1 00:00:00 --> 00:00:00 2 00:00:01 --> 00:00:02,611 assemble charges, I have to do work, 3 00:00:02,611 --> 00:00:06,789 we discussed that earlier. And we call that electrostatic 4 00:00:06,789 --> 00:00:09,998 potential energy. Today, I will look at this 5 00:00:09,998 --> 00:00:14,251 energy concept in a different way, and I will evaluate the 6 00:00:14,251 --> 00:00:17,012 energy in terms of the electric field. 7 00:00:17,012 --> 00:00:21,19 Suppose I have two parallel plates, and I charge this one 8 00:00:21,19 --> 00:00:24,771 with positive charge, which is the surface charge 9 00:00:24,771 --> 00:00:28,428 density times the area of the plate, and this one, 10 00:00:28,428 --> 00:00:31,338 negative charge, which 11 00:00:31,338 --> 00:00:36,407 is the surface charge density negative times the area of the 12 00:00:36,407 --> 00:00:39,071 plate. And let's assume that the 13 00:00:39,071 --> 00:00:44,227 separation between these two is H, and so we have an electric 14 00:00:44,227 --> 00:00:49,468 field, which is approximately constant, and the electric field 15 00:00:49,468 --> 00:00:52,648 here is sigma divided by epsilon zero. 16 00:00:52,648 --> 00:00:57,718 And now, I'm going to take the upper plate, and I'm going to 17 00:00:57,718 --> 00:01:00,381 move it up. And so as I do that, 18 00:01:00,381 --> 00:01:05,488 I have to apply a force, because these two plates 19 00:01:05,488 --> 00:01:08,413 attract each other, so I have to do work. 20 00:01:08,413 --> 00:01:11,923 And as I move this up, and I will move it up over 21 00:01:11,923 --> 00:01:16,092 distance X, I am creating here, electric field that wasn't 22 00:01:16,092 --> 00:01:19,31 there before. And the electric field that I'm 23 00:01:19,31 --> 00:01:22,674 creating has exactly the same strength as this, 24 00:01:22,674 --> 00:01:26,843 because the charge on the plates is not changing when I am 25 00:01:26,843 --> 00:01:30,499 moving, the surface charge density is not changing, 26 00:01:30,499 --> 00:01:33,132 all I do is, I increase the distance. 27 00:01:33,132 --> 00:01:37,587 And so I am creating electric field in here. 28 00:01:37,587 --> 00:01:39,84 And for that, I have to do work, 29 00:01:39,84 --> 00:01:42,384 that's another way of looking at it. 30 00:01:42,384 --> 00:01:46,599 How much work do I have to do? What is the work that Walter 31 00:01:46,599 --> 00:01:50,669 Lewin has to do in moving this plate over the distance X? 32 00:01:50,669 --> 00:01:55,103 Well, that is the force that I have to apply over the distance 33 00:01:55,103 --> 00:01:56,847 X. The force is constant, 34 00:01:56,847 --> 00:02:00,99 and so I can simply multiply the force times the distance, 35 00:02:00,99 --> 00:02:04,624 that will give me work. And so the question now is, 36 00:02:04,624 --> 00:02:10,366 what is the force that I have to apply to move this plate up? 37 00:02:10,366 --> 00:02:13,959 And your first guess would be that the force would be the 38 00:02:13,959 --> 00:02:17,36 charge on the plate times the electric field strength, 39 00:02:17,36 --> 00:02:20,761 a complete reasonable guess, because, you would argue, 40 00:02:20,761 --> 00:02:24,676 "Well, if we have an electric field E, and we bring a charge Q 41 00:02:24,676 --> 00:02:27,628 in there, then the electric force is Q times E, 42 00:02:27,628 --> 00:02:31,542 I have to overcome that force, so my force is Q times E." Yes, 43 00:02:31,542 --> 00:02:34,687 that holds most of the time. But not in this case. 44 00:02:34,687 --> 00:02:38,409 It's a little bit more subtle. Let me take this plate here, 45 00:02:38,409 --> 00:02:42,388 and enlarge that plate. So here is the plate. 46 00:02:42,388 --> 00:02:46,631 So you see the thickness of the plate, now, this is one plate. 47 00:02:46,631 --> 00:02:50,178 We all agree that the plus charge is at the surface, 48 00:02:50,178 --> 00:02:53,448 well, but, of course, it has to be in the plate. 49 00:02:53,448 --> 00:02:57,552 And so there is here this layer of charge Q, which is at the 50 00:02:57,552 --> 00:03:01,099 bottom of the plate. And the thickness of that layer 51 00:03:01,099 --> 00:03:03,325 may only be one atomic thickness. 52 00:03:03,325 --> 00:03:06,664 But it's not zero. And on this side of the plate, 53 00:03:06,664 --> 00:03:10,072 is there electric field, which is sigma divided by 54 00:03:10,072 --> 00:03:13,689 epsilon zero. But inside the plate, 55 00:03:13,689 --> 00:03:17,823 which is a conductor, the electric field is zero. 56 00:03:17,823 --> 00:03:20,924 And therefore, the electric field is, 57 00:03:20,924 --> 00:03:25,058 in this charge Q, is the average between the two. 58 00:03:25,058 --> 00:03:29,02 And so the force on this charge, in this layer, 59 00:03:29,02 --> 00:03:32,723 is not Q times E, but is one-half Q times E. 60 00:03:32,723 --> 00:03:36,513 So I take the average between these E fields, 61 00:03:36,513 --> 00:03:39,527 and this E field is then this value. 62 00:03:39,527 --> 00:03:45,47 And so now I can calculate the work that I have to do, 63 00:03:45,47 --> 00:03:50,043 the work that I have to do is now my force, 64 00:03:50,043 --> 00:03:56,467 which is one-half Q times E, and I move that over a distance 65 00:03:56,467 --> 00:03:59,625 X. And so what I can do now is 66 00:03:59,625 --> 00:04:05,287 replace Q by sigma A, so I get one-half sigma A times 67 00:04:05,287 --> 00:04:10,84 E times X, and I multiply upstairs and downstairs by 68 00:04:10,84 --> 00:04:14,869 epsilon zero, so that multiply by one. 69 00:04:14,869 --> 00:04:19,769 And the reason why I do that is, 70 00:04:19,769 --> 00:04:24,385 because then I get another sigma divided by epsilon zero 71 00:04:24,385 --> 00:04:28,245 here -- divided by epsilon zero, and that is E, 72 00:04:28,245 --> 00:04:31,938 and therefore, I now have that the total work 73 00:04:31,938 --> 00:04:37,226 that I, Walter Lewin have to do -- has to do is one-half epsilon 74 00:04:37,226 --> 00:04:41,339 zero, E-squared times A times X. And look at this. 75 00:04:41,339 --> 00:04:44,78 A X is the new volume that I have created, 76 00:04:44,78 --> 00:04:49,732 it is the new volume in which I have created electric field. 77 00:04:49,732 --> 00:04:55,11 And this, now, calls for a work done by 78 00:04:55,11 --> 00:04:58,394 Walter Lewin. Per unit volume, 79 00:04:58,394 --> 00:05:03,15 and that, now, equals one-half epsilon zero 80 00:05:03,15 --> 00:05:08,132 times E squared. This is the work that I have 81 00:05:08,132 --> 00:05:13,567 done per unit volume. And since this work created 82 00:05:13,567 --> 00:05:18,21 electric field, we called it "field energy 83 00:05:18,21 --> 00:05:24,473 density". And it is in joules per cubic 84 00:05:24,473 --> 00:05:26,932 meter. And it can be shown that, 85 00:05:26,932 --> 00:05:31,373 in general, the electric field energy density is one-half 86 00:05:31,373 --> 00:05:35,418 epsilon zero E squared, not only for this particular 87 00:05:35,418 --> 00:05:38,511 charge configuration, but for any charge 88 00:05:38,511 --> 00:05:40,573 configuration. And so, now, 89 00:05:40,573 --> 00:05:45,173 we have a new way of looking at the energy that it takes to 90 00:05:45,173 --> 00:05:48,98 assemble charges. Earlier, we calculated the work 91 00:05:48,98 --> 00:05:52,628 that we have to do to put the charges in place, 92 00:05:52,628 --> 00:05:56,188 now, if it is more convenient, 93 00:05:56,188 --> 00:06:00,4 we could calculate that the energy electrostatic potential 94 00:06:00,4 --> 00:06:04,611 energy, is the integral of one-half epsilon zero E-squared, 95 00:06:04,611 --> 00:06:09,114 over all space -- if necessary, you have to go all the way down 96 00:06:09,114 --> 00:06:12,018 to infinity -- and here, I have now, D V, 97 00:06:12,018 --> 00:06:15,068 this is volume. This has nothing to do with 98 00:06:15,068 --> 00:06:18,626 potential, this V, in physics, we often run out of 99 00:06:18,626 --> 00:06:22,039 symbols, V is sometimes potential, in this case, 100 00:06:22,039 --> 00:06:25,234 it is volume. And the only reason why I chose 101 00:06:25,234 --> 00:06:28,945 H there is I already have a D 102 00:06:28,945 --> 00:06:32,726 here, so I didn't want two Ds. Normally, we take D as the 103 00:06:32,726 --> 00:06:35,291 separation between plates. And so this, 104 00:06:35,291 --> 00:06:39,071 now, is another way of looking at electrostatic potential 105 00:06:39,071 --> 00:06:41,636 energy. We look at it now only from the 106 00:06:41,636 --> 00:06:45,619 point of view of all the energy being in the electric field, 107 00:06:45,619 --> 00:06:49,535 and we no longer think of it, perhaps, as the work that you 108 00:06:49,535 --> 00:06:51,897 have done to assemble these charges. 109 00:06:51,897 --> 00:06:55,678 I will demonstrate later today that as I separate the two 110 00:06:55,678 --> 00:06:59,12 plates from these charged planes, 111 00:06:59,12 --> 00:07:01,226 that indeed, I have to do work. 112 00:07:01,226 --> 00:07:05,227 I will convince you that by creating electric fields that, 113 00:07:05,227 --> 00:07:08,385 indeed, I will be doing work. So, from now on, 114 00:07:08,385 --> 00:07:12,035 uh, we have the choice. If you want to calculate what 115 00:07:12,035 --> 00:07:16,106 the electrostatic potential energy is, you either calculate 116 00:07:16,106 --> 00:07:20,107 the work that you have to do to bring all these charges in 117 00:07:20,107 --> 00:07:24,177 place, or, if it is easier, you can take the electric field 118 00:07:24,177 --> 00:07:26,774 everywhere in space, if you know that, 119 00:07:26,774 --> 00:07:30,564 and do an integration over all space. 120 00:07:30,564 --> 00:07:32,574 We could do that, for instance, 121 00:07:32,574 --> 00:07:36,593 for these two parallel plates now, and we can ask what is now 122 00:07:36,593 --> 00:07:40,077 the total energy in these plates -- uh, in the field. 123 00:07:40,077 --> 00:07:42,153 And at home, I would advise you, 124 00:07:42,153 --> 00:07:45,234 to do that the way that it's done in your book, 125 00:07:45,234 --> 00:07:48,919 whereby you actually assemble the charges minus Q at the 126 00:07:48,919 --> 00:07:52,938 bottom and plus Q at the top, and you calculate how much work 127 00:07:52,938 --> 00:07:55,282 you have to do. That's one approach. 128 00:07:55,282 --> 00:07:58,565 I will now choose the other approach, and that is, 129 00:07:58,565 --> 00:08:03,857 by simply saying that the total energy in the field of these 130 00:08:03,857 --> 00:08:07,6 plane-parallel plates, is the integral of one-half 131 00:08:07,6 --> 00:08:11,727 epsilon zero E-squared, over the entire volume of these 132 00:08:11,727 --> 00:08:14,936 two plates. And since the electric field is 133 00:08:14,936 --> 00:08:18,145 outside, zero, everywhere, it's a very easy 134 00:08:18,145 --> 00:08:20,819 integral, because I know the volume. 135 00:08:20,819 --> 00:08:24,945 The volume that I have, if the separation is H -- so we 136 00:08:24,945 --> 00:08:29,606 still have them H apart -- this volume that I have is simply A 137 00:08:29,606 --> 00:08:34,267 times H, and the electric field is constant, and so I get here 138 00:08:34,267 --> 00:08:38,064 that this is one-half epsilon zero. 139 00:08:38,064 --> 00:08:41,572 For E, if I want to, I can write sigma divided by 140 00:08:41,572 --> 00:08:43,838 epsilon zero, I can square that, 141 00:08:43,838 --> 00:08:47,2 and D V, in- doing the integral over all space, 142 00:08:47,2 --> 00:08:51,439 means simply I get A times H, it is the volume of that box. 143 00:08:51,439 --> 00:08:54,874 So I get A times H. And so this is now the total 144 00:08:54,874 --> 00:08:58,09 energy that I have, I lose one epsilon here, 145 00:08:58,09 --> 00:09:01,89 I have an epsilon zero squared and I have an epsilon. 146 00:09:01,89 --> 00:09:08,249 I also remember that the charge Q on the plate is A times sigma, 147 00:09:08,249 --> 00:09:10,718 and that the potential difference V, 148 00:09:10,718 --> 00:09:14,387 this now is not volume, it's the potential difference 149 00:09:14,387 --> 00:09:17,844 between the plates, is the electric field times H. 150 00:09:17,844 --> 00:09:22,218 The electric field is constant, it can go from one plate to the 151 00:09:22,218 --> 00:09:26,381 other, the integral E dot D L in going from one plate to the 152 00:09:26,381 --> 00:09:29,203 other, gives me the potential difference. 153 00:09:29,203 --> 00:09:33,295 And so I can substitute that now in here, I can take for A, 154 00:09:33,295 --> 00:09:37,317 sigma, I can put in the Q, and you can also show that this 155 00:09:37,317 --> 00:09:39,636 is one-half Q V. 156 00:09:39,636 --> 00:09:42,421 V being, now, the potential difference 157 00:09:42,421 --> 00:09:45,958 between the plates. And so this is a rather fast 158 00:09:45,958 --> 00:09:50,248 way that you can calculate what the total energy is in the 159 00:09:50,248 --> 00:09:52,506 field, or, say, the same thing, 160 00:09:52,506 --> 00:09:56,645 the total work you have to do to assemble these charges. 161 00:09:56,645 --> 00:10:00,785 Or, to say it differently, the total work you have to do 162 00:10:00,785 --> 00:10:04,473 to create electric fields. You have crela- created 163 00:10:04,473 --> 00:10:07,634 electric fields that were not there before. 164 00:10:07,634 --> 00:10:11,623 I now will introduce something that 165 00:10:11,623 --> 00:10:17,431 we haven't had before, that is the word "capacitance". 166 00:10:17,431 --> 00:10:24,117 I will define the capacitance of an object to be the charge of 167 00:10:24,117 --> 00:10:29,706 that object divided by the potential of that object. 168 00:10:29,706 --> 00:10:35,405 And so the unit is coulombs per volt, this V is volt, 169 00:10:35,405 --> 00:10:42,091 now, it's potential. Uh, but we never say that it is 170 00:10:42,091 --> 00:10:46,585 coulombs per volt in physics, we write for that a capital F, 171 00:10:46,585 --> 00:10:48,718 which is Farad, we call that, 172 00:10:48,718 --> 00:10:52,907 one farad is the unit of capacitance, undoubtedly called 173 00:10:52,907 --> 00:10:57,173 after the great maestro Faraday, we will learn more about 174 00:10:57,173 --> 00:11:00,601 Faraday later in this course. So let us go to, 175 00:11:00,601 --> 00:11:05,4 um, a sphere which has a radius R, and let us calculate what the 176 00:11:05,4 --> 00:11:09,361 capacitance is of this sphere. Think of it as being a 177 00:11:09,361 --> 00:11:13,932 conductor, and we bring a certain charge Q on 178 00:11:13,932 --> 00:11:18,231 this conductor, it will then get a potential V, 179 00:11:18,231 --> 00:11:23,184 which we know is Q divided by four pi, epsilon zero R. 180 00:11:23,184 --> 00:11:27,764 We've seen this many times, and so, by definition, 181 00:11:27,764 --> 00:11:32,343 the capacitance now is Q divided by the potential, 182 00:11:32,343 --> 00:11:36,269 and therefore, this becomes four pi epsilon 183 00:11:36,269 --> 00:11:39,82 zero R. So that is the capacitance of a 184 00:11:39,82 --> 00:11:43,839 single sphere. And so we can now look at the 185 00:11:43,839 --> 00:11:47,135 values as a function of R. 186 00:11:47,135 --> 00:11:50,504 I have here some numbers, I calculated it for the 187 00:11:50,504 --> 00:11:53,733 VandeGraaff, and I calculated it for the Earth. 188 00:11:53,733 --> 00:11:57,032 If you want one Farad capacitance, that's a real 189 00:11:57,032 --> 00:12:00,963 biggie, you need a radius of 9 times ten to the 9 meters, 190 00:12:00,963 --> 00:12:04,542 that's the four pi epsilon zero that comes in there. 191 00:12:04,542 --> 00:12:07,35 That's huge, that's twenty-five times the 192 00:12:07,35 --> 00:12:11,491 distance from the Earth to the moon, that's a big sphere to 193 00:12:11,491 --> 00:12:16,455 have a capacitance of one Farad. The Earth itself, 194 00:12:16,455 --> 00:12:19,44 with a radius of sixty-four hundred kilometers, 195 00:12:19,44 --> 00:12:22,75 would have seven hundred microfarad, the VandeGraaff 196 00:12:22,75 --> 00:12:25,801 thirty centimeters radius would be 30 picofarad, 197 00:12:25,801 --> 00:12:28,072 the pico is ten to the minus twelve. 198 00:12:28,072 --> 00:12:31,707 And if you take a sphere with a radius of one centimeter, 199 00:12:31,707 --> 00:12:33,394 then you have, uh, roughly, 200 00:12:33,394 --> 00:12:36,25 one picofarad, ten to the minus twelve Farad. 201 00:12:36,25 --> 00:12:39,885 So this gives you a rough idea about the size of objects, 202 00:12:39,885 --> 00:12:42,546 and how they connect to their capacitance. 203 00:12:42,546 --> 00:12:45,921 So if I bring all these spheres, 204 00:12:45,921 --> 00:12:49,496 uh, at the same potential, so I charge them all up to the 205 00:12:49,496 --> 00:12:52,306 same potential, then the one with the largest 206 00:12:52,306 --> 00:12:54,988 capacitance, uh, will have the most charge. 207 00:12:54,988 --> 00:12:58,245 And that, of course, is where the word "capacitance" 208 00:12:58,245 --> 00:13:02,204 comes from, it is the capability of holding charge for a given, 209 00:13:02,204 --> 00:13:05,141 uh, electric potential. Don't confuse that with 210 00:13:05,141 --> 00:13:08,078 electric fields, because if you bring all these 211 00:13:08,078 --> 00:13:11,974 spheres at the same potential, then the one with the strongest 212 00:13:11,974 --> 00:13:14,719 electric field, that's the one which has the 213 00:13:14,719 --> 00:13:18,11 short -- smallest radius, 214 00:13:18,11 --> 00:13:23,423 we discussed that last time. Now, I will look at the 215 00:13:23,423 --> 00:13:26,965 situation a little bit differently. 216 00:13:26,965 --> 00:13:29,569 I have, here, a sphere, B, 217 00:13:29,569 --> 00:13:34,777 positively charged, and I place it close to another 218 00:13:34,777 --> 00:13:38,736 sphere, A, which is negatively charged. 219 00:13:38,736 --> 00:13:44,465 And so, by my definition, I can say that the capacitance 220 00:13:44,465 --> 00:13:49,57 of B is the charge that I have on B 221 00:13:49,57 --> 00:13:54,67 divided by the potential of B. That will be my definition. 222 00:13:54,67 --> 00:13:58,608 But, there is here, this object which charged 223 00:13:58,608 --> 00:14:01,292 negative. And how did we define 224 00:14:01,292 --> 00:14:04,604 potential? Potential was work per unit 225 00:14:04,604 --> 00:14:06,751 charge. I go to infinity, 226 00:14:06,751 --> 00:14:10,241 I put plus Q in my pocket, I approach B, 227 00:14:10,241 --> 00:14:15,611 and the work I have to do per unit charge is the potential of 228 00:14:15,611 --> 00:14:20,354 B, that's the definition of potential. 229 00:14:20,354 --> 00:14:24,388 But B is repelling me. So I have to do positive work. 230 00:14:24,388 --> 00:14:28,888 But A is now attracting me. And so the work I have to do is 231 00:14:28,888 --> 00:14:33,621 less the work per unit charge. And so, because of the presence 232 00:14:33,621 --> 00:14:37,423 of A, the potential of B goes down, and therefore, 233 00:14:37,423 --> 00:14:41,924 the capacitance of B goes up. And so now, you see that that 234 00:14:41,924 --> 00:14:46,346 the presence of this charged sphere here has an influence, 235 00:14:46,346 --> 00:14:49,76 an important impact, on the capacitance of B, 236 00:14:49,76 --> 00:14:53,096 and, therefore, it is really 237 00:14:53,096 --> 00:14:56,52 unintelligible to call this the capacitance of B. 238 00:14:56,52 --> 00:15:00,299 We think of it as the capacitance of B in the presence 239 00:15:00,299 --> 00:15:02,866 of A. So it's no longer just B alone. 240 00:15:02,866 --> 00:15:07,145 And so I'm now going to change the definition of capacitance. 241 00:15:07,145 --> 00:15:10,497 And I'm going to change it in the following way. 242 00:15:10,497 --> 00:15:14,134 I have two conductors. And these two conductors have 243 00:15:14,134 --> 00:15:17,058 the same charge, but different polarities. 244 00:15:17,058 --> 00:15:21,55 And now the capacitance of this combination of two conductors is 245 00:15:21,55 --> 00:15:26,126 the charge on one of them -- which is the same, 246 00:15:26,126 --> 00:15:30,907 of course, on the charge of the other, except different polarity 247 00:15:30,907 --> 00:15:33,791 -- divided by the potential difference. 248 00:15:33,791 --> 00:15:36,523 So that, now, is my new definition of 249 00:15:36,523 --> 00:15:39,407 capacitance. So we always deal with two 250 00:15:39,407 --> 00:15:43,202 objects, not with one in isolation, if you have the 251 00:15:43,202 --> 00:15:46,921 charge on one of the two, and you divide it by the 252 00:15:46,921 --> 00:15:49,653 potential difference between the two. 253 00:15:49,653 --> 00:15:53,22 Uh, you may say, "Well, it's a little artificial 254 00:15:53,22 --> 00:15:56,93 to have two, eh, conductors and one is 255 00:15:56,93 --> 00:15:59,511 positively charged, and the other has exactly the 256 00:15:59,511 --> 00:16:01,608 same amount of negatively charge." Well, 257 00:16:01,608 --> 00:16:03,759 it is not so artificial as you may think. 258 00:16:03,759 --> 00:16:05,963 Uh, remember, then, we have this Windhurst 259 00:16:05,963 --> 00:16:09,136 machine, which I was cranking, and I was charging one plate 260 00:16:09,136 --> 00:16:11,018 positive and the other one negative. 261 00:16:11,018 --> 00:16:13,922 And without my doing anything, if one becomes positive, 262 00:16:13,922 --> 00:16:16,986 the other one becomes negative by exactly the same amount, 263 00:16:16,986 --> 00:16:19,514 because you cannot create charge out of nothing. 264 00:16:19,514 --> 00:16:22,31 So if you charge one thing positive, chances are that 265 00:16:22,31 --> 00:16:25,16 something else is charged negative by the same amount, 266 00:16:25,16 --> 00:16:30,151 but with opposite polarity. So it's not so artificial, 267 00:16:30,151 --> 00:16:33,895 that you have two conductors with the same charge but 268 00:16:33,895 --> 00:16:37,568 opposite polarities. So, now, we have two conductors 269 00:16:37,568 --> 00:16:41,528 there, so if we go to this -- these two parallel plates, 270 00:16:41,528 --> 00:16:44,121 the question, now, is what is not the 271 00:16:44,121 --> 00:16:47,649 capacitance, then, according to our new definition 272 00:16:47,649 --> 00:16:51,394 of these parallel plates? Well, that's capacitance C, 273 00:16:51,394 --> 00:16:54,994 is the charge on one plate divided by the potential 274 00:16:54,994 --> 00:16:58,595 difference between the two plates. 275 00:16:58,595 --> 00:17:01,001 And the charge on one plate is sigma A. 276 00:17:01,001 --> 00:17:04,357 And the potential difference between the plates is the 277 00:17:04,357 --> 00:17:07,586 integral of E dot D L, they are separated there by a 278 00:17:07,586 --> 00:17:09,802 -- a distance H. I will change that, 279 00:17:09,802 --> 00:17:12,335 now, to a D, because that's more commonly 280 00:17:12,335 --> 00:17:15,185 done, that the separation between plates is D. 281 00:17:15,185 --> 00:17:18,541 There was a reason why I didn't want to put a D there, 282 00:17:18,541 --> 00:17:21,137 because I didn't want to get you confused, 283 00:17:21,137 --> 00:17:25,063 but now, there is no confusion. And so the potential difference 284 00:17:25,063 --> 00:17:28,925 is the electric field between the plates times the distance D. 285 00:17:28,925 --> 00:17:32,281 But E itself is sigma divided by 286 00:17:32,281 --> 00:17:34,287 epsilon zero, so we get here, 287 00:17:34,287 --> 00:17:37,366 sigma divided by epsilon zero, divided by D, 288 00:17:37,366 --> 00:17:40,446 I lose my sigma, and so, two parallel plates 289 00:17:40,446 --> 00:17:44,743 have this as the capacitance. It's linearly proportional with 290 00:17:44,743 --> 00:17:48,396 the area of the plates, that's intuitively pleasing. 291 00:17:48,396 --> 00:17:52,048 The larger the plate, the more charge you can put on 292 00:17:52,048 --> 00:17:54,698 there. And it's inversely proportional 293 00:17:54,698 --> 00:17:57,277 with the distance between the plates. 294 00:17:57,277 --> 00:18:00,929 The smaller you make the distance, the larger is the 295 00:18:00,929 --> 00:18:05,065 capacitance. Well, that goes back to this 296 00:18:05,065 --> 00:18:09,103 idea, that the closer A is to B, the larger effect that will 297 00:18:09,103 --> 00:18:12,524 have on the capacitance. And if you bring them very 298 00:18:12,524 --> 00:18:15,466 close together, this potential will go down, 299 00:18:15,466 --> 00:18:17,724 and so the capacitance will go up. 300 00:18:17,724 --> 00:18:21,625 So it's not too surprising that you see D here downstairs. 301 00:18:21,625 --> 00:18:25,183 The closer you bring the plates together, the higher, 302 00:18:25,183 --> 00:18:28,672 uh, the capacitance will be. Let us look at a -- uh, 303 00:18:28,672 --> 00:18:33,189 at some numbers. Suppose I have a a plate, 304 00:18:33,189 --> 00:18:38,932 very large, twenty five meters long, and five centimeters wide 305 00:18:38,932 --> 00:18:43,922 -- twenty five meters long, and five centimeters wide. 306 00:18:43,922 --> 00:18:48,159 I have two of them. Called a plate capacitor. 307 00:18:48,159 --> 00:18:53,055 And let the distance between them, D, let D be -- oh, 308 00:18:53,055 --> 00:18:57,857 let's make it very small, because we want a real big 309 00:18:57,857 --> 00:19:01,153 capacitor, point oh one millimeters. 310 00:19:01,153 --> 00:19:07,448 Very small game between them. So, now I substitute the 311 00:19:07,448 --> 00:19:10,39 numbers in there, I can calculate the area, 312 00:19:10,39 --> 00:19:14,383 I have to calculate the area here for the plates in square 313 00:19:14,383 --> 00:19:17,396 meters, of course, multiply by epsilon zero, 314 00:19:17,396 --> 00:19:20,898 and divide it by D in meters, and when you do that, 315 00:19:20,898 --> 00:19:25,102 you find that the capacitance of this big monster is only one 316 00:19:25,102 --> 00:19:27,203 microfarad. It's not very much. 317 00:19:27,203 --> 00:19:31,196 And when you go to Radio Shack, and you buy yourself a one 318 00:19:31,196 --> 00:19:34,769 microfarad capacitor, you don't by something that is 319 00:19:34,769 --> 00:19:38,544 twenty five meters long, and yea big. 320 00:19:38,544 --> 00:19:42,362 Well, you may actually have -- you may actually buy that 321 00:19:42,362 --> 00:19:46,11 without you realizing that. Because these large plates, 322 00:19:46,11 --> 00:19:49,72 these very long ribbons of conductors, two very close 323 00:19:49,72 --> 00:19:52,982 together, separated by some insulating material, 324 00:19:52,982 --> 00:19:55,342 very thin, they're rolled up often. 325 00:19:55,342 --> 00:19:58,743 And you don't notice that, but they are rolled up, 326 00:19:58,743 --> 00:20:02,699 and they are put in a little canister, and that then gives 327 00:20:02,699 --> 00:20:06,656 you a parallel plate capacitor. Uh, I brought one with me, 328 00:20:06,656 --> 00:20:11,464 unintelligible one that I have used for several years, 329 00:20:11,464 --> 00:20:15,187 but, today I decided to cut it open for you so that you can 330 00:20:15,187 --> 00:20:18,205 look inside, and then you actually will see the, 331 00:20:18,205 --> 00:20:21,671 um, you're going to see, there, this is the canister in 332 00:20:21,671 --> 00:20:24,496 which it was, and so I cut the canister open, 333 00:20:24,496 --> 00:20:27,385 and when you look here, you see, there is this 334 00:20:27,385 --> 00:20:31,044 conductor -- looks like aluminum foil -- and then there is 335 00:20:31,044 --> 00:20:33,74 insulating material, and then you find more 336 00:20:33,74 --> 00:20:37,464 conductor, on the other side. And so you -- and it's rolled 337 00:20:37,464 --> 00:20:41,361 up. Here, if I unroll it here -- 338 00:20:41,361 --> 00:20:44,778 I'm breaking it, but that's OK -- so you see the 339 00:20:44,778 --> 00:20:48,777 idea of a parallel plate capacitor, how it can be rolled 340 00:20:48,777 --> 00:20:53,429 up nicely, and you not realizing that you're really talking often 341 00:20:53,429 --> 00:20:56,119 about meters, many meters of material. 342 00:20:56,119 --> 00:20:59,827 Now, through chemical techniques, the distance D can 343 00:20:59,827 --> 00:21:03,389 easily be made a thousand times smaller than this. 344 00:21:03,389 --> 00:21:06,661 And if the distance is thousand times smaller, 345 00:21:06,661 --> 00:21:10,368 then you would get a capacitance of 346 00:21:10,368 --> 00:21:14,329 one thousand microfarads. Compare that with the Earth, 347 00:21:14,329 --> 00:21:17,243 which is only seven hundred microfarads. 348 00:21:17,243 --> 00:21:21,129 So a capacitor like this is one thousand microfarads. 349 00:21:21,129 --> 00:21:24,566 If we bring the potential difference over here, 350 00:21:24,566 --> 00:21:28,227 then we get a tremendous amount of charge on here. 351 00:21:28,227 --> 00:21:32,711 In fact, if I hold this in my hands, and if I assume that the 352 00:21:32,711 --> 00:21:37,269 potential difference between my left hand and my right hand is 353 00:21:37,269 --> 00:21:40,332 ten millivolts, then I would bring on this 354 00:21:40,332 --> 00:21:45,615 capacitor, ten microCoulombs. That is a tremendous amount of 355 00:21:45,615 --> 00:21:47,829 charge. In fact, ten microCoulombs is 356 00:21:47,829 --> 00:21:51,334 the maximum charge we can ever put on the big VandeGraaff, 357 00:21:51,334 --> 00:21:54,287 we calculated it last time. If we put more on the 358 00:21:54,287 --> 00:21:56,439 VandeGraaff, it goes into discharge. 359 00:21:56,439 --> 00:21:59,638 And by simply holding this in my hands, I can put ten 360 00:21:59,638 --> 00:22:01,852 microCoulombs here on this capacitor. 361 00:22:01,852 --> 00:22:03,881 Now, you may say, "Well, yes, but, 362 00:22:03,881 --> 00:22:07,695 uh, potential difference would be your right hand and your left 363 00:22:07,695 --> 00:22:10,032 hand, ten millivolts, isn't that funny? 364 00:22:10,032 --> 00:22:12,061 No, not really. Uh, in the future, 365 00:22:12,061 --> 00:22:17,146 I will give a lecture and then discuss electrocardiograms. 366 00:22:17,146 --> 00:22:20,5 And you will see, then, that there is a potential 367 00:22:20,5 --> 00:22:24,903 difference between the left side of your body and the right side 368 00:22:24,903 --> 00:22:28,886 which is several millivolts. So it is not as artificial as 369 00:22:28,886 --> 00:22:31,401 you may think. Actually, we'll take a 370 00:22:31,401 --> 00:22:34,895 cardiogram in -- in class, so you can see it really 371 00:22:34,895 --> 00:22:37,55 working. How much energy can I store in 372 00:22:37,55 --> 00:22:40,275 a capacitor? Well, we already calculated 373 00:22:40,275 --> 00:22:42,162 that. Uh, we had the energy, 374 00:22:42,162 --> 00:22:48,334 is it, uh this was the plate capacitor, one-half Q V, 375 00:22:48,334 --> 00:22:53,932 and we can now substitute for, um, , we can substitute in 376 00:22:53,932 --> 00:22:59,13 there the capacitance C, and the C is Q divided by V, 377 00:22:59,13 --> 00:23:05,027 and so this is also one-half C V-squared, that's one and the 378 00:23:05,027 --> 00:23:09,025 same thing. So either you take the charge 379 00:23:09,025 --> 00:23:12,424 on the capacitor, multiply it by V, 380 00:23:12,424 --> 00:23:19,197 or you take the capacitance and multiply it by V-squared. 381 00:23:19,197 --> 00:23:23,174 The capacitance is never a function of the charge that is 382 00:23:23,174 --> 00:23:25,588 on the object. V- if you look here, 383 00:23:25,588 --> 00:23:28,712 the capacitance is only a matter of geometry. 384 00:23:28,712 --> 00:23:31,837 And when you look there, the plate capacitor, 385 00:23:31,837 --> 00:23:36,098 it's only a matter of geometry, never does the charge show up 386 00:23:36,098 --> 00:23:38,938 in there. So I mentioned that I can bring 387 00:23:38,938 --> 00:23:42,063 ten microCoulombs on this capacitor, and yet, 388 00:23:42,063 --> 00:23:45,187 on the VandeGraaff, I can also only bring ten 389 00:23:45,187 --> 00:23:48,099 microCoulombs, that's the maximum I can do 390 00:23:48,099 --> 00:23:53,927 before it goes into breakdown. We can think of a capacitor as 391 00:23:53,927 --> 00:23:57,268 a device that can store, uh, electric energy. 392 00:23:57,268 --> 00:24:01,975 I will now return to my promise that I was going to demonstrate 393 00:24:01,975 --> 00:24:05,847 to you that I have to do positive work when I create 394 00:24:05,847 --> 00:24:08,201 electric fields. In other words, 395 00:24:08,201 --> 00:24:12,832 when I take these two charged plates, and I bring them further 396 00:24:12,832 --> 00:24:16,249 away from each other, that I do positive work. 397 00:24:16,249 --> 00:24:19,134 And how am I going to show that to you? 398 00:24:19,134 --> 00:24:24,525 I have two parallel plates. They're on the table there, 399 00:24:24,525 --> 00:24:28,14 you're going to see them shortly, projected there. 400 00:24:28,14 --> 00:24:31,239 And we have, here, a current meter -- I put 401 00:24:31,239 --> 00:24:35,297 an A in there for amperes, symbolic for current meter -- 402 00:24:35,297 --> 00:24:39,355 and I'm going to have a power supply and put a potential 403 00:24:39,355 --> 00:24:43,192 difference over here, this is the capacitance C -- we 404 00:24:43,192 --> 00:24:47,767 normally use for capacitor the symbol of two parallel lines -- 405 00:24:47,767 --> 00:24:52,12 I'm going to put a potential difference V over the capacitor 406 00:24:52,12 --> 00:24:56,891 of thousand volts. So let me put a delta here to 407 00:24:56,891 --> 00:25:00,029 remind you that it's the difference between the two 408 00:25:00,029 --> 00:25:01,284 plates. As I do that, 409 00:25:01,284 --> 00:25:04,233 as I connect the power supply to these two ends, 410 00:25:04,233 --> 00:25:07,433 charge will flow on here, and so you will see a very 411 00:25:07,433 --> 00:25:10,822 short surge of current. So the amp meter will give you, 412 00:25:10,822 --> 00:25:14,022 only for the short amount of time that I am charging 413 00:25:14,022 --> 00:25:17,85 [wssshhht], will see you -- will show you that there is charge 414 00:25:17,85 --> 00:25:19,732 flowing. And you will see that. 415 00:25:19,732 --> 00:25:22,87 But that's not really the goal of my demonstration. 416 00:25:22,87 --> 00:25:27,742 What I'm now going to do is, I'm now going to increase the 417 00:25:27,742 --> 00:25:30,693 separation, the instance D of these two plates. 418 00:25:30,693 --> 00:25:34,67 And remember that the potential difference over the capac- over 419 00:25:34,67 --> 00:25:38,648 the plates, which I call now a capacitor, is the electric field 420 00:25:38,648 --> 00:25:41,47 times the distance, and the electric field is 421 00:25:41,47 --> 00:25:43,844 constant. If I charge the capacitor up 422 00:25:43,844 --> 00:25:46,602 with a certain charge, there is plus Q here, 423 00:25:46,602 --> 00:25:49,746 there's minus Q there, and then I remove the power 424 00:25:49,746 --> 00:25:53,082 supply, it's no longer there, that charge is trapped, 425 00:25:53,082 --> 00:25:56,738 that charge can never change. And so if the charge doesn't 426 00:25:56,738 --> 00:26:00,19 change, the charge surface density 427 00:26:00,19 --> 00:26:02,836 doesn't change, and so the electric field 428 00:26:02,836 --> 00:26:06,342 inside remains constant. So exactly what we did there. 429 00:26:06,342 --> 00:26:09,253 And now I'm going to move them further apart, 430 00:26:09,253 --> 00:26:13,288 therefore I'm going to make D larger, and that can only happen 431 00:26:13,288 --> 00:26:16,992 if the potential difference between the plates increases. 432 00:26:16,992 --> 00:26:19,638 And I will start off with thousand volts, 433 00:26:19,638 --> 00:26:23,343 whereby D is one millimeter, and then I will open up this 434 00:26:23,343 --> 00:26:26,849 gap up to ten millimeters. And then I have a potential 435 00:26:26,849 --> 00:26:30,222 difference of ten thousand volts. 436 00:26:30,222 --> 00:26:34,05 But since the energy in the capacitor is one-half Q times 437 00:26:34,05 --> 00:26:38,22 the potential difference V -- this V is the same as this delta 438 00:26:38,22 --> 00:26:42,185 V -- and if Q is not changing, but if I go from V from one 439 00:26:42,185 --> 00:26:46,217 thousand volts to ten thousand volts, it's very clear that I 440 00:26:46,217 --> 00:26:48,61 have done work, I have increased the 441 00:26:48,61 --> 00:26:52,848 electrostatic potential energy. And this is what I want to show 442 00:26:52,848 --> 00:26:56,676 you, we're going to have that there -- so I've changed my 443 00:26:56,676 --> 00:27:01,461 television, and I will have to change the lights 444 00:27:01,461 --> 00:27:05,268 a little bit so that you can see that -- well, 445 00:27:05,268 --> 00:27:07,89 turn this one off, this one off, 446 00:27:07,89 --> 00:27:12,121 and all them -- let's wait for the light to settle, 447 00:27:12,121 --> 00:27:15,42 and we want also the the current meter. 448 00:27:15,42 --> 00:27:20,243 So the one on the right there is the, uh -- the amp meter, 449 00:27:20,243 --> 00:27:23,965 the current meter, and you see here these two 450 00:27:23,965 --> 00:27:28,534 plates, they are separated now by about one millimeter. 451 00:27:28,534 --> 00:27:34,965 I have here a very thin sheet, transparency which I can move 452 00:27:34,965 --> 00:27:39,028 in between to make sure that they don't make contact -- and 453 00:27:39,028 --> 00:27:41,901 here is my power supply, and I have there, 454 00:27:41,901 --> 00:27:45,964 this, uh, propeller-type thing which is some kind of a volt 455 00:27:45,964 --> 00:27:48,346 meter. And if it's going to move in 456 00:27:48,346 --> 00:27:51,288 this direction, that means that the voltage 457 00:27:51,288 --> 00:27:55,351 between the plates increases. And so I'm going to charge it 458 00:27:55,351 --> 00:27:59,274 now, with a potential difference of, uh, thousand volts, 459 00:27:59,274 --> 00:28:02,637 and as I do that, you will see a very short surge 460 00:28:02,637 --> 00:28:07,834 here on this amp meter. That's not very spectacular, 461 00:28:07,834 --> 00:28:11,177 but at least you can see, for the first time in your 462 00:28:11,177 --> 00:28:14,912 life, that charge is actually flowing from my power supply 463 00:28:14,912 --> 00:28:17,141 onto the plates. Then you will see, 464 00:28:17,141 --> 00:28:20,876 [pssshhht], and that's it. There will only be a current as 465 00:28:20,876 --> 00:28:24,415 long as the charge is flowing. So let my first do that, 466 00:28:24,415 --> 00:28:27,299 look at the amp meter there, three, two, one, 467 00:28:27,299 --> 00:28:29,461 zero. That's all it took to charge 468 00:28:29,461 --> 00:28:31,821 these plates. It's now fully charged, 469 00:28:31,821 --> 00:28:35,032 thousand-volt difference, and now, as I'm going to 470 00:28:35,032 --> 00:28:39,161 increase the gap, there's no reason for any 471 00:28:39,161 --> 00:28:42,645 charge to go away from the plates, so the amp meter will 472 00:28:42,645 --> 00:28:46,32 not do much, probably nothing, but you're going to see this 473 00:28:46,32 --> 00:28:50,185 propeller which indicates the potential difference between the 474 00:28:50,185 --> 00:28:54,113 plates, you're going to see it move, because I'm doing all this 475 00:28:54,113 --> 00:28:57,535 work, I'm going from one millimeter to ten millimeters, 476 00:28:57,535 --> 00:29:01,337 I'm creating all this electric field, and this hard work pays 477 00:29:01,337 --> 00:29:05,265 off in terms of increasing the potential from thousand volts to 478 00:29:05,265 --> 00:29:07,356 ten thousand volts. So there I go, 479 00:29:07,356 --> 00:29:11,323 I'm two millimeters now, look at the volt meter, 480 00:29:11,323 --> 00:29:13,765 there's going -- aargh, three millimeters, 481 00:29:13,765 --> 00:29:17,159 I'm doing all this hard work while you're doing nothing -- 482 00:29:17,159 --> 00:29:20,018 four millimeters, I'm creating electric fields -- 483 00:29:20,018 --> 00:29:23,233 you should be proud of me, I'm creating electric field, 484 00:29:23,233 --> 00:29:25,556 look at that. The electric field remains 485 00:29:25,556 --> 00:29:29,01 constant between the plates, because the charge is trapped, 486 00:29:29,01 --> 00:29:32,464 the charge can't go anywhere. I'm not at seven millimeters, 487 00:29:32,464 --> 00:29:34,965 seven thousand volts, eight thousand volts, 488 00:29:34,965 --> 00:29:38,121 I'm at nine millimeters, nine thousand volts -- notice 489 00:29:38,121 --> 00:29:41,705 that the amp meter does nothing, 490 00:29:41,705 --> 00:29:46,095 no charge is flowing to the plates, no charge is flowing 491 00:29:46,095 --> 00:29:49,527 from the plates, I'm not at ten millimeters, 492 00:29:49,527 --> 00:29:53,597 and now I have created a huge volume electric field, 493 00:29:53,597 --> 00:29:58,305 and the potential difference is ten times larger than it was 494 00:29:58,305 --> 00:30:00,7 before, and so, you see that I, 495 00:30:00,7 --> 00:30:04,69 indeed, have done work. You see it here in front of 496 00:30:04,69 --> 00:30:09,479 your own eyes. All right, let's get this down, 497 00:30:09,479 --> 00:30:14,124 and I'll take the -- bring the lights back up, 498 00:30:14,124 --> 0. and we go back to normal. 499 0. --> 00:30:16,809 500 00:30:16,809 --> 00:30:22,074 I have here a hundred microfarad capacitor -- it's a 501 00:30:22,074 --> 00:30:28,269 dangerous baby -- and we can charge that up to three thousand 502 00:30:28,269 --> 00:30:33,534 volts, and when we do that, we get three-tenths of a 503 00:30:33,534 --> 00:30:39,109 Coulomb of charge on that capacitor. 504 00:30:39,109 --> 00:30:44,65 So the, um, I'll give you some numbers -- so it is one hundred 505 00:30:44,65 --> 00:30:50,191 microfarads, I'm going to put a potential difference over it of 506 00:30:50,191 --> 00:30:54,749 three thousand volts, that gives it a charge Q of oh 507 00:30:54,749 --> 00:30:59,307 point three Coulombs, and that means that one-half C 508 00:30:59,307 --> 00:31:03,329 V squared, which is the energy that is stored, 509 00:31:03,329 --> 00:31:07,619 then, in the capacitor, is four hundred and fifty 510 00:31:07,619 --> 00:31:12,067 joules. And this will take fifteen 511 00:31:12,067 --> 00:31:15,041 minutes. And so th- I'm going to charge 512 00:31:15,041 --> 00:31:19,502 it now, because at the end of the lecture, I need a charge 513 00:31:19,502 --> 00:31:24,277 capacitor for a demonstration. And so I can show you there the 514 00:31:24,277 --> 00:31:28,738 potential difference over the capacitor, which will slowly 515 00:31:28,738 --> 00:31:32,965 change, and we'll keep an eye on it during the lecture, 516 00:31:32,965 --> 00:31:36,096 and then, by the time it's fully charged, 517 00:31:36,096 --> 00:31:40,636 we will have reached the end of the lecture and then we can 518 00:31:40,636 --> 00:31:43,936 continue. So here is, then, 519 00:31:43,936 --> 00:31:47,098 this monster, the hundred microfarad -- I 520 00:31:47,098 --> 00:31:51,683 call it a monster because the amount of energy that you can 521 00:31:51,683 --> 00:31:56,11 pump in there is frightening, it's four hundred and fifty 522 00:31:56,11 --> 00:31:58,877 joules. And my power supply is here, 523 00:31:58,877 --> 00:32:01,248 that will deliver, comfortably, 524 00:32:01,248 --> 00:32:05,675 the three thousand volts. In fact, this is the voltage of 525 00:32:05,675 --> 00:32:09,074 the power supply, this is about thirty eight 526 00:32:09,074 --> 00:32:12,473 hundred volts. And so, now, 527 00:32:12,473 --> 00:32:16,514 the idea is that I'm going to charge this capacitor -- always 528 00:32:16,514 --> 00:32:20,487 have to be very slow and careful that I don't make mistakes, 529 00:32:20,487 --> 00:32:24,663 because this is really a device that could be lethal if you are 530 00:32:24,663 --> 00:32:26,818 not careful. So I think we're OK. 531 00:32:26,818 --> 00:32:30,454 Uh, the moment that I'm going to charge this capacitor, 532 00:32:30,454 --> 00:32:34,495 the reading there will show you the potential difference over 533 00:32:34,495 --> 00:32:37,256 these plates, and it will take a long time 534 00:32:37,256 --> 00:32:40,017 for that to go up to three thousand volts. 535 00:32:40,017 --> 00:32:45,666 And so I think I'm ready to go, and I'm going to charge it now. 536 00:32:45,666 --> 00:32:49,72 So you see now that the potential difference over the 537 00:32:49,72 --> 00:32:52,371 plates is very low, it's near zero, 538 00:32:52,371 --> 00:32:56,503 but if you wait just a -- a few seconds, you will see, 539 00:32:56,503 --> 00:32:59,621 very slowly, that, um, it is charging up, 540 00:32:59,621 --> 00:33:04,065 and fifteen minutes from now, we will be very close to the 541 00:33:04,065 --> 00:33:08,041 three thousand volt mark, and then we will return to 542 00:33:08,041 --> 00:33:10,692 this. So we'll leave it on just for 543 00:33:10,692 --> 00:33:14,901 now, while it is charging. The idea of a photo flash is 544 00:33:14,901 --> 00:33:21,465 that you charge up a capacitor, and that you discharge it over 545 00:33:21,465 --> 00:33:25,671 a light source. So the idea being that you have 546 00:33:25,671 --> 00:33:31,249 a capacitor -- let me erase some of this -- and that we charge 547 00:33:31,249 --> 00:33:35,547 the capacitor up, put a certain amount of energy 548 00:33:35,547 --> 00:33:40,303 in there, and then we dump all that energy in a bulb. 549 00:33:40,303 --> 00:33:45,149 So here is the capacitor, we're going to charge it up, 550 00:33:45,149 --> 00:33:49,538 we have a switch here, and here is a 551 00:33:49,538 --> 00:33:54,487 light bulb, and when we throw the switch, then all the energy 552 00:33:54,487 --> 00:33:59,519 will be going to the light bulb, if this is positively charged 553 00:33:59,519 --> 00:34:04,468 and this is negatively charged, a current will start to flow, 554 00:34:04,468 --> 00:34:07,19 and you will see a flash of light. 555 00:34:07,19 --> 00:34:10,324 I have, here, a capacitance of thousand 556 00:34:10,324 --> 00:34:12,881 microfarad. So C equals thousand 557 00:34:12,881 --> 00:34:17,83 microfarad, I'm going to put a potential difference over that 558 00:34:17,83 --> 00:34:24,252 capacitor of one hundred volts, which then gives me a energy of 559 00:34:24,252 --> 00:34:27,812 one-half C V squared, which is five joules. 560 00:34:27,812 --> 00:34:32,897 In fact, this is not just one capacitor, but these are twelve 561 00:34:32,897 --> 00:34:37,728 capacitors which I hooked up in such a way that the twelve 562 00:34:37,728 --> 00:34:43,068 capacitors of eighty microfarad each are a combined capacitor of 563 00:34:43,068 --> 00:34:47,645 one thousand microfarads. And so I'm going to charge it 564 00:34:47,645 --> 00:34:52,391 up, and then I'm going to discharge the capacitor through 565 00:34:52,391 --> 00:34:56,255 the light, and then you will be able to 566 00:34:56,255 --> 00:34:59,262 see some lights, perhaps, depending on how much 567 00:34:59,262 --> 00:35:02,856 energy we dump through there. So concentrate now on this 568 00:35:02,856 --> 00:35:05,601 light bulb. The hundred volts -- you should 569 00:35:05,601 --> 00:35:09,195 see here, do you see it? -- so it's set at hundred volts 570 00:35:09,195 --> 00:35:12,921 now, and I'm now going to charge it, and the moment that I 571 00:35:12,921 --> 00:35:16,254 charge, you will see the voltage over the capacitor, 572 00:35:16,254 --> 00:35:19,064 and so it takes a while for it to charge up, 573 00:35:19,064 --> 00:35:22,92 so it goes unintelligible down to zero and then slowly comes 574 00:35:22,92 --> 00:35:26,384 back to a hundred, it may take five 575 00:35:26,384 --> 00:35:28,92 or ten seconds. So if you're ready, 576 00:35:28,92 --> 00:35:32,426 then there we go. Took only five or six seconds. 577 00:35:32,426 --> 00:35:36,679 And so now we have a hundred volts, so we have five joules 578 00:35:36,679 --> 00:35:40,185 stored in there, and I'm going to discharge that 579 00:35:40,185 --> 00:35:43,244 now over this light bulb, if you're ready, 580 00:35:43,244 --> 00:35:44,811 three, two, one, zero. 581 00:35:44,811 --> 00:35:48,093 A little bit of light. I can tell that you're 582 00:35:48,093 --> 00:35:50,779 disappointed. It's not very exciting. 583 00:35:50,779 --> 00:35:53,092 It's not really my style, is it? 584 00:35:53,092 --> 00:35:56,822 Well, what we can do, we can increase the voltage a 585 00:35:56,822 --> 00:35:59,09 little bit. 586 00:35:59,09 --> 00:36:02 Uh, we could go to two hundred and fifty volts, 587 00:36:02 --> 00:36:04,72 in which case, since it goes with V-squared, 588 00:36:04,72 --> 00:36:08,389 we would have six times more energy, so then we have thirty 589 00:36:08,389 --> 00:36:11,679 joules, so let's see whether that's a little bit more 590 00:36:11,679 --> 00:36:14,02 exciting. So now I have to jack up the 591 00:36:14,02 --> 00:36:17,689 voltage to two hundred fifty volts -- now you see the power 592 00:36:17,689 --> 00:36:21,169 supply again -- two hundred fifty volts -- we've getting 593 00:36:21,169 --> 00:36:24,206 there, we don't have -- oh, boy, huh, am I lucky, 594 00:36:24,206 --> 00:36:28,001 on the button. So two hundred fifty volts, 595 00:36:28,001 --> 00:36:31,981 and noW I can charge up again, and it will take a little 596 00:36:31,981 --> 00:36:35,744 longer, so you'll see the voltage over the capacitor, 597 00:36:35,744 --> 00:36:37,915 hundred forty, hundred seventy, 598 00:36:37,915 --> 00:36:40,52 two hundred, two fifty, there we are. 599 00:36:40,52 --> 00:36:44,717 And now we can see whether we get a little bit more light. 600 00:36:44,717 --> 00:36:48,19 So you go from five joules now, to thirty joules. 601 00:36:48,19 --> 00:36:49,709 Three, two, one, zero. 602 00:36:49,709 --> 00:36:52,242 Waahaa, now we're getting somewhere. 603 00:36:52,242 --> 00:36:55,281 Now you really see how a photo flash works. 604 00:36:55,281 --> 00:36:59,985 Now, we all, of course, have destructi- 605 00:36:59,985 --> 00:37:04,165 destructive instincts. And so you wonder right? 606 00:37:04,165 --> 00:37:08,167 You- you're thinking the same thing that I do. 607 00:37:08,167 --> 00:37:13,237 Shall we try three hundred forty volts and see whether the 608 00:37:13,237 --> 00:37:15,816 bulb [ptchee], maybe explodes? 609 00:37:15,816 --> 00:37:20,085 I don't know how high this voltage supply can go, 610 00:37:20,085 --> 00:37:23,554 let's see. Let's - let's go all the way. 611 00:37:23,554 --> 00:37:26,4 Three hundred thirty seven volts. 612 00:37:26,4 --> 00:37:31,025 OK. So that would mean that we 613 00:37:31,025 --> 00:37:34,606 have fifty joules, roughly. 614 00:37:34,606 --> 00:37:42,321 It goes as the voltage squared. Well, let's charge again, 615 00:37:42,321 --> 00:37:47,006 so we're charging now. Two hundred, 616 00:37:47,006 --> 00:37:52,241 two eighty, three hundred, there we go, 617 00:37:52,241 --> 00:37:57,2 three hundred and thirty seven volts. 618 00:37:57,2 --> 00:38:01,747 Now let's see -- AAAAH, we did it! 619 00:38:01,747 --> 0. It broke! 620 0. --> 00:38:06,018 621 00:38:06,018 --> 00:38:09,606 I have a photo flash, and I have the photo flash 622 00:38:09,606 --> 00:38:14,494 here, and this photo flash has a capacitor of about five thousand 623 00:38:14,494 --> 00:38:18,846 microfarads, a real biggie, and we can charge that up to a 624 00:38:18,846 --> 00:38:21,977 potential difference of one hundred volts, 625 00:38:21,977 --> 00:38:26,024 even though the batteries in there are only six volts, 626 00:38:26,024 --> 00:38:30,682 there is a circuit in there -- we'll learn about that later -- 627 00:38:30,682 --> 00:38:34,271 which converts the six volts to a hundred volts, 628 00:38:34,271 --> 00:38:39,414 and so we can charge up this capacitor to a hundred volts. 629 00:38:39,414 --> 00:38:42,236 And that means that the one-half C V squared, 630 00:38:42,236 --> 00:38:44,929 the energy stored, then, in that capacitor, 631 00:38:44,929 --> 00:38:48,648 will be twenty five joules. And I can dump that energy over 632 00:38:48,648 --> 00:38:51,534 the light bulb, and then we see a bright flash 633 00:38:51,534 --> 00:38:55,06 of light, because this discharge can occur in something, 634 00:38:55,06 --> 00:38:58,587 like, only a millisecond. So you get a tremendous amount 635 00:38:58,587 --> 00:39:00,832 of light, only for that millisecond. 636 00:39:00,832 --> 00:39:03,204 And I want to demonstrate that to you. 637 00:39:03,204 --> 00:39:06,474 And the only way I can demonstrate that to you is by 638 00:39:06,474 --> 00:39:11,441 aiming this flashlight you -- I don't want to damage your 639 00:39:11,441 --> 00:39:15,023 eyes, so I warn you in advance -- so I am charging up, 640 00:39:15,023 --> 00:39:17,659 now, my capacitor, it will take a while, 641 00:39:17,659 --> 00:39:19,957 and I'm going to take your picture. 642 00:39:19,957 --> 00:39:23,066 I might as well. But, um, it's going to be very 643 00:39:23,066 --> 00:39:26,31 dark in the back, there, and so I've asked Marcos 644 00:39:26,31 --> 00:39:30,23 and Bill to also have some flashlights, which go off at the 645 00:39:30,23 --> 00:39:32,73 same time that my flashlight goes off. 646 00:39:32,73 --> 00:39:35,704 Now, you may say, "Well, how can you do that, 647 00:39:35,704 --> 00:39:39,219 because if this flash only lasts a 648 00:39:39,219 --> 00:39:41,653 millisecond, how can you synchronize that?" 649 00:39:41,653 --> 00:39:44,783 Well, the way that's done is that those flashlights are 650 00:39:44,783 --> 00:39:48,261 waiting for my light signal to reach them, and that goes with 651 00:39:48,261 --> 00:39:50,58 the speed of light. Takes way less than a 652 00:39:50,58 --> 00:39:53,652 millisecond to get there, and they go at the same time 653 00:39:53,652 --> 00:39:55,507 that they receive my light flash. 654 00:39:55,507 --> 00:39:57,42 And so we call them flash-assists. 655 00:39:57,42 --> 00:39:59,971 And so let's, uh, let's see whether we can do 656 00:39:59,971 --> 00:40:01,825 this. I, uh, I have a green light 657 00:40:01,825 --> 00:40:04,318 here, that means I can take my picture, and, 658 00:40:04,318 --> 00:40:07,216 uh, yes, you can -- oh, you don't have to comb your 659 00:40:07,216 --> 00:40:10,463 hair, but -- you're looking good. 660 00:40:10,463 --> 00:40:12,72 OK, let me -- let me, let me focus, 661 00:40:12,72 --> 00:40:16,571 because that's important -- so make sure you see the flash. 662 00:40:16,571 --> 00:40:19,294 You ready for this? Did you see the flash? 663 00:40:19,294 --> 00:40:20,887 Did it flash? Oh, it did. 664 00:40:20,887 --> 00:40:23,942 Oh, you can say yes. So, um, did the -- did the 665 00:40:23,942 --> 00:40:27,594 light-assists also flash? OK, but you haven't seen that, 666 00:40:27,594 --> 00:40:30,117 yet, right? Because you were looking at 667 00:40:30,117 --> 00:40:32,375 them. You should have looked -- you 668 00:40:32,375 --> 00:40:36,558 really should have looked at me. So why don't we take a picture, 669 00:40:36,558 --> 00:40:38,749 Marcos, Bill, aim the fli- li- the 670 00:40:38,749 --> 00:40:42,467 flash-assists at the students here, 671 00:40:42,467 --> 00:40:45,794 and then we'll try it again. You ready? 672 00:40:45,794 --> 00:40:46,757 OK. Oh, boy. 673 00:40:46,757 --> 00:40:49,997 Why don't you say cheese for a change? 674 00:40:49,997 --> 00:40:54,111 OK, look at me -- oh, boy, you're looking great, 675 00:40:54,111 --> 00:40:57,701 you really -- unintelligible out of focus. 676 00:40:57,701 --> 00:41:02,604 Uh, one person's sleeping there, oh, we'll let him sleep, 677 00:41:02,604 --> 00:41:04,705 that's OK. Did that work? 678 00:41:04,705 --> 00:41:07,682 Did you see the flash? You did, eh? 679 00:41:07,682 --> 00:41:10,571 Twenty five -- twenty five joules. 680 00:41:10,571 --> 00:41:16,179 But those haven't seen it yet. So Marcos, Bill, 681 00:41:16,179 --> 00:41:21,04 make sure that we go this way, and give them a chance to see 682 00:41:21,04 --> 00:41:24,501 this light flash. So we get a little bit of 683 00:41:24,501 --> 00:41:28,291 assistance there, the lights, and let's see how 684 00:41:28,291 --> 00:41:31,916 this works, make sure that you see the flash, 685 00:41:31,916 --> 00:41:36,86 very good, you can -- going to see another twenty five joules 686 00:41:36,86 --> 00:41:40,815 going through this light bulb -- very good -- oh, 687 00:41:40,815 --> 00:41:42,875 oh, oh, yes, yes, uh, yes, 688 00:41:42,875 --> 00:41:47,191 your hand is in front of your mouth, 689 00:41:47,191 --> 00:41:49,906 sir, yes, that's OK, thank you. 690 00:41:49,906 --> 00:41:52,802 Very good. Did you see the flash? 691 00:41:52,802 --> 00:41:56,332 Did the f- did the -- did the assist go? 692 00:41:56,332 --> 00:42:00,224 So that's the idea of, um, of photo flashes. 693 00:42:00,224 --> 00:42:05,473 So you dump a lot of energy in a very short amount of time, 694 00:42:05,473 --> 00:42:08,279 and you get a very bright flash. 695 00:42:08,279 --> 00:42:12,895 Professor Edgerton at MIT became very famous for his 696 00:42:12,895 --> 00:42:16,515 flashlights. He invented flashed that can 697 00:42:16,515 --> 00:42:20,788 handle way more energy than this 698 00:42:20,788 --> 00:42:25,157 flash, and they can dump that energy in less that one 699 00:42:25,157 --> 00:42:28,686 microsecond. And so this opened up the road 700 00:42:28,686 --> 00:42:33,224 to high-speed photography, and that made it possible to 701 00:42:33,224 --> 00:42:38,097 study the motion of objects on time scales of microseconds, 702 00:42:38,097 --> 00:42:42,802 and even shorter than that. And I'd like to show you some 703 00:42:42,802 --> 00:42:47,76 of the pictures that were taken with Doc Edgerton's flashes. 704 00:42:47,76 --> 00:42:53,222 The first slide -- you see a bullet coming from the 705 00:42:53,222 --> 00:42:56,605 right going for a light bulb. The exposure of this, 706 00:42:56,605 --> 00:42:58,906 uh, picture, is only one-third of a 707 00:42:58,906 --> 00:43:02,764 microsecond, during which the bullet probably moved only a 708 00:43:02,764 --> 00:43:05,674 third of a millimeter, so it looks like it's 709 00:43:05,674 --> 00:43:09,261 completely standing still. And the bulb is heading for 710 00:43:09,261 --> 00:43:11,833 disaster, but it doesn't know that yet. 711 00:43:11,833 --> 00:43:13,795 Uh, the bullet, uh, moves, uh, 712 00:43:13,795 --> 00:43:16,976 in hundred microseconds about eight centimeters, 713 00:43:16,976 --> 00:43:20,969 and then next picture is taken a hundred microseconds later, 714 00:43:20,969 --> 00:43:24,489 again one-third of a microseconds 715 00:43:24,489 --> 00:43:27,229 exposure. So if we can look at that -- 716 00:43:27,229 --> 00:43:29,97 there, you see, so the bullet now just 717 00:43:29,97 --> 00:43:33,97 penetrates the light bulb, and then the next picture is 718 00:43:33,97 --> 00:43:38,118 another hundred microseconds later, and there you see the 719 00:43:38,118 --> 00:43:40,71 bullet emerging from the light bulb. 720 00:43:40,71 --> 00:43:43,599 And, uh, this, uh, light bulb has hardly 721 00:43:43,599 --> 00:43:47,747 realized that it is broken. But it's beginning to dawn on 722 00:43:47,747 --> 00:43:52,414 it, and and then the next slide is one unintelligible wonderful 723 00:43:52,414 --> 00:43:57,302 picture of a boy who is popping a balloon, 724 00:43:57,302 --> 00:44:02,835 and you see half the balloon doesn't even know yet, 725 00:44:02,835 --> 00:44:07,814 that it is broken. Doc Edgerton also -- that's 726 00:44:07,814 --> 00:44:13,678 enough for these slides -- he also developed a lot of, 727 00:44:13,678 --> 00:44:18,325 um, strobes. A strobe -- I have one here -- 728 00:44:18,325 --> 00:44:23,525 is an instrument that repeatedly discharges, um, 729 00:44:23,525 --> 00:44:30,164 energy over a -- over the light bulb, and so you get repeated 730 00:44:30,164 --> 00:44:33,458 flashes, and that, then, 731 00:44:33,458 --> 00:44:35,463 gives you instrument like this. 732 00:44:35,463 --> 00:44:39,085 Uh, you've seen them in use -- uh, they are being used at 733 00:44:39,085 --> 00:44:42,707 airplanes, just for warning signals, and you've also seen 734 00:44:42,707 --> 00:44:46,393 them on tall towers in the airports, also warning signals, 735 00:44:46,393 --> 00:44:50,015 but there are lot of more things you can do with strobes. 736 00:44:50,015 --> 00:44:53,055 And later, in eight oh two, uh, I will show you, 737 00:44:53,055 --> 00:44:55,448 for instance, that you can measure the 738 00:44:55,448 --> 00:44:58,1 rotation rate of motors with flash lights, 739 00:44:58,1 --> 00:44:59,911 with these, uh, stroboscopes, 740 00:44:59,911 --> 00:45:04,791 and the motors are going to play a more important 741 00:45:04,791 --> 00:45:08,402 role in eight oh two than, uh, than you may have guessed 742 00:45:08,402 --> 00:45:11,881 before you took this course. You can also measure with 743 00:45:11,881 --> 00:45:14,835 strobes the rotation, the speed of your record 744 00:45:14,835 --> 00:45:18,708 player, if you still have one, and then you can adjust it so 745 00:45:18,708 --> 00:45:21,925 that it just has the right speed that is required. 746 00:45:21,925 --> 00:45:25,339 So [inaudible] lot of things you can do with strobes, 747 00:45:25,339 --> 00:45:28,621 and some of which we will see also in eight oh two. 748 00:45:28,621 --> 00:45:31,181 So, now, I return to my capacitor there. 749 00:45:31,181 --> 00:45:34,522 And let's see how it is doing. 750 00:45:34,522 --> 00:45:38,03 Oh, boy, we are close to the three thousand, 751 00:45:38,03 --> 00:45:41,293 which was my goal. It takes a -- you see, 752 00:45:41,293 --> 00:45:45,372 a good fifteen minutes, to actually reach the three 753 00:45:45,372 --> 00:45:50,104 thousand volts on this huge capacitor, and to get in there, 754 00:45:50,104 --> 00:45:54,591 the energy, the four hundred fifty joules that I wanted. 755 00:45:54,591 --> 00:45:58,017 And why is it that I want to show you this? 756 00:45:58,017 --> 00:46:02,015 Well, I want you to appreciate the idea of a fuse. 757 00:46:02,015 --> 00:46:05,751 You have lots of fuses at home. 758 00:46:05,751 --> 00:46:10,211 A fuse is a safety device. A fuse is something that melts, 759 00:46:10,211 --> 00:46:14,671 something that breaks if the current that you are using is 760 00:46:14,671 --> 00:46:17,331 too high. Suppose you have a short, 761 00:46:17,331 --> 00:46:20,07 electric short without realizing it, 762 00:46:20,07 --> 00:46:23,748 in your desk lamp, and a very high current could 763 00:46:23,748 --> 00:46:26,643 start to flow, then the fuse will say, 764 00:46:26,643 --> 00:46:30,164 "Sorry, you can't do that, the fuse will melt, 765 00:46:30,164 --> 00:46:35,016 and then that's -- prevents you from a 766 00:46:35,016 --> 00:46:37,312 disaster, which, actually, might, 767 00:46:37,312 --> 00:46:40,039 give you a fire. And we already showed, 768 00:46:40,039 --> 00:46:43,985 in a way, the idea of a fuse, because when we broke this 769 00:46:43,985 --> 00:46:46,712 light bulb, that was, in a way, a fuse. 770 00:46:46,712 --> 00:46:50,228 We dumped too much energy through that light bulb, 771 00:46:50,228 --> 00:46:54,462 and so, the light bulb itself [klk] was already like a fuse. 772 00:46:54,462 --> 00:46:58,121 This is really more like a fuse that we are used to, 773 00:46:58,121 --> 00:47:01,996 it is a -- we have a wire there, which is an iron wire, 774 00:47:01,996 --> 00:47:05,8 which is twelve inches long, and it has a thickness of 775 00:47:05,8 --> 00:47:09,301 thirty thousandths of an inch. 776 00:47:09,301 --> 00:47:13,16 And we're going to dump the four hundred fifty joules 777 00:47:13,16 --> 00:47:16,648 through that wire. So the idea is very much like 778 00:47:16,648 --> 00:47:21,175 we had the -- the photo flash, we, um, have all this energy in 779 00:47:21,175 --> 00:47:24,07 the capacitor, and instead of dumping it 780 00:47:24,07 --> 00:47:27,41 through the light bulb, which was this system, 781 00:47:27,41 --> 00:47:30,824 we now have here, a wire, and when I throw this 782 00:47:30,824 --> 00:47:34,015 switch, the energy will go through the wire. 783 00:47:34,015 --> 00:47:37,875 And chances are that you may see the 784 00:47:37,875 --> 00:47:40,913 wire glowing a little bit, and then it would melt, 785 00:47:40,913 --> 00:47:43,827 and that would then give you the idea of a fuse. 786 00:47:43,827 --> 00:47:47,052 And it's also possible that, after we have done that, 787 00:47:47,052 --> 00:47:50,339 that there may still be energy left on this capacitor, 788 00:47:50,339 --> 00:47:54,059 and I can show that to you too, then, because I can short out 789 00:47:54,059 --> 00:47:57,594 the two ends of the capacitor and see whether we still see 790 00:47:57,594 --> 00:48:00,384 some -- some sparks, which would indicate that 791 00:48:00,384 --> 00:48:03,919 there's still some energy left. So if you are ready -- I'm 792 00:48:03,919 --> 00:48:08,26 always a little bit scared with this demonstration -- 793 00:48:08,26 --> 00:48:14,02 not so much about what's going happen, that thing will probably 794 00:48:14,02 --> 00:48:18,851 just melt, and maybe we'll see a little bit of light, 795 00:48:18,851 --> 00:48:23,589 that's not the issue -- but I'm afraid of this baby, 796 00:48:23,589 --> 00:48:27,677 because that has, now, a tremendous amount of 797 00:48:27,677 --> 00:48:30,929 energy. So I stop the charging -- so 798 00:48:30,929 --> 00:48:36,503 let's do that -- and if you're ready, then I will try to dump 799 00:48:36,503 --> 00:48:39,569 all that energy through this wire. 800 00:48:39,569 --> 00:48:41,52 Three, two, one, zero. 801 00:48:41,52 --> 00:48:46,9 [bang] [hum] [bang]. This is the way a fuse works. 802 00:48:46,9 --> 00:48:49,177 This is very effective, as you see. 803 00:48:49,177 --> 00:48:52,324 And if you hear this happening in your basement, 804 00:48:52,324 --> 00:48:54,401 then, well, maybe that's a fuse. 805 00:48:54,401 --> 00:48:57,883 We can now check whether there is energy left on that 806 00:48:57,883 --> 00:48:59,892 capacitor. Maybe not very much, 807 00:48:59,892 --> 00:49:03,241 but it's unlikely that everything was dumped in the 808 00:49:03,241 --> 00:49:06,255 iron, so let's see whether there is some left, 809 00:49:06,255 --> 00:49:09,469 if I'm going to be able to short it out with this 810 00:49:09,469 --> 00:49:12,349 conducting bar, and see whether we can get a 811 00:49:12,349 --> 00:49:14,848 spark. And we can. 812 00:49:14,848 --> 00:49:17,119 So there's still some energy left. 813 00:49:17,119 --> 49:22 OK, see you Friday.