1 00:00:00 --> 00:00:03,993 2 00:00:03,993 --> 00:00:11,767 Today I'm going to work with you on a new concept and that is 3 00:00:11,767 --> 00:00:17,209 the concept of what we call electric field. 4 00:00:17,209 --> 00:00:23,04 We spend the whole lecture on electric fields. 5 00:00:23,04 --> 00:00:28,223 If I have a -- a charge, I just choose Q, 6 00:00:28,223 --> 00:00:34,572 capital Q and plus at a particular location and at 7 00:00:34,572 --> 00:00:40,802 another location I have another charge little Q, 8 00:00:40,802 --> 00:00:43,709 I think of that as my test charge. 9 00:00:43,709 --> 00:00:48,29 And there is a separation between the two which is R. 10 00:00:48,29 --> 00:00:53,664 The unit vector from capital Q to li- little Q is this vector. 11 00:00:53,664 --> 00:00:59,126 And so now I know that the two charges if they were positive -- 12 00:00:59,126 --> 00:01:04,5 let's suppose that little Q is positive, they would repel each 13 00:01:04,5 --> 00:01:07,759 other. Little Q is negative they would 14 00:01:07,759 --> 00:01:13,219 attract each other. And let this force be F and 15 00:01:13,219 --> 00:01:18,323 last time we introduced Coulomb's law that force equals 16 00:01:18,323 --> 00:01:24,09 little Q times capital Q times Coulomb's constant divided by R 17 00:01:24,09 --> 00:01:27,304 squared in the direction of R roof. 18 00:01:27,304 --> 00:01:32,03 The two have the same sign. It's in this direction. 19 00:01:32,03 --> 00:01:37,135 If they have opposite sign it's in the other direction. 20 00:01:37,135 --> 00:01:42,617 And now I introduce the idea of electric field for which we 21 00:01:42,617 --> 00:01:46,389 write the symbol capital E. 22 00:01:46,389 --> 00:01:51,941 And capital E at that location P where I have my test charge 23 00:01:51,941 --> 00:01:57,398 little Q at that location P is simply the force that a test 24 00:01:57,398 --> 00:02:01,726 charge experienced divided by that test charge. 25 00:02:01,726 --> 00:02:07,372 So I eliminate the test charge. So I get something that looks 26 00:02:07,372 --> 00:02:13,017 quite similar but it doesn't have the little Q in it anymore. 27 00:02:13,017 --> 00:02:18,193 And it is also a vector. And by convention, 28 00:02:18,193 --> 00:02:22,801 we choose the force such that if this is a positive test 29 00:02:22,801 --> 00:02:27,997 charge then we say the E field is away from Q if Q is positive, 30 00:02:27,997 --> 00:02:32,354 if Q is negative the force is in the other direction, 31 00:02:32,354 --> 00:02:35,789 and therefore E is in the other direction. 32 00:02:35,789 --> 00:02:40,733 So we adopt the convention that the E field is always in the 33 00:02:40,733 --> 00:02:45,175 direction that the force is on a positive test charge. 34 00:02:45,175 --> 00:02:49,281 What you have gained now is that you 35 00:02:49,281 --> 00:02:53,67 have taken out the little Q. In other words the force here 36 00:02:53,67 --> 00:02:57,058 depends on little Q. Electric field does not. 37 00:02:57,058 --> 00:03:01,217 The electric field is a representation for what happens 38 00:03:01,217 --> 00:03:04,682 around the charge plus Q. This could be a very 39 00:03:04,682 --> 00:03:07,146 complicated charge configuration. 40 00:03:07,146 --> 00:03:11,304 An electric field tells you something about that charge 41 00:03:11,304 --> 00:03:14,77 configuration. The unit for electric field you 42 00:03:14,77 --> 00:03:17,696 can see is newtons divided by coulombs. 43 00:03:17,696 --> 00:03:22,085 In SI units and normally we won't even indicate the um the 44 00:03:22,085 --> 00:03:26,909 unit, we just leave that as it is. 45 00:03:26,909 --> 00:03:32,54 Now we have graphical representations for the electric 46 00:03:32,54 --> 00:03:36,047 field. Electric field is a vector. 47 00:03:36,047 --> 00:03:42,741 So you expect arrows and I have here an example of a -- a charge 48 00:03:42,741 --> 00:03:47,204 plus three. So by convention the arrows are 49 00:03:47,204 --> 00:03:53,26 pointing away from the charge in the same direction that a 50 00:03:53,26 --> 00:03:57,751 positive test charge would experience the 51 00:03:57,751 --> 00:04:00,197 force. And you notice that very close 52 00:04:00,197 --> 00:04:03,799 to the charge the arrows are larger than farther away. 53 00:04:03,799 --> 00:04:07,672 That it that sort of represents is trying to represent the 54 00:04:07,672 --> 00:04:11,545 inverse R square relationship. Of course it cannot be very 55 00:04:11,545 --> 00:04:14,399 quantitative. But the basic idea is this is 56 00:04:14,399 --> 00:04:18,34 of course spherically symmetric, if this is a point charge. 57 00:04:18,34 --> 00:04:22,078 The basic idea is here you see the field vectors and the 58 00:04:22,078 --> 00:04:26,155 direction of the arrow tells you in which direction the force 59 00:04:26,155 --> 00:04:29,613 would be. If it is a positive test 60 00:04:29,613 --> 00:04:31,981 charge. And the length of the vector 61 00:04:31,981 --> 00:04:34,214 give you an idea of the magnitude. 62 00:04:34,214 --> 00:04:36,92 And here I have another charge minus one. 63 00:04:36,92 --> 00:04:40,574 Doesn't matter whether it is minus one coulomb or minus 64 00:04:40,574 --> 00:04:42,807 microcoulomb. Just it's a relative 65 00:04:42,807 --> 00:04:45,581 representation. And you see now that the E 66 00:04:45,581 --> 00:04:48,219 field vectors are reversed in direction. 67 00:04:48,219 --> 00:04:51,941 They're pointing towards the minus charge by convention. 68 00:04:51,941 --> 00:04:55,932 And when you go further out they are smaller and you have to 69 00:04:55,932 --> 00:05:00,159 go all the way to infinity of course 70 00:05:00,159 --> 00:05:05,095 for the field to become zero. Because the one over R square 71 00:05:05,095 --> 00:05:10,286 field falls off and you have to be infinitely far away for you 72 00:05:10,286 --> 00:05:15,222 to not experience at least in principle any effect from the 73 00:05:15,222 --> 00:05:19,137 from the charge. What do we do now when we have 74 00:05:19,137 --> 00:05:22,966 more than one charge? Well, if we have several 75 00:05:22,966 --> 00:05:28,072 charges -- here we have Q one and here we have Q two and here 76 00:05:28,072 --> 00:05:32,413 we have Q three and let's say here we 77 00:05:32,413 --> 00:05:35,386 have Q of I, we have I charges. 78 00:05:35,386 --> 00:05:41,431 And now we want to know what is the electric field at point P. 79 00:05:41,431 --> 00:05:46,783 So it's independent of the test charge that I put here. 80 00:05:46,783 --> 00:05:52,63 You can think of it if you want to as the the force per unit 81 00:05:52,63 --> 00:05:56,297 charge. You've divided out the charge. 82 00:05:56,297 --> 00:06:01,748 So now I can say what is the E field due to Q one alone? 83 00:06:01,748 --> 00:06:06,307 Well, that would be if Q one were 84 00:06:06,307 --> 00:06:11,517 positive then this might be a representation for E one. 85 00:06:11,517 --> 00:06:16,631 If Q two were negative, this might be a representation 86 00:06:16,631 --> 00:06:21,166 for E two, pointing towards the negative charge. 87 00:06:21,166 --> 00:06:26,376 And if this one were negative, then I would have here a 88 00:06:26,376 --> 00:06:29,368 contribution E three, and so on. 89 00:06:29,368 --> 00:06:33,903 And now we use the superposition principle as we 90 00:06:33,903 --> 00:06:39,209 did last time with Coulomb's law, that the 91 00:06:39,209 --> 00:06:44,789 net electric field at point P as a vector is E one in 92 00:06:44,789 --> 00:06:51,119 reference of charge Q one plus the vector E two plus E three 93 00:06:51,119 --> 00:06:57,234 and so on and if you have I charges it is the sum of all I 94 00:06:57,234 --> 00:07:00,989 charges of the individual E vectors. 95 00:07:00,989 --> 00:07:06,568 Is it obvious that the superposition principle works? 96 00:07:06,568 --> 00:07:08,285 No. Does it work? 97 00:07:08,285 --> 00:07:11,182 Yes. How do we 98 00:07:11,182 --> 00:07:14,579 know it works? Because it's consistent with 99 00:07:14,579 --> 00:07:19,189 all our experimental results. So we take the superposition 100 00:07:19,189 --> 00:07:22,748 principle for granted and that is acceptable. 101 00:07:22,748 --> 00:07:26,307 But it's not obvious. If you tell me what the 102 00:07:26,307 --> 00:07:31,16 electric field at this point is which is the vectorial sum of 103 00:07:31,16 --> 00:07:36,094 the individual E field vectors then I can always tell you what 104 00:07:36,094 --> 00:07:41,595 the force will be if I bring a charge at that location. 105 00:07:41,595 --> 00:07:45,37 I take any charge that I always would carry in my pocket, 106 00:07:45,37 --> 00:07:49,145 I take it out of my pocket and I put it at that location. 107 00:07:49,145 --> 00:07:52,584 And the charge that I have in my pocket is little Q. 108 00:07:52,584 --> 00:07:55,887 Then the force on that charge is always Q times E. 109 00:07:55,887 --> 00:07:58,314 Doesn't matter whether Q is positive. 110 00:07:58,314 --> 00:08:01,146 Then it will be in the same direction as E. 111 00:08:01,146 --> 00:08:05,123 If it is negative it will be in the opposite direction as E. 112 00:08:05,123 --> 00:08:07,618 If Q is large the force will be large. 113 00:08:07,618 --> 00:08:10,112 If Q is small the force will be small. 114 00:08:10,112 --> 00:08:15,834 So once you know the E field it could be the result of 115 00:08:15,834 --> 00:08:19,46 very complicated charge configurations, 116 00:08:19,46 --> 00:08:24,707 the real secret behind the concept of an E field is that 117 00:08:24,707 --> 00:08:30,432 you bring any charge at that location and you know what force 118 00:08:30,432 --> 00:08:33,581 acts at that point on that charge. 119 00:08:33,581 --> 00:08:37,97 If we try to be a little bit more quantitative, 120 00:08:37,97 --> 00:08:43,122 suppose I had here a charge plus three and here I had a 121 00:08:43,122 --> 00:08:47,457 charge minus one. Here's minus one. 122 00:08:47,457 --> 00:08:51,832 And I want to know what the field configuration is as a 123 00:08:51,832 --> 00:08:56,611 result of these two charges. So you can go to any particular 124 00:08:56,611 --> 00:08:59,366 point. You get an E vector which is 125 00:08:59,366 --> 00:09:04,308 going away from the plus three, you get one that goes to minus 126 00:09:04,308 --> 00:09:07,872 one, and you have to vectorially add the two. 127 00:09:07,872 --> 00:09:12,814 If you are very close to minus one, it's very clear because of 128 00:09:12,814 --> 00:09:16,946 the inverse R square relationship that the minus one 129 00:09:16,946 --> 00:09:20,141 is probably going to win. 130 00:09:20,141 --> 00:09:23,629 Let's in our mind take a plus test charge now. 131 00:09:23,629 --> 00:09:27,737 And we put a plus test charge very close to minus one, 132 00:09:27,737 --> 00:09:30,915 say put it here, even though plus three is 133 00:09:30,915 --> 00:09:34,558 trying to push it out, clearly minus one is most 134 00:09:34,558 --> 00:09:38,046 likely to win. And so there will probably be a 135 00:09:38,046 --> 00:09:41,223 force on my test charge in this direction. 136 00:09:41,223 --> 00:09:44,324 The net result of the effects of the two. 137 00:09:44,324 --> 00:09:48,432 Suppose I take the same positive test charge and I put 138 00:09:48,432 --> 00:09:54,133 it here, very far away, much farther away than this 139 00:09:54,133 --> 00:09:57,778 separation. What do you think now is the 140 00:09:57,778 --> 00:10:01,517 direction of the force on my plus charge? 141 00:10:01,517 --> 00:10:03,76 Very far away. Excuse me. 142 00:10:03,76 --> 00:10:06,845 Why do you think it's to the left? 143 00:10:06,845 --> 00:10:10,864 Do you think minus one wins? A: [inaudible]. 144 00:10:10,864 --> 00:10:16,285 Do you really think the minus one is stronger than the plus 145 00:10:16,285 --> 00:10:22,173 three because the plus three will push it out and 146 00:10:22,173 --> 00:10:48,551 the minus one tries to lure it in, right, if the test charge is 147 00:10:48,551 --> 00:10:54,508 positive. A: 148 00:10:54,508 --> 00:10:56,732 plus two. So if you're far away from a 149 00:10:56,732 --> 00:10:59,498 configuration like this, even if you were here, 150 00:10:59,498 --> 00:11:02,143 or if you were there, or if you're way there, 151 00:11:02,143 --> 00:11:04,728 clearly the field is like a plus two charge. 152 00:11:04,728 --> 00:11:06,832 And falls off as one over R squared. 153 00:11:06,832 --> 00:11:10,56 So therefore if you're far away the force is in this direction. 154 00:11:10,56 --> 00:11:12,845 And now look, what is very interesting. 155 00:11:12,845 --> 00:11:16,332 Here if you're close to the minus one, the force is in this 156 00:11:16,332 --> 00:11:18,797 direction. Here when you're very far away, 157 00:11:18,797 --> 00:11:22,284 maybe I should be all the way here, it's in that direction. 158 00:11:22,284 --> 00:11:26,072 So that means there must be somewhere here 159 00:11:26,072 --> 00:11:28,987 the point where the E field is zero. 160 00:11:28,987 --> 00:11:33,985 Because if the force is here in this direction but ultimately 161 00:11:33,985 --> 00:11:38,984 turns over in that direction, there must be somewhere a point 162 00:11:38,984 --> 00:11:42,316 where E is zero. And that is part of your 163 00:11:42,316 --> 00:11:45,648 assignment. I want you to find that point 164 00:11:45,648 --> 00:11:48,73 for a particular charge configuration. 165 00:11:48,73 --> 00:11:53,145 So let's now go to some graphical representations of a 166 00:11:53,145 --> 00:11:58,476 situation which is actually plus three minus one, 167 00:11:58,476 --> 00:12:02,215 try to improve on the light situation. 168 00:12:02,215 --> 00:12:06,256 And let's see how these electric vectors, 169 00:12:06,256 --> 00:12:11,61 how they show up in the vicinity of these two charges. 170 00:12:11,61 --> 00:12:16,46 So here you see the plus three and the minus one, 171 00:12:16,46 --> 00:12:20,905 relative units, and let's take a look at this 172 00:12:20,905 --> 00:12:25,451 in some detail. First of all the length of the 173 00:12:25,451 --> 00:12:30,402 arrows again indicates the strength. 174 00:12:30,402 --> 00:12:32,828 It gives you a feeling for the strength. 175 00:12:32,828 --> 00:12:35,068 It's not very quantitative of course. 176 00:12:35,068 --> 00:12:38,49 And so let's first look at the plus three, which is very 177 00:12:38,49 --> 00:12:40,855 powerful. You see that these arrows all 178 00:12:40,855 --> 00:12:44,65 go away from the plus three and when you're closer to the plus 179 00:12:44,65 --> 00:12:47,886 three, they're stronger, which is a representation of 180 00:12:47,886 --> 00:12:51,246 the inverse R square field. If you're very close to the 181 00:12:51,246 --> 00:12:54,792 minus one, ah the arrows are pointing in towards the minus 182 00:12:54,792 --> 00:12:58,152 one, because the one over R square, the minus one wins. 183 00:12:58,152 --> 00:13:02,214 And so you see they're clearly going into the 184 00:13:02,214 --> 00:13:06,031 direction of the minus one. Well, if you're in between the 185 00:13:06,031 --> 00:13:09,915 plus and the minus on this line, always the E field will be 186 00:13:09,915 --> 00:13:12,258 pointing from the plus to the minus. 187 00:13:12,258 --> 00:13:16,209 Because the plus is pushing out and the minus is sucking in. 188 00:13:16,209 --> 00:13:20,293 So the two support each other. But now if you go very far away 189 00:13:20,293 --> 00:13:24,177 from this charge configuration, anywhere but very far away, 190 00:13:24,177 --> 00:13:27,793 much farther than the distance between the two charges, 191 00:13:27,793 --> 00:13:30,27 so somewhere here, or somewhere there, 192 00:13:30,27 --> 00:13:34,629 or somewhere there, or here, notice that always the 193 00:13:34,629 --> 00:13:37,785 arrows are pointing away. And the reason is that plus 194 00:13:37,785 --> 00:13:41,305 three and minus one is as good as a plus two if you're very 195 00:13:41,305 --> 00:13:43,976 very far away. But of course when you're very 196 00:13:43,976 --> 00:13:47,253 close in, then the field configuration can be very very 197 00:13:47,253 --> 00:13:49,742 complicated. But you see very clearly that 198 00:13:49,742 --> 00:13:52,048 these arrows are all pointing outwards. 199 00:13:52,048 --> 00:13:54,415 None of them come back to the minus one. 200 00:13:54,415 --> 00:13:57,146 None of them point to the minus one direction. 201 00:13:57,146 --> 00:14:00,667 And that's because the plus three is more powerful and then 202 00:14:00,667 --> 00:14:04,821 there is here this point and only point 203 00:14:04,821 --> 00:14:10,072 whereby the electric field is zero, if you put a positive test 204 00:14:10,072 --> 00:14:15,064 charge here, the minus will attract it, the plus will repel 205 00:14:15,064 --> 00:14:20,4 it, and therefore there comes a point where the two cancel each 206 00:14:20,4 --> 00:14:23,929 other exactly. Now there is another way of 207 00:14:23,929 --> 00:14:28,491 electric field representation which is more organized. 208 00:14:28,491 --> 00:14:33,741 And we call these field lines. So you see again the plus three 209 00:14:33,741 --> 00:14:37,816 and you see there the minus one. 210 00:14:37,816 --> 00:14:42,852 If I release right here or I place here a positive test 211 00:14:42,852 --> 00:14:48,447 charge all I know is that the force will be tangential to the 212 00:14:48,447 --> 00:14:52,178 field lines. That is the meaning of these 213 00:14:52,178 --> 00:14:55,442 lines. So if I'm here the force will 214 00:14:55,442 --> 00:15:00,292 be in this direction. If I put a positive test charge 215 00:15:00,292 --> 00:15:06,726 here, the force will be in this direction, and of course, 216 00:15:06,726 --> 00:15:09,879 if it's a negative charge the force flips over. 217 00:15:09,879 --> 00:15:13,785 So the meaning of the field lines are that it always tells 218 00:15:13,785 --> 00:15:17,28 you in which direction a charge experiences a force. 219 00:15:17,28 --> 00:15:21,049 A force a positive charge always in the direction of the 220 00:15:21,049 --> 00:15:24,681 arrows, tangentially to the field lines and a negative 221 00:15:24,681 --> 00:15:26,874 charge in the opposite direction. 222 00:15:26,874 --> 00:15:29,546 How many field lines are there in space? 223 00:15:29,546 --> 00:15:32,493 Well of course there are an infinite number. 224 00:15:32,493 --> 00:15:35,782 Just like these little arrows that we had before, 225 00:15:35,782 --> 00:15:39,346 we only sprinkled in a few but of 226 00:15:39,346 --> 00:15:43,1 course in every single point there is an electric field and 227 00:15:43,1 --> 00:15:46,919 so you can put in an infinite number of field lines and that 228 00:15:46,919 --> 00:15:50,155 would make this a representation of course useless. 229 00:15:50,155 --> 00:15:53,262 So we always limit ourselves to a certain number. 230 00:15:53,262 --> 00:15:57,017 If you look very close to the minus one notice that all the 231 00:15:57,017 --> 00:15:59,347 field lines come in on the minus one. 232 00:15:59,347 --> 00:16:03,166 We understand that of course because a positive charge would 233 00:16:03,166 --> 00:16:06,726 want to go to the minus one. If you're very close to the 234 00:16:06,726 --> 00:16:10,61 plus and they all go away from the plus because they're being 235 00:16:10,61 --> 00:16:14,571 repelled. You can sort of think as these 236 00:16:14,571 --> 00:16:18,581 field lines if you want to imagine the configuration that 237 00:16:18,581 --> 00:16:21,874 the plus charges blow out air like a hairdryer, 238 00:16:21,874 --> 00:16:25,598 and that the minus suck in air like a vacuum cleaner, 239 00:16:25,598 --> 00:16:29,966 and then you get a feeling for there is on this left side here 240 00:16:29,966 --> 00:16:34,334 this hairdryer which wants to blow out stuff and then there is 241 00:16:34,334 --> 00:16:38,344 that little sucker that wants to suck something in and it 242 00:16:38,344 --> 00:16:41,995 succeeds to some degree, it's not as powerful as the 243 00:16:41,995 --> 00:16:44,304 plus three, though. 244 00:16:44,304 --> 00:16:47,373 Have we lost all information about field strength? 245 00:16:47,373 --> 00:16:50,943 We had earlier with these arrows, we had the length of the 246 00:16:50,943 --> 00:16:54,013 arrow, the magnitude of the field was represented. 247 00:16:54,013 --> 00:16:57,019 Yeah, you have lost that, but there is still some 248 00:16:57,019 --> 00:17:00,339 information on field strength. If the lines are closer 249 00:17:00,339 --> 00:17:02,969 together, the density of the lines is high, 250 00:17:02,969 --> 00:17:06,664 the electric field is stronger than when the density becomes 251 00:17:06,664 --> 00:17:08,606 low. So if you look for instance 252 00:17:08,606 --> 00:17:12,051 here, look how many lines there are per few millimeters, 253 00:17:12,051 --> 00:17:15,371 and when you go further out these 254 00:17:15,371 --> 00:17:18,91 lines spread out, that tells you the E field is 255 00:17:18,91 --> 00:17:22,987 going down, the strength of the E field is going down. 256 00:17:22,987 --> 00:17:26,219 It's the one over R square field of course. 257 00:17:26,219 --> 00:17:30,373 If you want to make these drawings what you could do to 258 00:17:30,373 --> 00:17:34,143 make them look good, you can make three times more 259 00:17:34,143 --> 00:17:38,914 field lines going out from the plus in this case than return to 260 00:17:38,914 --> 00:17:42,068 the minus one. So the field lines are very 261 00:17:42,068 --> 00:17:46,915 powerful and we will often think in terms of electric fields and 262 00:17:46,915 --> 00:17:51,377 the line configurations and you will have 263 00:17:51,377 --> 00:17:57,154 several homework problems that deal with electric fields and 264 00:17:57,154 --> 00:18:02,833 with the electric field lines. If an electric field line is 265 00:18:02,833 --> 00:18:08,218 straight, so I have electric fields, get some red chalk, 266 00:18:08,218 --> 00:18:13,505 say we have fields that are like this, straight E field 267 00:18:13,505 --> 00:18:19,281 lines, and I release a charge there, for instance a positive 268 00:18:19,281 --> 00:18:22,829 charge, then the positive charge would 269 00:18:22,829 --> 00:18:26,401 experience a force exactly in the same direction as the field 270 00:18:26,401 --> 00:18:29,914 lines, because the tangential now is in the direction of the 271 00:18:29,914 --> 00:18:33,248 field line, it would become accelerated in this direction 272 00:18:33,248 --> 00:18:35,629 and would always stay on the field lines. 273 00:18:35,629 --> 00:18:38,903 If I release it with zero speed, start to accelerate and 274 00:18:38,903 --> 00:18:40,808 it would stay on the field lines. 275 00:18:40,808 --> 00:18:43,428 In a similar way, if we think of the earth as 276 00:18:43,428 --> 00:18:46,94 having a gravitational field, with eight oh one we may never 277 00:18:46,94 --> 00:18:49,321 have used that word, gravitational field, 278 00:18:49,321 --> 00:18:53,36 but in physics we think of the -- of gravity 279 00:18:53,36 --> 00:18:56,834 also being a field. If I have here a piece of chalk 280 00:18:56,834 --> 00:19:00,516 the um the field lines, the gravitational field lines, 281 00:19:00,516 --> 00:19:04,614 here in twenty-six one hundred, nicely parallel and straight 282 00:19:04,614 --> 00:19:08,574 and if I release this piece of chalk at zero speed it will 283 00:19:08,574 --> 00:19:11,978 begin to move in the direction of the field lines, 284 00:19:11,978 --> 00:19:14,41 and it will stay on the field lines. 285 00:19:14,41 --> 00:19:18,648 So now you can ask yourself the question if I release a charge 286 00:19:18,648 --> 00:19:22,469 would it always follow the field lines? 287 00:19:22,469 --> 00:19:26,732 And the answer is no. Only in this very special case. 288 00:19:26,732 --> 00:19:30,585 But suppose now that the field lines are curved. 289 00:19:30,585 --> 00:19:34,521 So here are field lines as you have seen in those 290 00:19:34,521 --> 00:19:37,145 configurations. It's very common. 291 00:19:37,145 --> 00:19:41,818 If now I release a -- a charge in here, say I have a point 292 00:19:41,818 --> 00:19:46,492 charge here, it will experience a force in this direction. 293 00:19:46,492 --> 00:19:50,427 So it will get an acceleration in this direction, 294 00:19:50,427 --> 00:19:54,527 so it will immediately abandon that 295 00:19:54,527 --> 00:19:57,153 field line. And so if now you ask me what 296 00:19:57,153 --> 00:19:59,648 is the trajectory of that charge, well, 297 00:19:59,648 --> 00:20:02,734 it could become very complicated, I really don't 298 00:20:02,734 --> 00:20:04,835 know. Maybe it's going like this, 299 00:20:04,835 --> 00:20:08,906 and by the time it reaches this point, what I do know that then 300 00:20:08,906 --> 00:20:11,992 the force will be tangential to this field line, 301 00:20:11,992 --> 00:20:15,734 so will be in this direction. And so as it marches out and 302 00:20:15,734 --> 00:20:18,426 picks up speed, locally it will experience 303 00:20:18,426 --> 00:20:21,841 forces representative of those field lines and so the 304 00:20:21,841 --> 00:20:25,518 trajectory can be rather complicated. 305 00:20:25,518 --> 00:20:28,624 So field lines are not trajectories, 306 00:20:28,624 --> 00:20:34,126 and not even when you release a charge with uh with zero speed. 307 00:20:34,126 --> 00:20:38,741 Only in case that the field lines are straight lines. 308 00:20:38,741 --> 00:20:43,357 Let's now look at a field configuration which Maxwell 309 00:20:43,357 --> 00:20:48,504 himself, the great maestro, in some of his publications put 310 00:20:48,504 --> 00:20:51,522 there. And it's a ratio one to four 311 00:20:51,522 --> 00:20:58 and whether it is plus four plus one or minus four minus one 312 00:20:58 --> 00:21:02,139 is not important because that's just a matter of the direction 313 00:21:02,139 --> 00:21:04,785 of the arrows. But uh Maxwell didn't put 314 00:21:04,785 --> 00:21:07,092 arrows in. So I leave it up to you. 315 00:21:07,092 --> 00:21:11,026 If it's plus four and plus one you have to put arrows going 316 00:21:11,026 --> 00:21:13,537 outwards. And what you see now here is 317 00:21:13,537 --> 00:21:16,861 this airblower effect. Think of them as both being 318 00:21:16,861 --> 00:21:19,168 positive. So there is the plus four 319 00:21:19,168 --> 00:21:23,103 trying to blow air out like a hairdryer and the plus one is 320 00:21:23,103 --> 00:21:26,359 trying to do its own thing and so you get a field 321 00:21:26,359 --> 00:21:28,123 configuration, field lines, 322 00:21:28,123 --> 00:21:33,329 which are sort of not perhaps easy but you can sort 323 00:21:33,329 --> 00:21:36,661 of imagine why it has this peculiar shape. 324 00:21:36,661 --> 00:21:41,049 If you um put a plus test charge in between the one and 325 00:21:41,049 --> 00:21:45,762 the four, then the four will repel it but the one will also 326 00:21:45,762 --> 00:21:50,068 repel it and so there's going to be a point somewhere, 327 00:21:50,068 --> 00:21:54,294 probably close to one, whereby the two forces exactly 328 00:21:54,294 --> 00:21:57,706 cancel out. Therefore E will be zero there. 329 00:21:57,706 --> 00:22:02,744 In a similar way between the moon and the earth, 330 00:22:02,744 --> 00:22:07,184 there is a point not too far away from the moon where the 331 00:22:07,184 --> 00:22:11,941 gravitational attraction from the earth and the gravitational 332 00:22:11,941 --> 00:22:16,223 attraction from the moon exactly cancel each other out. 333 00:22:16,223 --> 00:22:19,79 That's not too dissimilar from this situation. 334 00:22:19,79 --> 00:22:23,358 So when you have charges of the same polarity, 335 00:22:23,358 --> 00:22:27,56 you always find in between somewhere a point where the 336 00:22:27,56 --> 00:22:31,762 electric field is zero. Let's now go to a very special 337 00:22:31,762 --> 00:22:36,281 case whereby I make the two charges equal in magnitude but 338 00:22:36,281 --> 00:22:41,127 opposite in sign and we have a name for that, 339 00:22:41,127 --> 00:22:45,348 we call that a dipole. The plus charge is here and the 340 00:22:45,348 --> 00:22:48,852 minus charge is there. Situation is extremely 341 00:22:48,852 --> 00:22:53,709 symmetric, as you would expect, because they have equal power. 342 00:22:53,709 --> 00:22:57,85 There's one airblower upstairs and one vacuum cleaner 343 00:22:57,85 --> 00:23:00,876 downstairs. If you're close to the plus 344 00:23:00,876 --> 00:23:05,654 charge notice that all the field lines go away from the plus. 345 00:23:05,654 --> 00:23:10,273 And if you're close to the minus, notice that all the field 346 00:23:10,273 --> 00:23:13,535 lines come in on the minus, 347 00:23:13,535 --> 00:23:16,887 you expect that. If you are far away from this 348 00:23:16,887 --> 00:23:21,431 dipole, now you have a problem. Before we had a plus three and 349 00:23:21,431 --> 00:23:25,602 a minus one and when you're far away the plus three wins. 350 00:23:25,602 --> 00:23:28,358 So it's like having a plus two charge. 351 00:23:28,358 --> 00:23:32,753 If you're far away you always expect the electric field then 352 00:23:32,753 --> 00:23:37,073 to be pointing away from the equivalent charge of plus two. 353 00:23:37,073 --> 00:23:40,872 But if you add up plus and minus and they have equal 354 00:23:40,872 --> 00:23:44,546 magnitude, let's say plus one and minus 355 00:23:44,546 --> 00:23:47,464 one, you get zero, so neither one wins if you're 356 00:23:47,464 --> 00:23:50,816 far away, and notice carefully if you're very far away, 357 00:23:50,816 --> 00:23:54,54 indeed you do not see arrows either pointing out nor pointing 358 00:23:54,54 --> 00:23:56,029 in. Nature cannot decide, 359 00:23:56,029 --> 00:23:58,947 there isn't one that is stronger than the other. 360 00:23:58,947 --> 00:24:01,802 And that makes dipole fields very very special. 361 00:24:01,802 --> 00:24:04,719 In the case of the plus three and the minus one, 362 00:24:04,719 --> 00:24:07,885 if you're very far away, it's like having a plus two 363 00:24:07,885 --> 00:24:11,733 charge and the E field when you go further and further out will 364 00:24:11,733 --> 00:24:14,939 fall off as one over R squared. 365 00:24:14,939 --> 00:24:18,934 With a dipole your intuition sort of tells you that it will 366 00:24:18,934 --> 00:24:22,24 probably fall off faster than one over R squared. 367 00:24:22,24 --> 00:24:26,304 And that is part of a homework assignment that you have this 368 00:24:26,304 --> 00:24:28,715 week. In fact I can already give you 369 00:24:28,715 --> 00:24:30,919 the answer. You have to prove it. 370 00:24:30,919 --> 00:24:34,639 If you're far away from an electric dipole the electric 371 00:24:34,639 --> 00:24:37,05 field falls off as one over R cubed. 372 00:24:37,05 --> 00:24:39,667 It goes faster than one over R squared. 373 00:24:39,667 --> 00:24:44,695 There is not a single point in space where the electric 374 00:24:44,695 --> 00:24:48,845 field is zero. And you can think about that 375 00:24:48,845 --> 00:24:53,786 why that is the case. So these field configurations 376 00:24:53,786 --> 00:24:59,813 can be rather complicated and can be very interesting and each 377 00:24:59,813 --> 00:25:05,445 one has its own applications. Are dipoles rare in physics? 378 00:25:05,445 --> 00:25:09,1 Not at all. In fact, they're extremely 379 00:25:09,1 --> 00:25:11,966 common. You cannot avoid them. 380 00:25:11,966 --> 00:25:16,606 Remember last time, I told you if you have a 381 00:25:16,606 --> 00:25:19,438 spherical atom or we have a spherical molecule, 382 00:25:19,438 --> 00:25:23,133 and you bring that close to a charge -- let's now think of it 383 00:25:23,133 --> 00:25:26,397 you bring it in an electric field, it's another way of 384 00:25:26,397 --> 00:25:29,415 saying the same thing. So we have a nice spherical 385 00:25:29,415 --> 00:25:32,741 atom or a nice spherical molecule and we bring it in an 386 00:25:32,741 --> 00:25:35,142 electric field. The electrons want to go 387 00:25:35,142 --> 00:25:38,53 upstream the electric field vectors, they go against the 388 00:25:38,53 --> 00:25:42,286 direction of the electric field. And the positive charge wants 389 00:25:42,286 --> 00:25:45,119 to go in the direction, wants to go downstream. 390 00:25:45,119 --> 00:25:48,321 And so what are you going to do? 391 00:25:48,321 --> 00:25:52,125 The electrons will spend a little bit more time on one side 392 00:25:52,125 --> 00:25:56,126 of the nucleus than they would in the absence of that electric 393 00:25:56,126 --> 00:25:58,421 field. And therefore you are through 394 00:25:58,421 --> 00:26:01,7 induction turning that atom, turning that molecule, 395 00:26:01,7 --> 00:26:04,98 in becoming a dipole. If you have a little bit more 396 00:26:04,98 --> 00:26:07,537 charge on this side, averaged over time, 397 00:26:07,537 --> 00:26:11,275 you have the same amount of extra charge plus on that side 398 00:26:11,275 --> 00:26:14,489 averaged over time. So you make dipoles very often 399 00:26:14,489 --> 00:26:18,031 whether you like it or not. And later in this course we 400 00:26:18,031 --> 00:26:21,965 will learn more about the polarization of 401 00:26:21,965 --> 00:26:26,67 atoms and molecules creating dipoles when when we talk about 402 00:26:26,67 --> 00:26:29,939 dielectrics. And you will see that it will 403 00:26:29,939 --> 00:26:34,963 have an en- can have an enormous impact on the properties of the 404 00:26:34,963 --> 00:26:38,073 material. Could I make you a dipole here 405 00:26:38,073 --> 00:26:40,863 in class? Oh yeah, that's very easy. 406 00:26:40,863 --> 00:26:45,01 To make one of nonconductors is not so easy in class. 407 00:26:45,01 --> 00:26:48,04 To make one of conductors is very easy. 408 00:26:48,04 --> 00:26:54,18 And I'm going to do that with these two spheres that you have. 409 00:26:54,18 --> 00:26:56,836 Look at these two metal spheres. 410 00:26:56,836 --> 00:26:59,064 Conductors. Free electrons. 411 00:26:59,064 --> 00:27:01,721 It's very easy for them to move. 412 00:27:01,721 --> 00:27:06,691 And I'm going to bring this rubber rod which I will rub and 413 00:27:06,691 --> 00:27:11,661 becomes I think negatively charged if I remember correctly, 414 00:27:11,661 --> 00:27:16,889 and I will bring that so close to these two which are touching 415 00:27:16,889 --> 00:27:19,974 each other. So here is this one metal 416 00:27:19,974 --> 00:27:25,03 sphere and here is the other metal sphere and here comes the 417 00:27:25,03 --> 00:27:28,263 rubber. Negatively charged. 418 00:27:28,263 --> 00:27:29,873 Ah! What's going to happen? 419 00:27:29,873 --> 00:27:33,34 The electrons want to go away, so this becomes negatively 420 00:27:33,34 --> 00:27:36,931 charged, and therefore this remains a little bit positively 421 00:27:36,931 --> 00:27:39,345 charged. For every one electron that has 422 00:27:39,345 --> 00:27:41,884 is excess here, when I start it's neutral, 423 00:27:41,884 --> 00:27:45,227 there will be a positive excess there because charge is 424 00:27:45,227 --> 00:27:47,704 conserved. You can't create charge out of 425 00:27:47,704 --> 00:27:49,313 nothing. And now what I do, 426 00:27:49,313 --> 00:27:52,78 while this rubber is still here, while that rubber rod is 427 00:27:52,78 --> 00:27:56,124 there, I separate them, so here the- they're in contact 428 00:27:56,124 --> 00:27:59,157 with each other first, they 429 00:27:59,157 --> 00:28:03,089 have to be in contact, wow, we get some visitors. 430 00:28:03,089 --> 00:28:06,448 [clap-clap] Don't be late, that means you, 431 00:28:06,448 --> 00:28:08,495 pretty boy. I'm impressed. 432 00:28:08,495 --> 00:28:11,608 Thank you. Um so what I do now is while 433 00:28:11,608 --> 00:28:15,867 this rubber rod is still in place, I take them apart, 434 00:28:15,867 --> 00:28:20,864 and when I take them apart this negative charge is trapped and 435 00:28:20,864 --> 00:28:25,86 this positive charge is trapped. And so I have thereby created 436 00:28:25,86 --> 00:28:31,368 negative charge on this one. Positive on this one and it's 437 00:28:31,368 --> 00:28:33,97 equal in magnitude, so I have a dipole. 438 00:28:33,97 --> 00:28:37,668 What I want to demonstrate to you is that indeed I have 439 00:28:37,668 --> 00:28:40,338 positive charged here and negative here, 440 00:28:40,338 --> 00:28:44,173 that there is a difference in polarity between these two, 441 00:28:44,173 --> 00:28:47,46 and that's the way that I will do the experiment. 442 00:28:47,46 --> 00:28:51,5 I will not show you that the amount of charge is exactly the 443 00:28:51,5 --> 00:28:54,376 same on each, which of course it has to be. 444 00:28:54,376 --> 00:28:58,553 So let me give you some better light, or we have to get the uh 445 00:28:58,553 --> 00:29:01,77 view graph off, the overhead, 446 00:29:01,77 --> 00:29:05,303 you see there for the first time an electroscope, 447 00:29:05,303 --> 00:29:09,5 we discussed it last time, it is a piece of aluminum foil, 448 00:29:09,5 --> 00:29:13,401 very thin, with a metal rod next to it, and when I put 449 00:29:13,401 --> 00:29:17,524 charge on the rod it will also go into the aluminum foil, 450 00:29:17,524 --> 00:29:21,72 and they will repel each other, and so the -- the aluminum 451 00:29:21,72 --> 00:29:26,285 tinsel will go to the right and the more charge there is on it, 452 00:29:26,285 --> 00:29:28,641 the farther it goes to the right. 453 00:29:28,641 --> 00:29:34,088 So let me first put these two together, make sure they are 454 00:29:34,088 --> 00:29:37,601 completely discharged, and now I'm going to bring 455 00:29:37,601 --> 00:29:42,285 these two into an electric field which is produced by this rubber 456 00:29:42,285 --> 00:29:46,384 rod, I have to rub with the cat fur, and I believe it was 457 00:29:46,384 --> 00:29:50,629 negative but if you -- you'd never have to remember whether 458 00:29:50,629 --> 00:29:54,288 it's negative or positive of course, that is not so 459 00:29:54,288 --> 00:29:57,142 important, what is in a name, after all. 460 00:29:57,142 --> 00:29:59,484 But it did happen to be negative. 461 00:29:59,484 --> 00:30:01,021 OK. So now we go here. 462 00:30:01,021 --> 00:30:04,388 I bring it here, I hope that no sparks will fly 463 00:30:04,388 --> 00:30:08,682 over because that ruins the demonstration. 464 00:30:08,682 --> 00:30:12,416 And now notice what I do. While the -- while the rod is 465 00:30:12,416 --> 00:30:15,873 here I separate them. So as I was holding it there, 466 00:30:15,873 --> 00:30:20,022 things were going on in there that you and I couldn't see but 467 00:30:20,022 --> 00:30:23,618 electrons, the rubber rod is negative, electrons were 468 00:30:23,618 --> 00:30:27,905 shifting in this direction and this is now positive and that is 469 00:30:27,905 --> 00:30:30,878 now negative. If I take this one and I touch 470 00:30:30,878 --> 00:30:34,612 it with the electroscope, you clearly see that there is 471 00:30:34,612 --> 00:30:37,517 charge on this. How can I show you now that 472 00:30:37,517 --> 00:30:41,916 there is charge of different polarity on 473 00:30:41,916 --> 00:30:45,693 the other one? Well, the way I will do that is 474 00:30:45,693 --> 00:30:49,553 I will approach this electroscope by bring this 475 00:30:49,553 --> 00:30:54,169 sphere very close to it. And if this charge is different 476 00:30:54,169 --> 00:30:58,953 than the charge that is on it the electroscope will -- the 477 00:30:58,953 --> 00:31:02,646 reading will become smaller. And why is that? 478 00:31:02,646 --> 00:31:05,583 Why will the reading become smaller? 479 00:31:05,583 --> 00:31:09,612 Well, here is the situation of the 480 00:31:09,612 --> 00:31:13,691 electroscope now. And here is that ball that you 481 00:31:13,691 --> 00:31:19,073 see on top, this is upside-down there, if this is all negative, 482 00:31:19,073 --> 00:31:23,412 that's why it is apart, if now I approach this here 483 00:31:23,412 --> 00:31:28,013 with an object which is positively charged and I claim 484 00:31:28,013 --> 00:31:33,221 that this one now is positively charged, because this one was 485 00:31:33,221 --> 00:31:37,3 negatively charged, then electrons are afraid of 486 00:31:37,3 --> 00:31:42,228 the positive charge, so more will go -- excuse me, 487 00:31:42,228 --> 00:31:46,425 electrons love the positive charge, so the electrons want to 488 00:31:46,425 --> 00:31:50,481 come to the positive charge, so these electrons drift down 489 00:31:50,481 --> 00:31:54,109 again, and so if they come down, fewer will be here, 490 00:31:54,109 --> 00:31:57,524 and so you will see this. If however I put here a 491 00:31:57,524 --> 00:32:00,441 negative rod, then the electrons which are 492 00:32:00,441 --> 00:32:03,927 here want to go further away, they will stream up, 493 00:32:03,927 --> 00:32:07,058 and therefore the reading will become larger. 494 00:32:07,058 --> 00:32:11,113 So you can always through induction test what the polarity 495 00:32:11,113 --> 00:32:15,235 is of your charge. Let's hope that this one is 496 00:32:15,235 --> 00:32:17,777 still holding its charge while I was talking. 497 00:32:17,777 --> 00:32:20,955 So I claim now that if this polarity is different and if 498 00:32:20,955 --> 00:32:23,786 it's still there when I approach the electroscope, 499 00:32:23,786 --> 00:32:26,443 come very close, that the reading should become 500 00:32:26,443 --> 00:32:28,812 a little smaller without even touching it. 501 00:32:28,812 --> 00:32:31,759 Let's see whether that works. You see, it goes down. 502 00:32:31,759 --> 00:32:33,608 You see, it goes down. Goes down. 503 00:32:33,608 --> 00:32:36,67 So through induction I have demonstrated that this has 504 00:32:36,67 --> 00:32:39,039 indeed a different polarity from this one. 505 00:32:39,039 --> 00:32:42,332 If I approached it with this one, it would go further out, 506 00:32:42,332 --> 00:32:46,613 unless it already is at the maximum, 507 00:32:46,613 --> 00:32:50,826 let's try that, you see, it goes further out. 508 00:32:50,826 --> 00:32:56,091 So not only have I demonstrated that I created a dipole, 509 00:32:56,091 --> 00:33:01,74 but you've also seen that by means of induction that you can 510 00:33:01,74 --> 00:33:07,293 demonstrate uh that the -- there's a difference in polarity 511 00:33:07,293 --> 00:33:12,463 between the two spheres. If I create a dipole and I put 512 00:33:12,463 --> 00:33:17,846 that dipole in a -- in an electric field, 513 00:33:17,846 --> 00:33:21,411 the dipole will start to rotate. 514 00:33:21,411 --> 00:33:26,126 Let's first talk about it. Why it rotates. 515 00:33:26,126 --> 00:33:31,876 And then I will try to demonstrate that by making a 516 00:33:31,876 --> 00:33:34,981 dipole, a big one, this big. 517 00:33:34,981 --> 00:33:41,076 Right in front of you, almost as big as the one there. 518 00:33:41,076 --> 00:33:47,631 So let's have a -- an electric field like so. 519 00:33:47,631 --> 00:33:50,831 And I bring in this electric field a dipole, 520 00:33:50,831 --> 00:33:54,032 a biggie, here, this is the one I'm going to 521 00:33:54,032 --> 00:33:58,348 use for this demonstration. Ping Pong balls on either side, 522 00:33:58,348 --> 00:34:01,847 they are conducting, and they are con- connected 523 00:34:01,847 --> 00:34:04,377 with a rod which is not conducting. 524 00:34:04,377 --> 00:34:08,62 And so here is this dipole. To this rod is not conducting. 525 00:34:08,62 --> 00:34:12,193 And this is a conducting and this is a conductor. 526 00:34:12,193 --> 00:34:16,212 And let's suppose this is positive and this is negative 527 00:34:16,212 --> 00:34:19,902 for now. And I'll show you how we get 528 00:34:19,902 --> 00:34:22,974 the charge on it. Well, the positive charge will 529 00:34:22,974 --> 00:34:26,242 experience a force in this direction, always in the 530 00:34:26,242 --> 00:34:30,163 direction of the electric field, and the negative charge will 531 00:34:30,163 --> 00:34:32,386 experience a force always upstream. 532 00:34:32,386 --> 00:34:36,111 And now there is a torque on this and there is a torque on 533 00:34:36,111 --> 00:34:38,398 this dipole. It will start to rotate 534 00:34:38,398 --> 00:34:41,013 clockwise. And of course if it overshoots 535 00:34:41,013 --> 00:34:44,869 the field lines when it is in this direction the torque will 536 00:34:44,869 --> 00:34:46,829 reverse. It's very easy to see. 537 00:34:46,829 --> 00:34:52,279 And so what you will see, it's going to oscillate and if 538 00:34:52,279 --> 00:34:57,381 there is enough damping it will come to a halt more or less in 539 00:34:57,381 --> 00:35:00,057 the direction of the field lines. 540 00:35:00,057 --> 00:35:03,736 And this is something that I can demonstrate. 541 00:35:03,736 --> 00:35:08,754 First I have to make a dipole of this kind and the way I will 542 00:35:08,754 --> 00:35:12,517 do that is the following. This is a metal bar, 543 00:35:12,517 --> 00:35:16,615 it's this insulator, and here is this -- are these 544 00:35:16,615 --> 00:35:20,462 two Ping Pong balls, the one on this side has a 545 00:35:20,462 --> 00:35:25,296 yellow marker, the one on that side has an 546 00:35:25,296 --> 00:35:28,914 orange marker, and I'm going to attach them 547 00:35:28,914 --> 00:35:32,188 holding them up against this metal bar. 548 00:35:32,188 --> 00:35:35,203 In other words, here is this dipole, 549 00:35:35,203 --> 00:35:39,768 it's not a dipole yet, metal metal and here is a metal 550 00:35:39,768 --> 00:35:43,558 bar, this is a conductor which connects them. 551 00:35:43,558 --> 00:35:47,09 I'm going to turn on the VandeGraaff here, 552 00:35:47,09 --> 00:35:52,259 and the VandeGraaff creates an electric field, 553 00:35:52,259 --> 00:35:54,417 so we have the VandeGraaff here. 554 00:35:54,417 --> 00:35:58,386 And let's suppose that this VandeGraaff creates a positive 555 00:35:58,386 --> 00:36:01,032 charge. Sometimes a VandeGraaff creates 556 00:36:01,032 --> 00:36:04,723 positive charge on the dome, others can be designed to 557 00:36:04,723 --> 00:36:07,091 create negative charge on the dome. 558 00:36:07,091 --> 00:36:10,224 And remember for now I assume that's positive. 559 00:36:10,224 --> 00:36:13,636 What will happen now? Electrons want to go in this 560 00:36:13,636 --> 00:36:16,074 direction. So this becomes negative. 561 00:36:16,074 --> 00:36:18,58 Protons positive charge stays behind. 562 00:36:18,58 --> 00:36:21,505 So that becomes through induction a dipole. 563 00:36:21,505 --> 00:36:25,032 Because I have them connected. 564 00:36:25,032 --> 00:36:28,07 I have them connected with this metal bar. 565 00:36:28,07 --> 00:36:32,071 So these electrons can flow through this bar and end up 566 00:36:32,071 --> 00:36:33,998 here. Now I remove the bar. 567 00:36:33,998 --> 00:36:38,148 And so when I remove the bar I have created now a dipole. 568 00:36:38,148 --> 00:36:42,297 I have here an insulating thread and I have a fishing rod 569 00:36:42,297 --> 00:36:46,892 and at the end of my fishing rod I have now a permanent dipole. 570 00:36:46,892 --> 00:36:51,412 With that permanent dipole I'm now going to probe the electric 571 00:36:51,412 --> 00:36:56,969 field around this VandeGraaff. I could have chosen the same 572 00:36:56,969 --> 00:37:00,809 VandeGraaff but there's a reason why I picked this one and 573 00:37:00,809 --> 00:37:04,177 as I walk around this VandeGraaff you will see that 574 00:37:04,177 --> 00:37:08,085 this fishing rod at the end is this dipole, that the dipole 575 00:37:08,085 --> 00:37:12,059 always wants to go radially inwards or outwards depending on 576 00:37:12,059 --> 00:37:15,966 how you look at it of this field, so I can probe this field 577 00:37:15,966 --> 00:37:19,671 and make you see for the first time that there is indeed 578 00:37:19,671 --> 00:37:23,578 somewhere here a strong radial field going in or out of the 579 00:37:23,578 --> 00:37:26,273 VandeGraaff. And now comes something very 580 00:37:26,273 --> 00:37:30,324 interesting, which I found out this morning 581 00:37:30,324 --> 00:37:33,47 for the first time when I did this experiment. 582 00:37:33,47 --> 00:37:37,735 If the other VandeGraaff there is also positive when I run it, 583 00:37:37,735 --> 00:37:41,93 how do you think this dipole is going to align then if I walk 584 00:37:41,93 --> 00:37:44,237 into it? Will the negative ball be 585 00:37:44,237 --> 00:37:48,362 closer to the VandeGraaff or will the positive one go closer 586 00:37:48,362 --> 00:37:51,858 to the VandeGraaff? So I give you thirty seconds to 587 00:37:51,858 --> 00:37:54,934 think about it, so I make the dipole as it is 588 00:37:54,934 --> 00:38:00,108 here, let's assume this one is positive, this VandeGraaff. 589 00:38:00,108 --> 00:38:03,525 So this side becomes minus, I call that A, 590 00:38:03,525 --> 00:38:06,776 and this side become positive, that's B. 591 00:38:06,776 --> 00:38:11,193 I now walk with this dipole, I bring it in this field. 592 00:38:11,193 --> 00:38:14,694 And let's assume that one is also positive. 593 00:38:14,694 --> 00:38:19,111 We don't know that yet. How will the dipole align now? 594 00:38:19,111 --> 00:38:22,362 Will A go inwards or will A go outwards? 595 00:38:22,362 --> 00:38:25,363 Who thinks A goes inwards? Very good. 596 00:38:25,363 --> 00:38:27,696 Who says A goes outwards? OK. 597 00:38:27,696 --> 00:38:31,531 A will go inwards. If the two VandeGraaffs have 598 00:38:31,531 --> 00:38:37,076 the same polarity. So if that doesn't happen tha- 599 00:38:37,076 --> 00:38:40,604 that doesn't mean that physics doesn't work, 600 00:38:40,604 --> 00:38:45,116 it means the two VandeGraaffs have different polarities. 601 00:38:45,116 --> 00:38:49,711 And we'll see what happens. So let me first then create a 602 00:38:49,711 --> 00:38:52,665 dipole. So here is the -- the dipole. 603 00:38:52,665 --> 00:38:56,111 It's shorted out now. I turn on the -- this 604 00:38:56,111 --> 00:38:59,146 VandeGraaff. So induction takes place. 605 00:38:59,146 --> 00:39:03,987 Remember that the yellow is pointing towards the VandeGraaff 606 00:39:03,987 --> 00:39:08,253 and that the orange is away from the 607 00:39:08,253 --> 00:39:09,872 VandeGraaff. OK. 608 00:39:09,872 --> 00:39:12,461 So I induce a dipole. Oh. 609 00:39:12,461 --> 00:39:18,502 I really should redo that. I don't know what happens when 610 00:39:18,502 --> 00:39:22,602 it -- I have to remove the field first. 611 00:39:22,602 --> 00:39:25,299 OK. The yellow was inside, 612 00:39:25,299 --> 00:39:28,967 right, was that the way it was? OK. 613 00:39:28,967 --> 00:39:31,772 Yellow inside. There we go. 614 00:39:31,772 --> 00:39:39,108 So now it's creating a dipole through this metal bar. 615 00:39:39,108 --> 00:39:44,774 And I break contact and this should now be a dipole. 616 00:39:44,774 --> 00:39:51,219 Now I turn on the field of the -- so if the polarity is the 617 00:39:51,219 --> 00:39:56,553 same, yellow will go in. I will try to swing it a 618 00:39:56,553 --> 00:39:59,33 little. Notice two things. 619 00:39:59,33 --> 00:40:04,775 It's going to line up beautifully radially but the 620 00:40:04,775 --> 00:40:09,998 yellow is not in, the yellow is out. 621 00:40:09,998 --> 00:40:14,306 So the two VandeGraaffs have different polarities. 622 00:40:14,306 --> 00:40:17,383 But you will see they rotate nicely. 623 00:40:17,383 --> 00:40:22,571 And they end up beautifully radial and when I go all the way 624 00:40:22,571 --> 00:40:28,023 around here again they may swing a little, they may oscillate a 625 00:40:28,023 --> 00:40:33,386 little, but through damping they will come to a halt and look, 626 00:40:33,386 --> 00:40:38,75 the field is indeed beautifully radial and the yellow is so to 627 00:40:38,75 --> 00:40:43,058 speak on the wrong side. The two VandeGraaffs have 628 00:40:43,058 --> 00:40:46,754 different polarities. 629 00:40:46,754 --> 00:40:55,545 So you see how we can create a dipole and you've also seen how 630 00:40:55,545 --> 00:41:04,048 we often can make statements about uh the specific polarity. 631 00:41:04,048 --> 00:41:11,83 I can probe an electric field using grass seeds in oil. 632 00:41:11,83 --> 00:41:18,538 Grass seeds are elongated and when I put a grass seed in 633 00:41:18,538 --> 00:41:21,338 the electric field it will become polarized, 634 00:41:21,338 --> 00:41:23,616 there's nothing you can do about it. 635 00:41:23,616 --> 00:41:27,132 Here is a grass seed and the electric field is like so. 636 00:41:27,132 --> 00:41:31,233 And so the electrons want to go as far away in this direction as 637 00:41:31,233 --> 00:41:34,553 they can through induction. And so this side remains 638 00:41:34,553 --> 00:41:37,938 positive, and so what is this grass seed going to do? 639 00:41:37,938 --> 00:41:41,258 It's going to rotate. It's going to line up with the 640 00:41:41,258 --> 00:41:44,058 electric field. And this is the way that I'm 641 00:41:44,058 --> 00:41:47,963 going to show you now field configurations 642 00:41:47,963 --> 00:41:52,581 in the vicinity of a dipole. And I will also show you then 643 00:41:52,581 --> 00:41:56,955 field configurations in a vicinity of two charges which 644 00:41:56,955 --> 00:42:01,005 have equal polarity. You may have seen this in high 645 00:42:01,005 --> 00:42:04,569 school with magnetic fields, with iron files, 646 00:42:04,569 --> 00:42:08,457 that's kid stuff. That's the easiest thing to do. 647 00:42:08,457 --> 00:42:12,588 This is the real thing, this is the electric fields, 648 00:42:12,588 --> 00:42:17,367 I bet you you've never seen electric fields which are traced 649 00:42:17,367 --> 00:42:21,66 by these mysterious seeds. So I'll give you some light 650 00:42:21,66 --> 00:42:25,954 that may optimize the demonstration. 651 00:42:25,954 --> 00:42:31,783 These seeds first have to be oriented in a way so that it is 652 00:42:31,783 --> 00:42:35,34 chaos. The first thing you see is I'm 653 00:42:35,34 --> 00:42:41,565 going to make this -- I believe it's going to be a dipole first. 654 00:42:41,565 --> 00:42:45,616 Almost certain. So I'm going to charge one 655 00:42:45,616 --> 00:42:49,371 positive and charge the other negative. 656 00:42:49,371 --> 00:42:54,707 And then we'll see how these grass seeds will form each 657 00:42:54,707 --> 00:42:56,683 other. Watch closely. 658 00:42:56,683 --> 00:43:00,512 There you go. My goodness. 659 00:43:00,512 --> 00:43:03,346 That is a wonderful dipole field. 660 00:43:03,346 --> 00:43:08,747 Of course we don't know which one is plus or minus because the 661 00:43:08,747 --> 00:43:11,757 grass seeds have no arrows on them. 662 00:43:11,757 --> 00:43:16,185 But you clearly see these incredible lines radially 663 00:43:16,185 --> 00:43:21,675 inwards or outwards on each one of the charges and then you see 664 00:43:21,675 --> 00:43:26,191 these nice arcs in between. Who could see it easily? 665 00:43:26,191 --> 00:43:31,503 OK, you got something worth for your twenty thousand dollars' 666 00:43:31,503 --> 00:43:36,967 tuition. Put a little bit more charge on 667 00:43:36,967 --> 00:43:38,797 maybe. Very clear. 668 00:43:38,797 --> 00:43:45,043 And now which is perhaps more interesting, I'd like to show 669 00:43:45,043 --> 00:43:51,504 you the field surrounding two charges but now the charges are 670 00:43:51,504 --> 00:43:57,103 both the same polarity. So we have to undo the -- the 671 00:43:57,103 --> 00:44:03,134 memory of the grass seeds. OK, now we'll try to make them 672 00:44:03,134 --> 00:44:07,521 both the same polarity. 673 00:44:07,521 --> 00:44:16,254 And then watch this hairblower effect that I told you about. 674 00:44:16,254 --> 00:44:23,359 Maybe not make -- I'm not sure they made contact. 675 00:44:23,359 --> 00:44:27,947 OK, we'll try it again. Come on. 676 00:44:27,947 --> 00:44:34,608 It's very funny, you know, it looks like there 677 00:44:34,608 --> 00:44:38,54 is some -- some charge hidden 678 00:44:38,54 --> 00:44:43,183 because it doesn't look as beautiful as we had earlier on 679 00:44:43,183 --> 00:44:46,914 the Maxwell view graph. It seems like there is 680 00:44:46,914 --> 00:44:50,479 something here on the side which it prefers. 681 00:44:50,479 --> 00:44:54,708 And therefore the electric field is being distorted. 682 00:44:54,708 --> 00:44:59,185 Let me try to discharge it. I'm a reasonable conductor, 683 00:44:59,185 --> 00:45:03,248 so I should be able to take any stray charges off. 684 00:45:03,248 --> 00:45:04,989 Oh, wait a minute. Ha! 685 00:45:04,989 --> 00:45:10,416 I had it upside-down. [laughter] Oh my goodness. 686 00:45:10,416 --> 00:45:13,23 Can happen to anyone. All right. 687 00:45:13,23 --> 00:45:16,951 So they were never really in good contact, 688 00:45:16,951 --> 00:45:19,673 we ready now? Ah, look at that. 689 00:45:19,673 --> 00:45:23,031 Great. Now you really cle- clearly see 690 00:45:23,031 --> 00:45:28,205 these -- these field lines, and you see in between how the 691 00:45:28,205 --> 00:45:32,198 two airblowers are competing with each other. 692 00:45:32,198 --> 00:45:36,191 Very impressive. All right, so that's the way 693 00:45:36,191 --> 00:45:41,604 you see field lines now, electric field lines. 694 00:45:41,604 --> 00:45:46,359 And some of you may have seen with iron files uh magnetic 695 00:45:46,359 --> 00:45:50,009 field lines. If I have the VandeGraaff and I 696 00:45:50,009 --> 00:45:54 have the VandeGraaff here, and let's suppose the 697 00:45:54 --> 00:45:58,16 VandeGraaff is positive, I don't know whether it's 698 00:45:58,16 --> 00:46:01,556 positive or negative, let's suppose it's, 699 00:46:01,556 --> 00:46:06,48 I'm going to use the one over there, and I'm going to stand 700 00:46:06,48 --> 00:46:09,281 here, on the ground, Walter Lewin, 701 00:46:09,281 --> 00:46:13,356 what is going to happen with me? 702 00:46:13,356 --> 00:46:17,378 Through induction, the electrons being sucked out 703 00:46:17,378 --> 00:46:22,238 of the earth and coming up because they want to go close to 704 00:46:22,238 --> 00:46:26,177 the positive charge. So I will become negatively 705 00:46:26,177 --> 00:46:29,277 charged. What will the field lines do? 706 00:46:29,277 --> 00:46:32,461 Oh, they will be extremely complicated. 707 00:46:32,461 --> 00:46:36,399 Very complicated. But something like this maybe. 708 00:46:36,399 --> 00:46:40,756 Maybe something like this. Uh some may come out here. 709 00:46:40,756 --> 00:46:44,695 Some may end up on my neck here. 710 00:46:44,695 --> 00:46:46,355 Some may go here. Like so. 711 00:46:46,355 --> 00:46:48,812 Very complicated field configurations. 712 00:46:48,812 --> 00:46:52,065 But I want to probe that field. Somehow, a little. 713 00:46:52,065 --> 00:46:55,585 Get a feeling for how that -- what that field is like. 714 00:46:55,585 --> 00:46:59,104 And the way I'm going to do that is I'm going to put a 715 00:46:59,104 --> 00:47:01,893 charged balloon. There you see the balloon. 716 00:47:01,893 --> 00:47:04,749 It's a conductor. I'm going to put a charged 717 00:47:04,749 --> 00:47:08,335 balloon and put it here say. Well if it is a positively 718 00:47:08,335 --> 00:47:11,655 charged balloon it will take off in that direction. 719 00:47:11,655 --> 00:47:14,045 Right? The force is always tangential 720 00:47:14,045 --> 00:47:18,365 to the field lines. It will abandon the field 721 00:47:18,365 --> 00:47:22,091 lines, it won't stay on the field lines, there's a lot of 722 00:47:22,091 --> 00:47:25,684 damping on the balloon, that's why I chose the balloon, 723 00:47:25,684 --> 00:47:29,276 so it will move relatively slowly, and it'll ultimately 724 00:47:29,276 --> 00:47:31,605 maybe end up on my head, right here. 725 00:47:31,605 --> 00:47:35,464 Once it ends up on my head there, so it comes in maybe like 726 00:47:35,464 --> 00:47:39,257 this, now it will get the negative charge from my head and 727 00:47:39,257 --> 00:47:43,116 so it will become immediately negatively charged and so the 728 00:47:43,116 --> 00:47:47,706 force now will reverse and will be in this direction, 729 00:47:47,706 --> 00:47:50,831 tangential to this field line, and so it will go back. 730 00:47:50,831 --> 00:47:54,015 When it hits the VandeGraaff again it will get positive 731 00:47:54,015 --> 00:47:56,903 charge, reverse its polarity, and it will go back. 732 00:47:56,903 --> 00:48:00,264 And so it will b- bounce back and forth between me and the 733 00:48:00,264 --> 00:48:03,742 VandeGraaff and it gives you some rough feeling of what this 734 00:48:03,742 --> 00:48:07,161 field configuration is about, although I want to remind you 735 00:48:07,161 --> 00:48:10,168 that the charge does not follow exactly field lines. 736 00:48:10,168 --> 00:48:13,175 So I'm going to sit here and I will be part of this, 737 00:48:13,175 --> 00:48:16,712 so that's probably going to be positive, I will automatically 738 00:48:16,712 --> 00:48:21,682 become negative, there's nothing I have to do, 739 00:48:21,682 --> 00:48:27,696 all I turn is the VandeGraaff and we have to put a little bit 740 00:48:27,696 --> 00:48:33,007 of charge on that balloon. It will probably do that by 741 00:48:33,007 --> 00:48:39,422 itself, but I can always give it a little kick so that it goes to 742 00:48:39,422 --> 00:48:42,429 the VandeGraaff, there it goes. 743 00:48:42,429 --> 00:48:47,941 [laughter] Oh [inaudible] because my -- my glasses are a 744 00:48:47,941 --> 00:48:52,15 good insulator, so I better take my glasses 745 00:48:52,15 --> 00:48:57,061 off, so that every time it hits me. 746 00:48:57,061 --> 00:49:03,048 [laughter] Changes polarity. [laughter] So this is a way you 747 00:49:03,048 --> 00:49:07,513 can do physics and have fun at the same time. 748 00:49:07,513 --> 49:13 See you Monday. [applause]