1 00:00:00,060 --> 00:00:05,730 So instead of having only these indirect representations of the magnetic fields, why are there individual 2 00:00:05,730 --> 00:00:10,140 components we want to recreate now such a narrow plot? 3 00:00:10,740 --> 00:00:13,860 And this is possible with Python or with Matlock Leap. 4 00:00:14,250 --> 00:00:17,220 But first of all, we must enable the 3D option. 5 00:00:17,400 --> 00:00:19,980 So we must write something like our own plot. 6 00:00:20,070 --> 00:00:29,880 So this will be the name of the plot and we will use T dot axes and then projection is equal to 3D. 7 00:00:31,260 --> 00:00:38,730 And then we can just go ahead and say our plots, dots quiver. 8 00:00:39,810 --> 00:00:42,600 And now the syntax is as follows. 9 00:00:43,050 --> 00:00:46,350 We basically have to first provide a list of the coordinates. 10 00:00:46,710 --> 00:00:52,770 And the nice thing is, since we have used as mash grids command, we already have these readily available. 11 00:00:53,040 --> 00:00:56,650 We just have to be careful to ride like this and not just courts. 12 00:00:56,650 --> 00:00:57,720 So we have to write courts. 13 00:00:57,900 --> 00:01:02,700 Zero one two and then we must do the same thing for the magnetic fields. 14 00:01:03,600 --> 00:01:09,070 So like this, just change courts to be. 15 00:01:09,900 --> 00:01:13,170 And then we can run it. 16 00:01:16,360 --> 00:01:20,140 And first of all, we don't see anything, unfortunately. 17 00:01:20,740 --> 00:01:26,970 And I checked before what is the reason and the reason is that along magnetic fields is very tiny. 18 00:01:26,980 --> 00:01:31,810 So you see here the components are on the length scale of 10 to the minus six. 19 00:01:32,590 --> 00:01:36,010 And so here they are, really added as arrows. 20 00:01:36,160 --> 00:01:38,690 So an arrow after length 10 to the minus six. 21 00:01:38,690 --> 00:01:39,950 This added to these points. 22 00:01:39,970 --> 00:01:42,070 So of course, we do not see anything. 23 00:01:42,730 --> 00:01:44,560 So we must scale them by some number. 24 00:01:45,220 --> 00:01:50,920 And for this, I would just multiply all of the components with scale and then I will. 25 00:01:50,920 --> 00:01:59,080 Right scale is, for example, something like like this 0.2 times 10 to the power of six. 26 00:02:00,230 --> 00:02:03,520 And now we have some arrows here. 27 00:02:04,030 --> 00:02:11,860 They look a bit a bit funny because we don't see anything here, but this is basically because our image 28 00:02:11,860 --> 00:02:13,150 is just too small. 29 00:02:13,750 --> 00:02:21,460 And to change this, it's possible to change the figures of all of the figures in the notebook by using 30 00:02:21,460 --> 00:02:26,440 such a command here penalty that our rc params off figure and figure size. 31 00:02:26,440 --> 00:02:30,790 So this means we are changing like the internal parameters of the notebook. 32 00:02:31,150 --> 00:02:37,990 We are changing the standard figure size of all the following figures to this size 40 times 15. 33 00:02:38,770 --> 00:02:43,630 So this depends not a lot on your display, on your browser, on your Zoom. 34 00:02:43,990 --> 00:02:49,270 So I can show you what happens for me when I run both of these cells and we get such a large figure 35 00:02:49,270 --> 00:02:51,430 now where we can really see what's going on. 36 00:02:51,940 --> 00:02:55,870 And it could happen that in your case, you have a different resolution. 37 00:02:55,870 --> 00:02:59,740 For example, you need to change these numbers and make them smaller, for example. 38 00:03:00,790 --> 00:03:05,650 OK, so now we see that there aren't some arrows indeed. 39 00:03:05,650 --> 00:03:08,440 But still, it looks a bit funny, to be honest. 40 00:03:09,070 --> 00:03:17,470 And the reason is that the Z component only goes from minus 0.04 to + 0.04. 41 00:03:17,830 --> 00:03:29,560 So I always like to set the Z limits, so this will be set underscore ceiling to minus one and one because 42 00:03:29,560 --> 00:03:33,130 this is the range in which the arrows can point. 43 00:03:34,600 --> 00:03:37,030 And you see now it looks much, much better. 44 00:03:38,050 --> 00:03:44,320 So if you don't like the background here because it can be a bit confusing, we can also get rid of 45 00:03:44,320 --> 00:03:44,860 this one. 46 00:03:45,310 --> 00:03:50,770 So this would be background in visible. 47 00:03:52,000 --> 00:03:58,660 We could work just right arrow dot dot axis and then Capital F falls. 48 00:04:00,370 --> 00:04:02,770 And you see, this is now what we get. 49 00:04:03,970 --> 00:04:08,400 So our so-called quiver plot has generated the magnetic fields. 50 00:04:08,410 --> 00:04:14,290 And you see here does this really in real space, the setup of the magnetic field and you see it in 51 00:04:14,290 --> 00:04:19,480 the middle, there would be the wire going from negative z to positive Z, and the magnetic field is 52 00:04:19,480 --> 00:04:21,760 really circulating around the wire. 53 00:04:22,150 --> 00:04:25,750 And this is exactly as in this scenario. 54 00:04:26,770 --> 00:04:34,510 So you see, we have restored this very fundamental phenomenon or this very general observation that 55 00:04:34,510 --> 00:04:42,010 you get told very early in school that the magnetic field around a charged by her is such a rotational 56 00:04:42,010 --> 00:04:47,680 set up, such a toroidal set up where the magnetic fields rotates around the wire and using the methods 57 00:04:47,680 --> 00:04:53,050 of derivatives and integrals, we have been able to restore this result. 58 00:04:53,620 --> 00:05:00,700 So this was here an exercise for derivatives and multiple dimensions because we used here the kernel 59 00:05:00,700 --> 00:05:03,430 and reprogram to curl forward the vector potential. 60 00:05:03,850 --> 00:05:10,990 And it was also an exercise, of course, for integrals, because we have programmed also this equation, 61 00:05:10,990 --> 00:05:12,670 which is an integral equation.