1 00:00:00,000 --> 00:00:00,730 2 00:00:00,730 --> 00:00:03,590 Let's say we have a magnetic field that's coming out of the 3 00:00:03,590 --> 00:00:04,920 right side of the screen. 4 00:00:04,920 --> 00:00:09,340 And it's not just along the screen, it's actually three 5 00:00:09,340 --> 00:00:10,110 dimensional. 6 00:00:10,110 --> 00:00:13,470 So it's going above the screen, below, but the 7 00:00:13,470 --> 00:00:15,550 direction of the magnetic field is from the 8 00:00:15,550 --> 00:00:16,410 right to the left. 9 00:00:16,410 --> 00:00:17,760 Let me just draw that. 10 00:00:17,760 --> 00:00:20,790 And I'm not going to draw a bunch of the field vector 11 00:00:20,790 --> 00:00:24,060 arrows because that'll just take up a lot of valuable 12 00:00:24,060 --> 00:00:28,160 space on our-- so that's the vector magnetic field. 13 00:00:28,160 --> 00:00:30,430 It's down here, too. 14 00:00:30,430 --> 00:00:34,390 If I could, I would draw it above your screen and below 15 00:00:34,390 --> 00:00:34,780 your screen. 16 00:00:34,780 --> 00:00:36,630 But it's coming from the right to the left. 17 00:00:36,630 --> 00:00:38,380 And then in that magnetic field I 18 00:00:38,380 --> 00:00:41,390 have an electric circuit. 19 00:00:41,390 --> 00:00:42,750 I won't draw the whole circuit right now. 20 00:00:42,750 --> 00:00:43,525 I'll do that in a second. 21 00:00:43,525 --> 00:00:46,410 But let's say I have-- part of the electric 22 00:00:46,410 --> 00:00:47,640 circuit is a loop. 23 00:00:47,640 --> 00:00:48,760 And the loop looks like this. 24 00:00:48,760 --> 00:00:50,990 I'm trying to draw it carefully. 25 00:00:50,990 --> 00:00:53,820 So that we can-- because I think a careful drawing will 26 00:00:53,820 --> 00:00:56,210 be more useful in a second than an 27 00:00:56,210 --> 00:00:58,540 uncarefully drawn drawing. 28 00:00:58,540 --> 00:00:59,050 So let's see. 29 00:00:59,050 --> 00:01:00,540 So it's a loop. 30 00:01:00,540 --> 00:01:03,700 You can almost-- you could imagine taking a paper clip 31 00:01:03,700 --> 00:01:05,670 and putting it into this shape. 32 00:01:05,670 --> 00:01:08,660 33 00:01:08,660 --> 00:01:12,700 Oh, that's good enough, I think. 34 00:01:12,700 --> 00:01:15,250 And I have a current going in this direction 35 00:01:15,250 --> 00:01:16,190 in this paper clip. 36 00:01:16,190 --> 00:01:18,630 So this is the positive, that's the negative. 37 00:01:18,630 --> 00:01:20,210 So the current is going like that. 38 00:01:20,210 --> 00:01:23,130 39 00:01:23,130 --> 00:01:26,640 Current is going in a loop like that. 40 00:01:26,640 --> 00:01:27,930 The current's coming out of this end, it's 41 00:01:27,930 --> 00:01:30,260 coming into this end. 42 00:01:30,260 --> 00:01:34,420 And let's say that loop of-- it could be a paper clip or 43 00:01:34,420 --> 00:01:36,300 anything-- let's say that it can rotate. 44 00:01:36,300 --> 00:01:36,980 And that's important. 45 00:01:36,980 --> 00:01:38,300 What's going to happen? 46 00:01:38,300 --> 00:01:41,590 Well, my magnetic field is coming in this direction. 47 00:01:41,590 --> 00:01:45,600 The current is going down here, up here. 48 00:01:45,600 --> 00:01:48,610 What's going to be the net force of the magnetic 49 00:01:48,610 --> 00:01:50,600 field on this loop? 50 00:01:50,600 --> 00:01:51,980 Well, let's try it out. 51 00:01:51,980 --> 00:01:54,220 And it turns out it's going to be a different magnitude at 52 00:01:54,220 --> 00:01:55,950 different points of the current. 53 00:01:55,950 --> 00:01:57,140 So here. 54 00:01:57,140 --> 00:01:59,580 And we don't worry about-- all we're worried about right now 55 00:01:59,580 --> 00:02:00,620 is direction. 56 00:02:00,620 --> 00:02:03,190 And then maybe a little intuition of the magnitude. 57 00:02:03,190 --> 00:02:08,550 So we know that the force of the magnetic field is equal to 58 00:02:08,550 --> 00:02:12,830 the current times the length vector cross 59 00:02:12,830 --> 00:02:15,670 the magnetic field. 60 00:02:15,670 --> 00:02:20,390 Well, what would be the force of the magnetic field on this 61 00:02:20,390 --> 00:02:21,480 segment of wire? 62 00:02:21,480 --> 00:02:24,110 We could call this L. 63 00:02:24,110 --> 00:02:27,766 And that L goes in the same direction as the current. 64 00:02:27,766 --> 00:02:28,900 Well, let's see. 65 00:02:28,900 --> 00:02:31,390 Current is just a scalar, but L is going down. 66 00:02:31,390 --> 00:02:32,720 Magnetic field going to the left. 67 00:02:32,720 --> 00:02:34,000 Cross product. 68 00:02:34,000 --> 00:02:39,850 Cross product, I take my right hand, put my index finger in 69 00:02:39,850 --> 00:02:45,390 the direction of the current, or in the direction of L, 70 00:02:45,390 --> 00:02:46,980 because that's the first term of the cross product. 71 00:02:46,980 --> 00:02:48,760 So that's the index finger. 72 00:02:48,760 --> 00:02:52,000 So my index finger goes down, because that's the direction 73 00:02:52,000 --> 00:02:53,550 of the current. 74 00:02:53,550 --> 00:02:56,460 And then my middle finger-- and remember, you have to do 75 00:02:56,460 --> 00:02:57,020 this with the right hand. 76 00:02:57,020 --> 00:02:58,120 If you do it with the left hand, you're going to get the 77 00:02:58,120 --> 00:02:59,310 opposite result. 78 00:02:59,310 --> 00:03:01,400 And now my middle finger is going to go in the direction 79 00:03:01,400 --> 00:03:01,940 of the field. 80 00:03:01,940 --> 00:03:06,250 So let me point my middle finger. 81 00:03:06,250 --> 00:03:07,930 My middle finger is going to go in the 82 00:03:07,930 --> 00:03:09,870 direction of the field. 83 00:03:09,870 --> 00:03:11,800 I keep having to look at my own hand. 84 00:03:11,800 --> 00:03:13,900 And then my other two fingers are just going to do what they 85 00:03:13,900 --> 00:03:15,400 need to do. 86 00:03:15,400 --> 00:03:16,780 So that's my third finger. 87 00:03:16,780 --> 00:03:19,740 That's my pinky. 88 00:03:19,740 --> 00:03:23,810 And then what is my thumb going to do? 89 00:03:23,810 --> 00:03:25,240 What is my thumb going to do? 90 00:03:25,240 --> 00:03:30,020 Well, my hand-- that's my hand. 91 00:03:30,020 --> 00:03:31,240 This is what my hand is doing. 92 00:03:31,240 --> 00:03:33,350 I'm pointing downward. 93 00:03:33,350 --> 00:03:36,710 And my palm is kind of pointing at my body. 94 00:03:36,710 --> 00:03:39,360 So what is my thumb doing? 95 00:03:39,360 --> 00:03:40,320 I know it's hard to see. 96 00:03:40,320 --> 00:03:43,220 This is my middle finger right here. 97 00:03:43,220 --> 00:03:45,290 So my thumb is on the other side of this drawing. 98 00:03:45,290 --> 00:03:47,070 And my thumb is pointing downwards. 99 00:03:47,070 --> 00:03:48,350 I hope you see that. 100 00:03:48,350 --> 00:03:50,120 And you try it with your own hand. 101 00:03:50,120 --> 00:03:51,490 So my thumb is pointing downwards. 102 00:03:51,490 --> 00:03:54,900 So the direction of the force created by the magnetic field 103 00:03:54,900 --> 00:03:56,860 on this current is going to go downward. 104 00:03:56,860 --> 00:03:58,380 So let me draw that. 105 00:03:58,380 --> 00:04:01,740 So the force vector-- I'll do it in this 106 00:04:01,740 --> 00:04:03,350 orangey brown color. 107 00:04:03,350 --> 00:04:07,650 The force vector on this segment of the wire is going 108 00:04:07,650 --> 00:04:10,360 to be going down. 109 00:04:10,360 --> 00:04:12,660 Now what about this segment of the wire? 110 00:04:12,660 --> 00:04:13,440 Well, think about it. 111 00:04:13,440 --> 00:04:23,040 This segment of the wire, the L vector-- this L vector-- 112 00:04:23,040 --> 00:04:24,920 It's parallel to the magnetic field just in 113 00:04:24,920 --> 00:04:26,170 the opposite direction. 114 00:04:26,170 --> 00:04:29,040 And so when you take the cross product-- remember, the cross 115 00:04:29,040 --> 00:04:31,590 product is you're multiplying the magnitude of the vectors 116 00:04:31,590 --> 00:04:33,390 that are perpendicular to each other. 117 00:04:33,390 --> 00:04:36,480 But if this is the L vector right here, there's no 118 00:04:36,480 --> 00:04:38,260 component of it that it's perpendicular to 119 00:04:38,260 --> 00:04:39,510 the magnetic field. 120 00:04:39,510 --> 00:04:44,050 So the magnetic field and the current are in the same plane. 121 00:04:44,050 --> 00:04:45,250 They're parallel. 122 00:04:45,250 --> 00:04:46,450 They're not orthogonal at all. 123 00:04:46,450 --> 00:04:49,140 There's no components of them that are at 90 degrees. 124 00:04:49,140 --> 00:04:51,130 So when you take the cross product, you're going to see 125 00:04:51,130 --> 00:04:53,790 that the net force on this segment of the wire is 0. 126 00:04:53,790 --> 00:04:55,840 And likewise on this segment of the wire and this segment 127 00:04:55,840 --> 00:04:56,640 of the wire. 128 00:04:56,640 --> 00:04:59,080 Because they aren't in any way perpendicular. 129 00:04:59,080 --> 00:05:01,800 No components of them are even perpendicular. 130 00:05:01,800 --> 00:05:02,530 So fair enough. 131 00:05:02,530 --> 00:05:05,250 So all we know right now is the magnetic field is exerting 132 00:05:05,250 --> 00:05:08,860 a downward force on this side of our paper 133 00:05:08,860 --> 00:05:10,310 clip or of our circuit. 134 00:05:10,310 --> 00:05:11,620 Now what about this side? 135 00:05:11,620 --> 00:05:12,230 Well, same thing. 136 00:05:12,230 --> 00:05:13,940 Take the cross product. 137 00:05:13,940 --> 00:05:18,300 If this is our L, L cross B. 138 00:05:18,300 --> 00:05:22,380 So take your index finger in the direction--. 139 00:05:22,380 --> 00:05:25,760 So index finger goes like that. 140 00:05:25,760 --> 00:05:28,040 Your middle finger will go in the direction of the field. 141 00:05:28,040 --> 00:05:31,190 So your middle finger is going to look something like that. 142 00:05:31,190 --> 00:05:32,330 And then your other two fingers are 143 00:05:32,330 --> 00:05:33,490 going to be like that. 144 00:05:33,490 --> 00:05:34,770 And what is your thumb going to do? 145 00:05:34,770 --> 00:05:36,720 And this has to be your right hand to work. 146 00:05:36,720 --> 00:05:38,320 Your thumb is going to point straight up. 147 00:05:38,320 --> 00:05:40,000 This is like the heel of your thumb. 148 00:05:40,000 --> 00:05:42,500 Your thumb is going to--. 149 00:05:42,500 --> 00:05:44,530 I don't know if that's a good drawing of a thumb. 150 00:05:44,530 --> 00:05:48,290 But your thumb is essentially pointing out of the page. 151 00:05:48,290 --> 00:05:50,710 Middle finger in the direction of the current, or in the 152 00:05:50,710 --> 00:05:52,960 direction of our length. 153 00:05:52,960 --> 00:05:54,690 Sorry, index finger in the direction of the current. 154 00:05:54,690 --> 00:05:56,460 Middle finger in the direction of the field. 155 00:05:56,460 --> 00:05:58,170 Thumb points out of the page. 156 00:05:58,170 --> 00:06:00,270 Do that with your own right hand and you'll see that the 157 00:06:00,270 --> 00:06:02,360 net force of the magnetic field on this segment of the 158 00:06:02,360 --> 00:06:05,490 wire is going to be upwards. 159 00:06:05,490 --> 00:06:06,720 Let me do it in a different color just to get some 160 00:06:06,720 --> 00:06:09,910 contrast. 161 00:06:09,910 --> 00:06:10,800 So what's going to happen? 162 00:06:10,800 --> 00:06:13,770 Assuming that this circuit can rotate, 163 00:06:13,770 --> 00:06:14,880 what's going to happen? 164 00:06:14,880 --> 00:06:18,150 On this side there's a downward force. 165 00:06:18,150 --> 00:06:20,260 On this side there's an upward force. 166 00:06:20,260 --> 00:06:22,520 So the magnetic field is actually exerting a 167 00:06:22,520 --> 00:06:24,380 torque on this wire. 168 00:06:24,380 --> 00:06:27,100 169 00:06:27,100 --> 00:06:29,940 If you viewed this little dotted line as our axis of 170 00:06:29,940 --> 00:06:35,190 rotation, the whole coil is actually going to rotate 171 00:06:35,190 --> 00:06:36,400 around that line. 172 00:06:36,400 --> 00:06:39,890 And so there's some force over here, along this whole line 173 00:06:39,890 --> 00:06:41,610 being applied downwards. 174 00:06:41,610 --> 00:06:43,230 And it's actually perpendicular 175 00:06:43,230 --> 00:06:45,250 to our moment arm. 176 00:06:45,250 --> 00:06:47,980 If you remember what we had learned about torque. 177 00:06:47,980 --> 00:06:50,930 So it will actually exert all of that force-- that force 178 00:06:50,930 --> 00:06:52,890 times this distance will be the torque 179 00:06:52,890 --> 00:06:54,480 applied on this side. 180 00:06:54,480 --> 00:06:58,740 And then likewise there's a torque-- it's really the same 181 00:06:58,740 --> 00:07:01,650 sign, in the same direction, because here on the other side 182 00:07:01,650 --> 00:07:03,760 of the arm it's pushing upwards. 183 00:07:03,760 --> 00:07:04,770 So they're not going to cancel out. 184 00:07:04,770 --> 00:07:06,330 They're both going to reinforce. 185 00:07:06,330 --> 00:07:08,820 And this whole coil is going to be 186 00:07:08,820 --> 00:07:13,030 turning in this direction. 187 00:07:13,030 --> 00:07:15,690 Here it's going to be moving up out of your video screen. 188 00:07:15,690 --> 00:07:18,950 Here it's going to be moving down into your video screen. 189 00:07:18,950 --> 00:07:20,440 Now what happens? 190 00:07:20,440 --> 00:07:23,190 I'm going to try to not run out of time either. 191 00:07:23,190 --> 00:07:25,100 So it's going to start rotating. 192 00:07:25,100 --> 00:07:27,930 So the left hand side's going to go below the page. 193 00:07:27,930 --> 00:07:29,630 The right hand side's going to be above the page. 194 00:07:29,630 --> 00:07:31,015 I want to draw some perspective, that's why I'm 195 00:07:31,015 --> 00:07:32,610 just drawing it bigger. 196 00:07:32,610 --> 00:07:35,150 Maybe it looks like that. 197 00:07:35,150 --> 00:07:38,150 198 00:07:38,150 --> 00:07:40,950 Maybe my circuit starts to look like that. 199 00:07:40,950 --> 00:07:45,170 200 00:07:45,170 --> 00:07:48,926 And I'll redraw my axis of rotation. 201 00:07:48,926 --> 00:07:51,250 So this is my axis of rotation. 202 00:07:51,250 --> 00:07:54,220 And on the way I drew it-- this part, the axis of 203 00:07:54,220 --> 00:07:57,280 rotation is still in the plane of our video. 204 00:07:57,280 --> 00:07:59,190 But this part of the coil is, you could 205 00:07:59,190 --> 00:08:00,250 imagine it popping out. 206 00:08:00,250 --> 00:08:01,950 I wish you had 3D glasses on. 207 00:08:01,950 --> 00:08:03,630 It's popping out of your screen. 208 00:08:03,630 --> 00:08:06,720 This part is going into your screen. 209 00:08:06,720 --> 00:08:08,450 And the current is still going in the same direction. 210 00:08:08,450 --> 00:08:11,940 Current is going in that direction there. 211 00:08:11,940 --> 00:08:16,810 So using the same right hand rule, on this side of the wire 212 00:08:16,810 --> 00:08:19,130 the magnetic field is going to be exerting a 213 00:08:19,130 --> 00:08:21,420 net downward force. 214 00:08:21,420 --> 00:08:25,370 But the torque is actually going to be less because our 215 00:08:25,370 --> 00:08:28,320 moment arm distance is going to be like-- I want to draw it 216 00:08:28,320 --> 00:08:29,890 with some perspective. 217 00:08:29,890 --> 00:08:32,600 It's going to look something like that. 218 00:08:32,600 --> 00:08:36,780 So it's going to be going to the left and behind the page 219 00:08:36,780 --> 00:08:38,929 while the torque is still just into the page. 220 00:08:38,929 --> 00:08:40,630 So you would actually take the component of the torque that's 221 00:08:40,630 --> 00:08:41,808 perpendicular. 222 00:08:41,808 --> 00:08:43,719 So there's some component of the torque that's actually 223 00:08:43,720 --> 00:08:44,169 perpendicular. 224 00:08:44,169 --> 00:08:45,460 I don't want to confuse you too much. 225 00:08:45,460 --> 00:08:48,000 But you could imagine the torque lessens. 226 00:08:48,000 --> 00:08:50,630 Even though the net magnetic force is the same, the 227 00:08:50,630 --> 00:08:54,900 component of that force that's perpendicular to your moment 228 00:08:54,900 --> 00:08:56,150 arm, that lessens. 229 00:08:56,150 --> 00:08:58,500 So there's still going to be some torque that's going to be 230 00:08:58,500 --> 00:09:02,680 causing it to rotate downwards in that direction. 231 00:09:02,680 --> 00:09:03,000 Sorry. 232 00:09:03,000 --> 00:09:03,700 You know what? 233 00:09:03,700 --> 00:09:05,520 I drew this wrong here. 234 00:09:05,520 --> 00:09:07,740 We're pushing up on the right hand side, we're pushing down 235 00:09:07,740 --> 00:09:08,410 on the left hand side. 236 00:09:08,410 --> 00:09:14,030 So the direction is going to be like that. 237 00:09:14,030 --> 00:09:16,510 Pushing up on the right hand, down on the left hand. 238 00:09:16,510 --> 00:09:18,670 So you're still going to be doing the same thing here. 239 00:09:18,670 --> 00:09:20,215 You are going to be pushing up here. 240 00:09:20,215 --> 00:09:24,880 But you're going to be pushing up directly out of the page. 241 00:09:24,880 --> 00:09:26,610 But that's not completely perpendicular 242 00:09:26,610 --> 00:09:30,050 to the moment arm. 243 00:09:30,050 --> 00:09:33,100 So the component that is perpendicular, that's actually 244 00:09:33,100 --> 00:09:35,215 creating rotational torque, that's going 245 00:09:35,215 --> 00:09:36,090 to be a little less. 246 00:09:36,090 --> 00:09:38,370 And then you could imagine that all the way to the point, 247 00:09:38,370 --> 00:09:43,470 the coil's going to keep rotating with smaller torque. 248 00:09:43,470 --> 00:09:47,260 At some point you'll be looking at it head on. 249 00:09:47,260 --> 00:09:50,220 So I can just draw it like a straight line, right? 250 00:09:50,220 --> 00:09:51,000 You can imagine. 251 00:09:51,000 --> 00:09:53,710 This arm is on top and this arm is behind it. 252 00:09:53,710 --> 00:09:56,260 And at this point, what's going to happen? 253 00:09:56,260 --> 00:09:58,360 All the magnetic force on this top arm is going 254 00:09:58,360 --> 00:10:00,740 to be popping up. 255 00:10:00,740 --> 00:10:02,860 It's going to be popping up out of your page but it's not 256 00:10:02,860 --> 00:10:04,400 going to be providing any torque. 257 00:10:04,400 --> 00:10:08,270 Because it's not perpendicular anymore to your moment arm. 258 00:10:08,270 --> 00:10:11,610 And likewise, on the bottom behind this, if you could 259 00:10:11,610 --> 00:10:14,760 visualize this, it would be exerting a net downward force. 260 00:10:14,760 --> 00:10:16,260 And that's also not going to be helpful. 261 00:10:16,260 --> 00:10:20,510 But maybe they have some angular momentum so the wire 262 00:10:20,510 --> 00:10:23,130 will still rotate. 263 00:10:23,130 --> 00:10:24,220 But then when it still rotates, 264 00:10:24,220 --> 00:10:25,390 what's going to happen? 265 00:10:25,390 --> 00:10:26,610 And this is where I'll leave you with a 266 00:10:26,610 --> 00:10:29,370 little bit of a conundrum. 267 00:10:29,370 --> 00:10:31,490 Actually, I don't want to go over the Youtube limit, so I'm 268 00:10:31,490 --> 00:10:33,730 going to continue this in the next video and I'll show you 269 00:10:33,730 --> 00:10:34,110 the conundrum. 270 00:10:34,110 --> 00:00:00,000 See you soon.