seven millimeters. And this is what I did last 217 00:13:57,655 --> 00:14:00,098 time. The reason why I do it again, 218 00:14:00,098 --> 00:14:03,331 because I need this for my next demonstration. 219 00:14:03,331 --> 00:14:07,426 If I make the distance seven millimeters, then the charge, 220 00:14:07,426 --> 00:14:10,66 which I call now, Q free, but it is really the 221 00:14:10,66 --> 00:14:14,181 charge on the plates, is not going to be -- is not 222 00:14:14,181 --> 00:14:16,336 going to change, it is trapped. 223 00:14:16,336 --> 00:14:19,785 So there can be no change when I open up the gap. 224 00:14:19,785 --> 00:14:23,378 That means the amp meter will do 225 00:14:23,378 --> 00:14:28,008 nothing, you will not see any charge flow. 226 00:14:28,008 --> 00:14:33,881 The electric field E is unchanged, because E is sigma 227 00:14:33,881 --> 00:14:39,303 divided by epsilon zero. If sig- if Q free is not 228 00:14:39,303 --> 00:14:45,966 changing, sigma cannot change. So, no change in the electric 229 00:14:45,966 --> 00:14:49,581 field. But the potential V is now 230 00:14:49,581 --> 00:14:56,357 going to go up by a factor of seven, because V equals E times 231 00:14:56,357 --> 00:14:59,728 D. E remains constant, 232 00:14:59,728 --> 00:15:04,758 D goes up, V has to go up. And this is what I want to show 233 00:15:04,758 --> 00:15:09,083 you first, even though you have already seen this. 234 00:15:09,083 --> 00:15:14,378 And I need the new conditions for my demonstration that comes 235 00:15:14,378 --> 00:15:17,996 afterwards. I'm going from fifteen hundred 236 00:15:17,996 --> 00:15:23,203 volts to about ten thousand volts, it goes up by a factor of 237 00:15:23,203 --> 00:15:26,203 seven. And you're going to see that 238 00:15:26,203 --> 00:15:30,615 there. There you see your amp meter. 239 00:15:30,615 --> 00:15:34,765 I'm going to -- you see the, um, this is this propeller volt 240 00:15:34,765 --> 00:15:38,774 meter that we discussed last time, and here you see the -- 241 00:15:38,774 --> 00:15:41,517 the plates. They're one millimeter apart 242 00:15:41,517 --> 00:15:44,542 now, very close. And I'm going to charge the 243 00:15:44,542 --> 00:15:48,269 plates, I will count down, so you keep your amp meter, 244 00:15:48,269 --> 00:15:51,294 three, two, one, zero, and you saw a current 245 00:15:51,294 --> 00:15:53,615 surge. So I charged the capacitor. 246 00:15:53,615 --> 00:15:56,78 It is charged now. The volt meter doesn't show 247 00:15:56,78 --> 00:16:00,297 very much, fifteen hundred volts. 248 00:16:00,297 --> 00:16:02,895 Maybe it went up a little, but not very much, 249 00:16:02,895 --> 00:16:06,143 but now I'm going to increase the gap to ten -- to seven 250 00:16:06,143 --> 00:16:09,804 millimeters, and look that the amp meter is not doing anything, 251 00:16:09,804 --> 00:16:12,875 the charge is trapped, so there is no charge going to 252 00:16:12,875 --> 00:16:15,768 the plates, but look what the volt meter is doing. 253 00:16:15,768 --> 00:16:19,252 It's increasing the voltage, it's not approaching almost ten 254 00:16:19,252 --> 00:16:21,614 thousand volts, although this is not very 255 00:16:21,614 --> 00:16:24,094 quantitative, and now I have a gap of about 256 00:16:24,094 --> 00:16:26,634 seven millimeters, and that's what I wanted. 257 00:16:26,634 --> 00:16:29,882 We've seen that the plates on the left side here are now 258 00:16:29,882 --> 00:16:33,248 farther apart than they were before. 259 00:16:33,248 --> 00:16:38,53 So that is my demonstration number one, a repeat of what we 260 00:16:38,53 --> 00:16:41,991 did last time. So now comes number two. 261 00:16:41,991 --> 00:16:47,456 So now my initial conditions are that V is now ten kilovolts, 262 00:16:47,456 --> 00:16:52,192 so that's the potential difference between the plates 263 00:16:52,192 --> 00:16:56,473 that I have now, and D is now seven millimeters, 264 00:16:56,473 --> 00:16:59,388 and I'm not going to change that. 265 00:16:59,388 --> 00:17:01,938 At this moment, kappa is one. 266 00:17:01,938 --> 00:17:07,371 But now, I'm going to insert the dielectric. 267 00:17:07,371 --> 00:17:13,134 So I take a piece of glass, and I'll just put it into that 268 00:17:13,134 --> 00:17:16,166 gap. Q free cannot go anywhere, 269 00:17:16,166 --> 00:17:20,615 because I have disconnected the power supply. 270 00:17:20,615 --> 00:17:25,771 So Q free, no change. If there is no chee- no change 271 00:17:25,771 --> 00:17:30,724 in the free charge, the amp meter will do nothing. 272 00:17:30,724 --> 00:17:36,184 So as I plunge in this dielectric, you will not see any 273 00:17:36,184 --> 00:17:42,094 reading on the amp meter. But, as we discussed at length 274 00:17:42,094 --> 00:17:45,308 now, the electric field, which is the net electric 275 00:17:45,308 --> 00:17:47,931 field, will go down by that factor kappa. 276 00:17:47,931 --> 00:17:50,948 That's what the whole discussion was all about. 277 00:17:50,948 --> 00:17:53,244 That's going to be a factor of five. 278 00:17:53,244 --> 00:17:57,245 And since the potential equals electric field times D -- but I 279 00:17:57,245 --> 00:18:00,983 keep D at seven millimeters, I'm not going to change it -- 280 00:18:00,983 --> 00:18:04 if E goes down by a factor kappa, then clearly, 281 00:18:04 --> 00:18:07,214 the potential will also go down by a factor kappa. 282 00:18:07,214 --> 00:18:11,018 So now you're going to see the second part, and that is I'm 283 00:18:11,018 --> 00:18:13,704 going -- as it is now, 284 00:18:13,704 --> 00:18:17,3 I'm going to plunge in this glass, the seven millimeters 285 00:18:17,3 --> 00:18:20,896 thick, I put it in there, you expect to see no change on 286 00:18:20,896 --> 00:18:23,512 the amp meter, but you expect the voltage 287 00:18:23,512 --> 00:18:27,238 difference over the plates to go down by a factor of five, 288 00:18:27,238 --> 00:18:30,965 so you will see that -- that the propeller volt meter will 289 00:18:30,965 --> 00:18:33,907 have a smaller deflection. You ready for this? 290 00:18:33,907 --> 00:18:36,13 There we go. Now you have a smaller 291 00:18:36,13 --> 00:18:39,072 potential difference, but there was no current 292 00:18:39,072 --> 00:18:42,014 flowing through the plates or from the plates. 293 00:18:42,014 --> 00:18:47,353 When I take it out again, the potential difference comes 294 00:18:47,353 --> 00:18:52,224 back to the ten thousand volts. So that's demonstration number 295 00:18:52,224 --> 00:18:54,621 two. Now we go to number three. 296 00:18:54,621 --> 00:18:59,173 But before we go to number three, I want to ask myself the 297 00:18:59,173 --> 00:19:03,885 question, what actually happened with the capacitance when I 298 00:19:03,885 --> 00:19:07,16 bring the dielectric between those plates? 299 00:19:07,16 --> 00:19:11,153 Well, the capacitance is defined as the free charge 300 00:19:11,153 --> 00:19:16,424 divided by the potential difference over the plates. 301 00:19:16,424 --> 00:19:19,015 That's the definition of capacitance. 302 00:19:19,015 --> 00:19:22,397 And since, in this experiment, as you have seen, 303 00:19:22,397 --> 00:19:25,419 the voltage went down by a factor of kappa, 304 00:19:25,419 --> 00:19:28,585 the capacitance goes up by a factor of kappa, 305 00:19:28,585 --> 00:19:30,815 because Q free was not changing. 306 00:19:30,815 --> 00:19:34,989 And so, since the capacitance, as we derived this last time 307 00:19:34,989 --> 00:19:38,371 for plane -- plate capacitors, I still remember, 308 00:19:38,371 --> 00:19:42,76 it was the area times epsilon zero divided by the separation D 309 00:19:42,76 --> 00:19:46,43 -- since we now know that with the 310 00:19:46,43 --> 00:19:49,923 glass in place, that's -- the capacitance is 311 00:19:49,923 --> 00:19:54,472 higher by a factor of kappa, this is now the amendment we 312 00:19:54,472 --> 00:19:57,559 have to make. To calculate capacitance, 313 00:19:57,559 --> 00:20:02,271 we simply have to multiply, now, by the dielectric constant 314 00:20:02,271 --> 00:20:06,414 of the thin layer that separates the two conductors, 315 00:20:06,414 --> 00:20:10,964 the layer that has thickness D that is in between the two 316 00:20:10,964 --> 00:20:12,507 plates. In our case, 317 00:20:12,507 --> 00:20:16 I brought in glass. I could write down a few 318 00:20:16 --> 00:20:20,627 equations now that you can always hold on 319 00:20:20,627 --> 00:20:24,195 to in your life, and you can also use them in 320 00:20:24,195 --> 00:20:26,952 the two demonstrations that follow. 321 00:20:26,952 --> 00:20:30,683 And one is that E -- which is always the net E, 322 00:20:30,683 --> 00:20:35,387 when I write E it's always the net one -- equals sigma free 323 00:20:35,387 --> 00:20:38,225 divided by epsilon zero times kappa. 324 00:20:38,225 --> 00:20:41,956 There comes that kappa that we discussed today. 325 00:20:41,956 --> 00:20:44,794 Let's call that equation number one. 326 00:20:44,794 --> 00:20:49,011 The second one is that the potential 327 00:20:49,011 --> 00:20:53,176 difference over the plates is always the electric field 328 00:20:53,176 --> 00:20:57,65 between the plates times D, because the integral of E dot D 329 00:20:57,65 --> 00:21:01,583 L, over a certain pass, is the potential difference. 330 00:21:01,583 --> 00:21:06,057 That's not going to change. And then the third one that may 331 00:21:06,057 --> 00:21:09,913 come in handy is the one that I have already there, 332 00:21:09,913 --> 00:21:13,847 C equals Q free divided by the potential difference, 333 00:21:13,847 --> 00:21:18,32 which, in terms of the plate area, is A times epsilon zero, 334 00:21:18,32 --> 00:21:22,25 divided by D, times kappa. 335 00:21:22,25 --> 00:21:27,188 Let's call this equation number three. 336 00:21:27,188 --> 00:21:34,796 Now comes my third experiment. In the third demonstration, 337 00:21:34,796 --> 00:21:40,668 I am not going to disconnect my power supply. 338 00:21:40,668 --> 00:21:47,074 So now, in number three, I start out with fifteen 339 00:21:47,074 --> 00:21:54,147 hundred volts, just like we did with number 340 00:21:54,147 --> 00:21:59,57 one, but the power supply will stay in there throughout, 341 00:21:59,57 --> 00:22:03,908 never take it off. We start with D equals one 342 00:22:03,908 --> 00:22:08,443 millimeter, just like we did in experiment one. 343 00:22:08,443 --> 00:22:11,894 No glass. I'm going to charge it up, 344 00:22:11,894 --> 00:22:16,528 just like I did with number one, and, of course, 345 00:22:16,528 --> 00:22:21,556 I will see that the amp meter will show this charge. 346 00:22:21,556 --> 00:22:24,415 [clk]. See a surge of current. 347 00:22:24,415 --> 00:22:29,443 Now I'm going to increase D to seven 348 00:22:29,443 --> 00:22:32,875 millimeters. Now something very different 349 00:22:32,875 --> 00:22:37,337 will happen from what we saw in the first experiment. 350 00:22:37,337 --> 00:22:41,97 The reason is that the potential difference is going to 351 00:22:41,97 --> 00:22:46,603 be fixed, because the power supply is not disconnected, 352 00:22:46,603 --> 00:22:49,263 the power supply stays in place. 353 00:22:49,263 --> 00:22:52,094 Look, now, at equation number two. 354 00:22:52,094 --> 00:22:56,813 If that V cannot change, and if I increase D by a factor 355 00:22:56,813 --> 00:23:02,047 of seven, now the electric field must come down by a factor of 356 00:23:02,047 --> 00:23:06,292 seven. And so now the electric field 357 00:23:06,292 --> 00:23:10,993 will come down by that factor of seven, because I go from one 358 00:23:10,993 --> 00:23:15,458 millimeter to seven millimeters. So now the electric field 359 00:23:15,458 --> 00:23:19,924 changes, because D goes up. In case you were interested in 360 00:23:19,924 --> 00:23:23,371 the capacitance, the capacitance will also go 361 00:23:23,371 --> 00:23:27,601 down by a factor of seven, because, if you look at this 362 00:23:27,601 --> 00:23:31,675 equation, kappa is one. If I make D go up by a factor 363 00:23:31,675 --> 00:23:36,168 of seven, C goes down by a factor of seven. 364 00:23:36,168 --> 00:23:38,949 Just look at this, simple as that. 365 00:23:38,949 --> 00:23:42,572 So C must also go down by a factor of seven. 366 00:23:42,572 --> 00:23:45,774 Nothing to do with dielectric. Nothing. 367 00:23:45,774 --> 00:23:50,493 And so Q free must now also go down by a factor of seven, 368 00:23:50,493 --> 00:23:54,706 because if the potential difference doesn't change, 369 00:23:54,706 --> 00:23:59,509 but if Q free goes down a factor of seven -- or by -- if C 370 00:23:59,509 --> 00:24:04,733 goes down by a factor of seven, Q free must go down by a factor 371 00:24:04,733 --> 00:24:06,699 of seven. 372 00:24:06,699 --> 00:24:10,897 This goes down by a factor of seven, this doesn't change. 373 00:24:10,897 --> 00:24:14,569 So the free charge goes down by a factor of seven. 374 00:24:14,569 --> 00:24:18,392 And what does that mean? That means charge will flow 375 00:24:18,392 --> 00:24:21,165 from the plates, away from the plates, 376 00:24:21,165 --> 00:24:25,512 and so my amp meter will now -- will tell me that charge is 377 00:24:25,512 --> 00:24:29,635 flowing from the plates, and so that handle -- that hand 378 00:24:29,635 --> 00:24:32,333 there will go [wssshhht] to the left. 379 00:24:32,333 --> 00:24:36,08 And so, as I open up, depending upon how fast I can 380 00:24:36,08 --> 00:24:40,044 do that, charge will flow from the 381 00:24:40,044 --> 00:24:44,895 plates, in the other direction, it -- the charge will flow off 382 00:24:44,895 --> 00:24:48,711 the plates, and that current meter will show you, 383 00:24:48,711 --> 00:24:52,21 every time that I open it a little bit [klk], 384 00:24:52,21 --> 00:24:56,344 it will go to this direction. So let's do that first, 385 00:24:56,344 --> 00:25:00,638 no dielectric involved, simply keeping the power supply 386 00:25:00,638 --> 00:25:03,103 connected. So I have to go back, 387 00:25:03,103 --> 00:25:08,509 first, to one millimeter, which is what I'm doing now, 388 00:25:08,509 --> 00:25:13,115 I have here this thin sheet to make sure that I don't short 389 00:25:13,115 --> 00:25:17,323 them out, it's about one millimeter, and I am going to 390 00:25:17,323 --> 00:25:21,531 now connect the fifteen hundred volts, and keep it on, 391 00:25:21,531 --> 00:25:25,422 and as I charge it, you will see the current meter 392 00:25:25,422 --> 00:25:27,407 surge to the right, right? 393 00:25:27,407 --> 00:25:30,424 That always means we charge the plates. 394 00:25:30,424 --> 00:25:32,806 So there we go, did you see it? 395 00:25:32,806 --> 00:25:36,3 I didn't see it because I had to concentrate. 396 00:25:36,3 --> 00:25:39,589 Did it go like this? Good. 397 00:25:39,589 --> 00:25:43,032 So now it's charged. We don't take this connection 398 00:25:43,032 --> 00:25:46,827 off, it's connected with the power supply all the time. 399 00:25:46,827 --> 00:25:50,833 And now I'm going to open up, and as I'm going to open up, 400 00:25:50,833 --> 00:25:55,19 the potential remains the same, so this volt meter doesn't give 401 00:25:55,19 --> 00:25:59,126 a damn, it will stay exactly where it is, because fifteen 402 00:25:59,126 --> 00:26:02,148 hundred volts remains fifteen hundred volts, 403 00:26:02,148 --> 00:26:06,224 but now, we go -- as we open up, we're going to take charge 404 00:26:06,224 --> 00:26:11,071 off the plates and so this, I expect to go to the left. 405 00:26:11,071 --> 00:26:14,587 Every time that I give it a little jerk, I do it now, 406 00:26:14,587 --> 00:26:16,75 it went to the left. I go it now, 407 00:26:16,75 --> 00:26:20,469 again, I go to two millimeters, go to three millimeters, 408 00:26:20,469 --> 00:26:23,714 go to four millimeters, make it five millimeters, 409 00:26:23,714 --> 00:26:25,945 five millimeters, six millimeters, 410 00:26:25,945 --> 00:26:28,717 and I finally end up at seven millimeters. 411 00:26:28,717 --> 00:26:32,706 And every time that I made it larger, you saw the hand go to 412 00:26:32,706 --> 00:26:35,275 the left. Every time I took some charge 413 00:26:35,275 --> 00:26:37,641 off. So that is demonstration number 414 00:26:37,641 --> 00:26:39,467 three. Why did I go to seven 415 00:26:39,467 --> 00:26:43,551 millimeters? You've guessed it! 416 00:26:43,551 --> 00:26:47,319 Now I want to plunge in the dielectric. 417 00:26:47,319 --> 00:26:52,972 So my experiment number four, I start with fifteen hundred 418 00:26:52,972 --> 00:26:57,535 volts, I start with D equals seven millimeters, 419 00:26:57,535 --> 00:27:00,708 and I'm not going to change that. 420 00:27:00,708 --> 00:27:06,857 There's no dielectric in place, but now, I put a dielectric in. 421 00:27:06,857 --> 00:27:12,609 So kappa goes in. What now is going to happen? 422 00:27:12,609 --> 00:27:16,039 Well, for sure, V is unchanged, 423 00:27:16,039 --> 00:27:21,068 because it's connected with the power supply, 424 00:27:21,068 --> 00:27:26,441 so that cannot change. What happens with Q free? 425 00:27:26,441 --> 00:27:32,385 Look at this equation. W hen I put in the dielectric, 426 00:27:32,385 --> 00:27:38,787 I know that the capacitance goes up by a factor of kappa. 427 00:27:38,787 --> 00:27:43,931 C will go up by a factor of kappa. 428 00:27:43,931 --> 00:27:48,324 If C goes up with a factor of kappa, and if V is not changing, 429 00:27:48,324 --> 00:27:51,421 then Q free must go up by a factor of kappa. 430 00:27:51,421 --> 00:27:54,23 Follows immediately from equation three. 431 00:27:54,23 --> 00:27:57,039 So this must go up by a factor of kappa. 432 00:27:57,039 --> 00:28:00,28 What does that mean? That the charge will flow 433 00:28:00,28 --> 00:28:03,666 through the plates. I increase the charge on the 434 00:28:03,666 --> 00:28:06,907 plates, and so my amp meter will tell me that. 435 00:28:06,907 --> 00:28:09,356 And so my amp meter will say, "Aha! 436 00:28:09,356 --> 00:28:14,614 I have to put charge on the plates," and so my amp meter 437 00:28:14,614 --> 00:28:19,513 will now do this. And that's what I want to show 438 00:28:19,513 --> 00:28:22,119 you. The remarkable thing, 439 00:28:22,119 --> 00:28:28,269 now, is that the electric field E, the net electric field E, 440 00:28:28,269 --> 00:28:31,814 will not change. And you may say, 441 00:28:31,814 --> 00:28:37,86 "But you put in a dielectric!" Sure, I put in a dielectric. 442 00:28:37,86 --> 00:28:42,446 But I kept the potential difference constant, 443 00:28:42,446 --> 00:28:47,31 and I kept the D constant. 444 00:28:47,31 --> 00:28:51,136 And since V is always E times D, if I keep this at fifteen 445 00:28:51,136 --> 00:28:54,156 hundred volts, and I keep the seven millimeter 446 00:28:54,156 --> 00:28:57,176 seven millimeters, then the net electric field 447 00:28:57,176 --> 00:28:59,726 cannot change, it's exactly what it was 448 00:28:59,726 --> 00:29:02,142 before. That is the reason why Q free 449 00:29:02,142 --> 00:29:04,222 has to change, think about that. 450 00:29:04,222 --> 00:29:07,444 Because you do introduce -- induce charges on the 451 00:29:07,444 --> 00:29:11,336 dielectric, and you have to compensate for that to keep the 452 00:29:11,336 --> 00:29:14,356 E field constant, and the only way that nature 453 00:29:14,356 --> 00:29:17,98 can com- compensate for that is to 454 00:29:17,98 --> 00:29:21,606 increase the charge on the plates, the free charge. 455 00:29:21,606 --> 00:29:24,579 And so that's what I want to show you now, 456 00:29:24,579 --> 00:29:28,422 which is the last part. So I'm going now to put in the 457 00:29:28,422 --> 00:29:32,773 dielectric, and what you will see, then, is that current will 458 00:29:32,773 --> 00:29:36,036 flow onto the plates, so the propeller will do 459 00:29:36,036 --> 00:29:39,806 nothing, will sit there, and you will see this one go 460 00:29:39,806 --> 00:29:43,722 klunk when I bring in the glass. And then it goes back, 461 00:29:43,722 --> 00:29:46,477 of course. There's only a little charge 462 00:29:46,477 --> 00:29:49,087 that comes off, and 463 00:29:49,087 --> 00:29:52,173 then it will go back. So as I plunge it in, 464 00:29:52,173 --> 00:29:55,331 you will see charge flowing onto the plates. 465 00:29:55,331 --> 00:29:57,682 There we go, you're ready for it? 466 00:29:57,682 --> 00:29:59,225 Three, two, one, zero. 467 00:29:59,225 --> 00:30:02,457 And you saw a charge flowing onto the plates. 468 00:30:02,457 --> 00:30:06,497 When I remove the glass, of course, then the charge goes 469 00:30:06,497 --> 00:30:09,582 off the plates again, and you see that now. 470 00:30:09,582 --> 00:30:12,08 I've shown you four demonstrations. 471 00:30:12,08 --> 00:30:14,871 None of this is intuitive. Not for you, 472 00:30:14,871 --> 00:30:19,425 and not for me. Whenever I do these things, 473 00:30:19,425 --> 00:30:22,096 I have to very carefully sit down and think, 474 00:30:22,096 --> 00:30:25,201 what actually is changing and what is not changing? 475 00:30:25,201 --> 00:30:27,126 I have not gut feeling for that. 476 00:30:27,126 --> 00:30:30,045 There is not something in me that says, "Oh yes, 477 00:30:30,045 --> 00:30:32,032 of course that's going to happen. 478 00:30:32,032 --> 00:30:34,454 Not at all. And I don't expect that from 479 00:30:34,454 --> 00:30:36,876 you, either. Then only advice I have for 480 00:30:36,876 --> 00:30:40,539 you, when you're dealing with these cases whereby dielectric 481 00:30:40,539 --> 00:30:43,272 goes in, dielectric goes in, plates separate, 482 00:30:43,272 --> 00:30:45,942 plates not separate, power supply connected, 483 00:30:45,942 --> 00:30:48,923 power supply not connected, approach it in a very 484 00:30:48,923 --> 00:30:54,045 cold-blooded way, a real classical MIT way, 485 00:30:54,045 --> 00:30:58,074 very cold-blooded. Think about what is not 486 00:30:58,074 --> 00:31:03,676 changing, and then pick it up from there, and see what the 487 00:31:03,676 --> 00:31:08,589 consequences would be. How can I build a very large 488 00:31:08,589 --> 00:31:13,307 capacitor, one that has a very large capacitance? 489 00:31:13,307 --> 00:31:16,55 Well, capacitance, C, is the area, 490 00:31:16,55 --> 00:31:19,694 times epsilon zero, divided by D, 491 00:31:19,694 --> 00:31:24,707 times kappa, which your book calls K. 492 00:31:24,707 --> 00:31:27,661 So give K -- make K large, make A large, 493 00:31:27,661 --> 00:31:30,616 and make D as small as you possibly can. 494 00:31:30,616 --> 00:31:34,783 Ah, but you have a limit for D. If you make D too small, 495 00:31:34,783 --> 00:31:39,101 you may get sparks between the conductors, because you may 496 00:31:39,101 --> 00:31:43,268 exceed the electric field, the breakdown electric field. 497 00:31:43,268 --> 00:31:47,056 So you must always stay below that breakdown field, 498 00:31:47,056 --> 00:31:51,072 which in A, it would be three million volts per meter. 499 00:31:51,072 --> 00:31:54,557 If you want a very large kappa, you would say, 500 00:31:54,557 --> 00:31:59,601 "Well, why don't you make the layer 501 00:31:59,601 --> 00:32:03,16 water, in between, that has a kappa of eighty." 502 00:32:03,16 --> 00:32:07,259 Ah, the problem is that water has a very low breakdown 503 00:32:07,259 --> 00:32:10,276 electric field, so you don't want water. 504 00:32:10,276 --> 00:32:14,531 If you take polyethylene -- I'll just call it poly here, 505 00:32:14,531 --> 00:32:18,63 to se- as abbreviation -- polyethylene has a breakdown 506 00:32:18,63 --> 00:32:22,498 electric field of eighteen million volts per meter, 507 00:32:22,498 --> 00:32:27,217 and it has a kappa, I believe of three. 508 00:32:27,217 --> 00:32:31,742 Many capacitors are made whereby the layer in between is 509 00:32:31,742 --> 00:32:35,198 polyethylene, although mica would be really 510 00:32:35,198 --> 00:32:37,419 superior. Be that as it may, 511 00:32:37,419 --> 00:32:40,134 I want to evaluate, now, with you, 512 00:32:40,134 --> 00:32:43,343 two capacitors, which each have the same 513 00:32:43,343 --> 00:32:46,47 capacitance of one hundred microfarads. 514 00:32:46,47 --> 00:32:49,596 But one of them, the manufacturer says, 515 00:32:49,596 --> 00:32:54,204 that you could put a maximum potential difference of four 516 00:32:54,204 --> 00:32:57,495 thousand volts over it, that's this baby. 517 00:32:57,495 --> 00:33:01,916 And the other, I got to Radio Shack, 518 00:33:01,916 --> 00:33:06,301 and it says you cannot exceed the potential difference, 519 00:33:06,301 --> 00:33:10,93 not more than forty volts. Well, if I have polyethylene in 520 00:33:10,93 --> 00:33:15,559 between the layers of the conductors, then I can calculate 521 00:33:15,559 --> 00:33:19,863 what the thickness D should be before I get breakdown. 522 00:33:19,863 --> 00:33:22,949 That's very easy, because V equals E D, 523 00:33:22,949 --> 00:33:26,766 and so I put in here, eighteen million volts per 524 00:33:26,766 --> 00:33:31,07 meter, and I go to four thousand volts, 525 00:33:31,07 --> 00:33:33,725 and then I see what I unintelligible D. 526 00:33:33,725 --> 00:33:36,868 And it turns out that the minimum value for D, 527 00:33:36,868 --> 00:33:40,779 you cannot go any thinner, is then two hundred and twenty 528 00:33:40,779 --> 00:33:44,481 microns, and so for this one, it is only two point two 529 00:33:44,481 --> 00:33:47,066 microns. You can make it much thinner, 530 00:33:47,066 --> 00:33:50,418 because the potential difference is hundred times 531 00:33:50,418 --> 00:33:52,723 lower. So you can make the layer a 532 00:33:52,723 --> 00:33:56,565 hundred times thinner before you get electric breakdown. 533 00:33:56,565 --> 00:34:00,337 I want the two capacitors to have the same capacitance. 534 00:34:00,337 --> 00:34:04,667 That means, since they have the same kappa, 535 00:34:04,667 --> 00:34:09,408 and they have the same epsilon zero, it means that A over D has 536 00:34:09,408 --> 00:34:12,008 to be the same for both capacitors. 537 00:34:12,008 --> 00:34:14,378 So A divided by D, for this one, 538 00:34:14,378 --> 00:34:17,972 must be the same as A divided by D for that one. 539 00:34:17,972 --> 00:34:22,025 But if D here is a hundred times larger than this one, 540 00:34:22,025 --> 00:34:25,466 then this A must also be hundred times larger, 541 00:34:25,466 --> 00:34:29,518 because A over D is constant. So if A here is hundred, 542 00:34:29,518 --> 00:34:34,03 then A is here one. But now, think about it. 543 00:34:34,03 --> 00:34:36,844 What determines the volume of a capacitor? 544 00:34:36,844 --> 00:34:40,826 That's really the area of the plates, times the thickness. 545 00:34:40,826 --> 00:34:43,915 And if I ignore, for now, the thickness of the 546 00:34:43,915 --> 00:34:47,21 conducting plates, then the volume of a capacitor 547 00:34:47,21 --> 00:34:51,124 clearly is the product between the area and the thickness, 548 00:34:51,124 --> 00:34:54,213 and so it tells me, then, that this capacitor, 549 00:34:54,213 --> 00:34:57,92 which has a hundred times larger area, is hundred times 550 00:34:57,92 --> 00:35:01,49 thicker, will have a ten thousand times larger volume 551 00:35:01,49 --> 00:35:06,571 than this capacitor. And this baby is four thousand 552 00:35:06,571 --> 00:35:10,554 volts, hundred microfarads, it has a length of about thirty 553 00:35:10,554 --> 00:35:14,468 centimeters, ten centimeters like this, twenty centimeters 554 00:35:14,468 --> 00:35:17,902 high, that is about ten thousand cubic centimeters. 555 00:35:17,902 --> 00:35:21,542 Ten thousand cubic centimeters. You go to Radio Shack, 556 00:35:21,542 --> 00:35:24,495 and you buy yourself a forty-volt capacitor, 557 00:35:24,495 --> 00:35:27,654 hundred microfarads, which will be ten thousand 558 00:35:27,654 --> 00:35:31,019 times smaller in volume. It will be only one cubic 559 00:35:31,019 --> 00:35:33,903 centimeter. And if I had one of them behind 560 00:35:33,903 --> 00:35:37,869 my ear, you wouldn't even notice 561 00:35:37,869 --> 00:35:41,982 that, would you? Could you tell me what it says 562 00:35:41,982 --> 00:35:45,022 here? One hundred micro microfarad. 563 00:35:45,022 --> 00:35:46,9 How many volts? Forty. 564 00:35:46,9 --> 00:35:49,135 Forty volts. That's small. 565 00:35:49,135 --> 00:35:53,695 Compared to this one, which can handle four thousand 566 00:35:53,695 --> 00:35:56,556 volts. But the capacitance is the 567 00:35:56,556 --> 00:35:58,344 same. So you see now, 568 00:35:58,344 --> 00:36:02,189 the connection with area and with thickness, 569 00:36:02,189 --> 00:36:08,132 by no means trivial. All this has been very rough on 570 00:36:08,132 --> 00:36:09,692 you. I realize that. 571 00:36:09,692 --> 00:36:14,29 It takes time to digest it, that you have to go over your 572 00:36:14,29 --> 00:36:15,932 notes. And therefore, 573 00:36:15,932 --> 00:36:20,695 for the remaining time -- we have quite some time left -- I 574 00:36:20,695 --> 00:36:25,704 will try to entertain you with something which is a little bit 575 00:36:25,704 --> 00:36:28,331 easier. A little nicer to digest. 576 00:36:28,331 --> 00:36:33,176 Professor Musschenbroek in the Netherlands, invented -- yes, 577 00:36:33,176 --> 00:36:38,184 you can say he invented the -- the capacitor. 578 00:36:38,184 --> 00:36:43,759 It was an accidental discovery. He called them a Leyden jar, 579 00:36:43,759 --> 00:36:48,577 because he worked in Leyden. And a Leyden jar is the 580 00:36:48,577 --> 00:36:51,695 following. This is a glass bottle, 581 00:36:51,695 --> 00:36:55,568 so all this is glass, that's an insulator, 582 00:36:55,568 --> 00:37:00,67 and he has outside the insulator, he has two conducting 583 00:37:00,67 --> 00:37:05,866 plates, so that's a beaker outside, and there's a beaker 584 00:37:05,866 --> 00:37:10,613 inside, conducting. That's a capacitor. 585 00:37:10,613 --> 00:37:14,06 Although he didn't call it a capacitor. 586 00:37:14,06 --> 00:37:19,32 And so he charged these up, and so you can have plus charge 587 00:37:19,32 --> 00:37:24,672 here, and minus Q on the inside, and he did experiments with 588 00:37:24,672 --> 00:37:27,937 that. The, um, the energy stored in a 589 00:37:27,937 --> 00:37:33,198 capacitor -- we discussed that last time -- equals one-half 590 00:37:33,198 --> 00:37:38,005 times the free charge times the potential 591 00:37:38,005 --> 00:37:41,783 difference, if you prefer one-half C V squared, 592 00:37:41,783 --> 00:37:45,89 that's the same thing, I have no problem with that, 593 00:37:45,89 --> 00:37:50,818 because the C is Q free divided by V, so it's the same thing. 594 00:37:50,818 --> 00:37:54,678 What I'm going to do, I'm going to put a certain 595 00:37:54,678 --> 00:37:59,441 potential difference over a Leyden jar, I will show you the 596 00:37:59,441 --> 00:38:04,04 Leyden jar that we have -- you'll see there -- and once I 597 00:38:04,04 --> 00:38:07,901 have put in -- put on some potential difference, 598 00:38:07,901 --> 00:38:13,479 put on some charge on the outer surface and on the inner 599 00:38:13,479 --> 00:38:16,93 surface -- you can see the outer surface there, 600 00:38:16,93 --> 00:38:21,431 the inner one is harder to see, but I will show that later to 601 00:38:21,431 --> 00:38:23,681 you. So here you see the glass, 602 00:38:23,681 --> 00:38:27,957 and here you see the outer conductor, and there's an inner 603 00:38:27,957 --> 00:38:30,883 one, too, which you can't see very well. 604 00:38:30,883 --> 00:38:34,184 Once I have done that, I will disassemble it. 605 00:38:34,184 --> 00:38:38,009 So I first charge it up so there is energy in there, 606 00:38:38,009 --> 00:38:41,535 this much energy. And then I will take the glass 607 00:38:41,535 --> 00:38:45,286 out, I will put the, um, the outside conductor here 608 00:38:45,286 --> 00:38:49,42 , the inside conductor here, 609 00:38:49,42 --> 00:38:51,923 I will discharge them completely. 610 00:38:51,923 --> 00:38:56,617 I will hold them in my hands, I will touch them with my face, 611 00:38:56,617 --> 00:39:00,215 I will lick them, I will do anything to get all 612 00:39:00,215 --> 00:39:03,422 the charge off. And then I will reassemble 613 00:39:03,422 --> 00:39:06,081 them. Well, if I get all the charge 614 00:39:06,081 --> 00:39:10,931 off, all this Q free [wssshhh] goes away, there's no longer any 615 00:39:10,931 --> 00:39:14,764 potential difference. When I reassemble that baby, 616 00:39:14,764 --> 00:39:18,049 then, clearly, there couldn't be any energy 617 00:39:18,049 --> 00:39:22,242 left. And the best way to demonstrate 618 00:39:22,242 --> 00:39:25,64 that, then, to you, is, to take these prongs, 619 00:39:25,64 --> 00:39:28,42 which I have here, conducting prongs, 620 00:39:28,42 --> 00:39:32,822 and see whether I can still draw a spark by connecting the 621 00:39:32,822 --> 00:39:37,609 inner part with the outer part. And you would not expect to see 622 00:39:37,609 --> 00:39:40,621 anything. So it is something that is not 623 00:39:40,621 --> 00:39:44,328 going to be too exciting. But let's do it anyhow. 624 00:39:44,328 --> 00:39:48,266 So here is this Leyden jar, and I'm turning the wind 625 00:39:48,266 --> 00:39:52,513 unintelligible to charge it up. I'm going to remove this 626 00:39:52,513 --> 00:39:59,106 connection, remove this connection, 627 00:39:59,106 --> 00:40:04,406 take this out, take this out, 628 00:40:04,406 --> 00:40:13,492 come on -- believe me, no charge on it any more. 629 00:40:13,492 --> 00:40:17,846 This one. It's all gone. 630 00:40:17,846 --> 00:40:25,407 Believe me. There we go. 631 00:40:25,407 --> 00:40:30,662 And now let's see what happens when I short out the outer 632 00:40:30,662 --> 00:40:33,852 conductor with the inner conductor. 633 00:40:33,852 --> 00:40:36,198 Watch it. That is amazing. 634 00:40:36,198 --> 00:40:40,608 There shouldn't be any energy on that capacitor. 635 00:40:40,608 --> 00:40:43,517 Nothing. And I saw a huge spark, 636 00:40:43,517 --> 00:40:47,552 not even a small one. When I saw this first, 637 00:40:47,552 --> 00:40:51,399 and I'm not joking, I was totally baffled. 638 00:40:51,399 --> 00:40:57,596 And I was thinking about it, and I couldn't sleep all night. 639 00:40:57,596 --> 00:41:00,665 I couldn't think of any reasonable explanation. 640 00:41:00,665 --> 00:41:04,469 And so my charter for you is, to also have a few sleepless 641 00:41:04,469 --> 00:41:07,938 nights, and to try to come up, why this is happening. 642 00:41:07,938 --> 00:41:11,675 How is it possible that I first bring charge on these two 643 00:41:11,675 --> 00:41:15,145 plates, disassemble them, totally take all the charge 644 00:41:15,145 --> 00:41:18,615 off, and nevertheless, when I reassembled them again, 645 00:41:18,615 --> 00:41:22,018 there is a huge potential difference between the two 646 00:41:22,018 --> 00:41:24,953 plates, otherwise, you wouldn't have seen the 647 00:41:24,953 --> 00:41:28,356 spark. So give that some thought, 648 00:41:28,356 --> 00:41:31,618 and later in the course, I will make an attempt to 649 00:41:31,618 --> 00:41:33,815 explain this. At least, that's the 650 00:41:33,815 --> 00:41:37,742 explanation that I came up with, it may not be the best one, 651 00:41:37,742 --> 00:41:40,871 but it's the only one that I could come up with. 652 00:41:40,871 --> 00:41:44,732 In the remaining eight minutes, I want to tell you the last 653 00:41:44,732 --> 00:41:47,661 secret, which I owe you, of the van der Graf. 654 00:41:47,661 --> 00:41:51,455 And that has to do with the potential that we can achieve. 655 00:41:51,455 --> 00:41:53,519 Remember the large van der Graf? 656 00:41:53,519 --> 00:41:58,445 We could get it up to about three hundred thousand volts. 657 00:41:58,445 --> 00:42:01,789 How do we charge a conducting sphere? 658 00:42:01,789 --> 00:42:06,9 Well, let's start off with a -- with this hollow sphere, 659 00:42:06,9 --> 00:42:12,289 which is what the con- the van der Graf is -- and suppose I 660 00:42:12,289 --> 00:42:16,748 have here a voltage supply, with a few kilovolts. 661 00:42:16,748 --> 00:42:20 I can buy that. And I have a sphere, 662 00:42:20 --> 00:42:24,925 and I touch with this sphere, which an insulating rod, 663 00:42:24,925 --> 00:42:30,592 I touch the output of the kilo- the few kilovolt 664 00:42:30,592 --> 00:42:35,425 supply, and I bring this -- so there's positive charge on here, 665 00:42:35,425 --> 00:42:39,088 say -- and I bring it close to the van der Graf, 666 00:42:39,088 --> 00:42:43,92 there will be an electric field between this charged object and 667 00:42:43,92 --> 00:42:46,882 the van der Graf, and the closer I get, 668 00:42:46,882 --> 00:42:50 the stronger that electric field will be. 669 00:42:50 --> 00:42:54,52 And when I touch the outer shell, then the charge will flow 670 00:42:54,52 --> 00:42:58,34 in the van der Graf. I go back to my power supply, 671 00:42:58,34 --> 00:43:02,393 I touch again the few thousand volts, 672 00:43:02,393 --> 00:43:05,211 and I keep spooning charge on the van der Graf. 673 00:43:05,211 --> 00:43:08,704 Will I be able to get the van der Graf up to three hundred 674 00:43:08,704 --> 00:43:11,401 thousand volts? No way, because there comes a 675 00:43:11,401 --> 00:43:15,077 time that the potential of this object -- which comes from my 676 00:43:15,077 --> 00:43:18,509 power supply -- is the same electric potential as the van 677 00:43:18,509 --> 00:43:21,696 der Graf, and then you can no longer exchange charge. 678 00:43:21,696 --> 00:43:24,882 What it comes down to is that when you come with this 679 00:43:24,882 --> 00:43:27,517 conductor and you approach the van der Graf, 680 00:43:27,517 --> 00:43:31,133 there will be no longer any electric fields between the two. 681 00:43:31,133 --> 00:43:35,666 So there will be no longer any potential difference. 682 00:43:35,666 --> 00:43:38,362 So you can't transfer any more charge. 683 00:43:38,362 --> 00:43:42,588 So you run very quickly into a situation which will freeze. 684 00:43:42,588 --> 00:43:45,794 You cannot get it above a few thousand volts. 685 00:43:45,794 --> 00:43:49,656 So now what do you do? And here comes the breakthrough 686 00:43:49,656 --> 00:43:53,154 by Professor van der Graf from MIT, who now said, 687 00:43:53,154 --> 00:43:55,267 "Ah. I don't have to bring the 688 00:43:55,267 --> 00:43:58,764 charge on this way, but I can bring the charge in 689 00:43:58,764 --> 00:44:02,043 this way." So now you go to your power supply, 690 00:44:02,043 --> 00:44:05,541 a few thousand volt, and you bring it inside this 691 00:44:05,541 --> 00:44:09,215 sphere, where there was no electric 692 00:44:09,215 --> 00:44:12,249 field to start with. When you charge the outside, 693 00:44:12,249 --> 00:44:15,663 there's going to be an electric field from this object, 694 00:44:15,663 --> 00:44:19,329 and there's going to be an electric field from this object, 695 00:44:19,329 --> 00:44:21,731 the net result will be zero in between. 696 00:44:21,731 --> 00:44:23,88 There was no electric field inside. 697 00:44:23,88 --> 00:44:27,04 If I now bring the positively charged sphere there, 698 00:44:27,04 --> 00:44:30,643 I'm going to get E field lines like this, problem two one, 699 00:44:30,643 --> 00:44:34,499 and so now there is a potential difference between this object 700 00:44:34,499 --> 00:44:37,28 and the sphere. What I have done by moving it 701 00:44:37,28 --> 00:44:41,633 from here to the inside, I have done positive work 702 00:44:41,633 --> 00:44:44,211 without having realized it, and therefore, 703 00:44:44,211 --> 00:44:47,48 I have brought this potential higher than the sphere. 704 00:44:47,48 --> 00:44:50,121 Now I touch the inside of the van der Graf, 705 00:44:50,121 --> 00:44:53,013 and now the charge will run on the outer shell. 706 00:44:53,013 --> 00:44:55,527 And I can keep doing that. Inside, touch. 707 00:44:55,527 --> 00:44:57,288 Inside, touch. Inside, touch. 708 00:44:57,288 --> 00:45:00,997 And every time I come in here, there is no electric field in 709 00:45:00,997 --> 00:45:03,009 there. So I can do that until I'm 710 00:45:03,009 --> 00:45:06,09 green in the face. Well, there comes a time that I 711 00:45:06,09 --> 00:45:10,931 can no longer increase the potential of the van der Graf, 712 00:45:10,931 --> 00:45:14,538 and that is when the van der Graf goes into electric 713 00:45:14,538 --> 00:45:17,296 breakdown. When I reach my three hundred 714 00:45:17,296 --> 00:45:19,348 thousand volts, it's all over. 715 00:45:19,348 --> 00:45:21,823 I can try to bring the potential up, 716 00:45:21,823 --> 00:45:24,652 but it's going to lose charge to the air. 717 00:45:24,652 --> 00:45:28,048 And so that is the -- ultimately the limit of the 718 00:45:28,048 --> 00:45:32,15 potential of the van der Graf. So how does the van der Graf 719 00:45:32,15 --> 00:45:33,848 work? Uh, we have a belt, 720 00:45:33,848 --> 00:45:38,304 which is run by a motor -- here is the van der Graf -- and right 721 00:45:38,304 --> 00:45:42,831 here, through corona discharge, we put charge 722 00:45:42,831 --> 00:45:45,381 on the belt. They're very sharp points, 723 00:45:45,381 --> 00:45:49,274 and we get a corona discharge at a relatively low potential 724 00:45:49,274 --> 00:45:52,697 difference, it goes on the belt, the belt goes here, 725 00:45:52,697 --> 00:45:55,516 and right here, there are two sharp points, 726 00:45:55,516 --> 00:45:58,872 which through corona discharge take the charge off. 727 00:45:58,872 --> 00:46:00,818 On the inside, that's the key. 728 00:46:00,818 --> 00:46:04,644 And then it goes through the dome, and then it charges up, 729 00:46:04,644 --> 00:46:07,933 up to the point that you begin to hear the sparks, 730 00:46:07,933 --> 00:46:11,759 and that you have breakdown. And I can demonstrate that to 731 00:46:11,759 --> 00:46:15,533 you. I built my own van der Graf. 732 00:46:15,533 --> 00:46:20,154 And the van der Graf that I built to you is this paint can. 733 00:46:20,154 --> 00:46:24,854 I'm going to charge that paint can by touching it repeatedly 734 00:46:24,854 --> 00:46:28,519 with a conductor, and the conductor has a -- is 735 00:46:28,519 --> 00:46:31,785 going to be -- yes, I'm going to touch the 736 00:46:31,785 --> 00:46:36,565 conductor with a few thousand volt power supply every time -- 737 00:46:36,565 --> 00:46:41,026 this is the power supply, turning it on now -- and you're 738 00:46:41,026 --> 00:46:44,771 going to see the potential of the 739 00:46:44,771 --> 00:46:47,72 van der Graf there. Uh, that is a very crude 740 00:46:47,72 --> 00:46:50,806 measure for the potential on the van der Graf, 741 00:46:50,806 --> 00:46:53,206 but very crudely, when it reads one, 742 00:46:53,206 --> 00:46:57,322 I have about ten thousand volts -- this is the probe that I'm 743 00:46:57,322 --> 00:47:00,682 using for that -- two, it's twenty thousand volts. 744 00:47:00,682 --> 00:47:03,7 My power supply is only a few thousand volts. 745 00:47:03,7 --> 00:47:07,061 But that's not very good. Well, I will first start 746 00:47:07,061 --> 00:47:11,107 charging it on the outside to demonstrate to you that I very 747 00:47:11,107 --> 00:47:16,342 quickly run into the wall that I just described. 748 00:47:16,342 --> 00:47:20,878 That if they have the same potential, then I can no longer 749 00:47:20,878 --> 00:47:24,777 transfer a charge. But then I'm going to change my 750 00:47:24,777 --> 00:47:29,393 tactics and then I go inside. And then you will see that it 751 00:47:29,393 --> 00:47:33,372 will go up further. So let's first see what happens 752 00:47:33,372 --> 00:47:36,237 if I now bring charge on the outside. 753 00:47:36,237 --> 00:47:39,579 There it goes. It's about a thousand volts, 754 00:47:39,579 --> 00:47:43,08 about two thousand volts, two thousand volts, 755 00:47:43,08 --> 00:47:47,378 keep an eye on it, two thousand volts, 756 00:47:47,378 --> 00:47:50,83 it's heading for three thousand volts, three thousand volts, 757 00:47:50,83 --> 00:47:53,289 three thousand volts, three thousand volts, 758 00:47:53,289 --> 00:47:55,747 three thousand volts, not getting anywhere, 759 00:47:55,747 --> 00:47:58,966 I'm beginning to reach the saturation, maybe three and a 760 00:47:58,966 --> 00:48:01,014 half thousand volts, three and half, 761 00:48:01,014 --> 00:48:04,35 it's slowly going to four, let's see whether we can get it 762 00:48:04,35 --> 00:48:06,866 much higher than four, I don't think we can. 763 00:48:06,866 --> 00:48:10,437 So this is the end of the story before Professor van der Graf. 764 00:48:10,437 --> 00:48:12,543 But then came Professor van der Graf. 765 00:48:12,543 --> 00:48:14,884 And he said, "Look, man, you've got to go 766 00:48:14,884 --> 00:48:17,342 inside. Now watch it. 767 00:48:17,342 --> 00:48:20,692 Now I have to concentrate on this scooping, 768 00:48:20,692 --> 00:48:25,318 so I would like you to tell me when we reach five thousand, 769 00:48:25,318 --> 00:48:28,986 you just scream. Oh, man, we already passed the 770 00:48:28,986 --> 00:48:31,06 five thousand, you dummies! 771 00:48:31,06 --> 00:48:33,931 Ten thousand, scream when you see ten 772 00:48:33,931 --> 00:48:35,765 thousand. [crowd roars]. 773 00:48:35,765 --> 00:48:38,636 Scream when you see fifteen thousand. 774 00:48:38,636 --> 00:48:41,507 Scream when you see fifteen thousand. 775 00:48:41,507 --> 00:48:44,936 [crowd roars]. Very good, keep an eye on it, 776 00:48:44,936 --> 00:48:49,402 tell me when you see twenty thousand. 777 00:48:49,402 --> 00:48:57,653 [noise] I don't hear anything! [crowd roars] Now I want you 778 00:48:57,653 --> 00:49:05,761 tell me every one thousand, because I think we're going to 779 00:49:05,761 --> 00:49:11,735 run into the wall very quickly. Twenty one? 780 00:49:11,735 --> 00:49:17,425 I want to hear twenty two. [crowd roars]. 781 00:49:17,425 --> 00:49:24,354 Already at twenty three. So I expect that very s- very 782 00:49:24,354 --> 00:49:29,132 quickly now -- [crowd roars] -- the can will go into discharge, 783 00:49:29,132 --> 00:49:32,831 you won't see that, but you get corona discharge, 784 00:49:32,831 --> 00:49:37,224 and then, no matter how hard I work, I will not be able to 785 00:49:37,224 --> 00:49:40,615 bring the potential up. But let's keep going. 786 00:49:40,615 --> 00:49:43,466 Are we already at twenty five hundred? 787 00:49:43,466 --> 00:49:47,242 Twenty five thousand, sorry, twenty five thousand? 788 00:49:47,242 --> 00:49:50,556 Twenty five thousand volts. Twenty five six. 789 00:49:50,556 --> 00:49:52,56 Twenty seven. Twenty seven. 790 00:49:52,56 --> 00:49:56,027 Twenty eight. Twenty eight. 791 00:49:56,027 --> 00:50:01,188 It looks like we are beginning to get into the corona 792 00:50:01,188 --> 00:50:03,471 discharge. Twenty eight! 793 00:50:03,471 --> 00:50:06,845 Boy, twenty eight! That's a record. 794 00:50:06,845 --> 00:50:09,922 Twenty-eight, keep an eye on it. 795 00:50:09,922 --> 00:50:12,304 Twenty nine? Twenty nine? 796 00:50:12,304 --> 00:50:15,778 Whew. You realize I'm doing all this 797 00:50:15,778 --> 00:50:18,656 work. Well, I get paid for it, 798 00:50:18,656 --> 00:50:22,129 I -- I think I've reached the limit. 799 00:50:22,129 --> 00:50:27,886 I've reached my own limit and I've reached the limit of the 800 00:50:27,886 --> 00:50:33,426 charging. Now, we have thirty thousand 801 00:50:33,426 --> 00:50:38,948 volts, and we started off with only a few thousand volts. 802 00:50:38,948 --> 00:50:43,386 Originally, it wasn't a very dangerous object. 803 00:50:43,386 --> 00:50:47,429 But now, thirty thousand volts -- shall I? 804 00:50:47,429 --> 50:52 OK, see you next week.