So instead of having only these indirect representations of the magnetic fields, why are there individual
components we want to recreate now such a narrow plot?
And this is possible with Python or with Matlock Leap.
But first of all, we must enable the 3D option.
So we must write something like our own plot.
So this will be the name of the plot and we will use T dot axes and then projection is equal to 3D.
And then we can just go ahead and say our plots, dots quiver.
And now the syntax is as follows.
We basically have to first provide a list of the coordinates.
And the nice thing is, since we have used as mash grids command, we already have these readily available.
We just have to be careful to ride like this and not just courts.
So we have to write courts.
Zero one two and then we must do the same thing for the magnetic fields.
So like this, just change courts to be.
And then we can run it.
And first of all, we don't see anything, unfortunately.
And I checked before what is the reason and the reason is that along magnetic fields is very tiny.
So you see here the components are on the length scale of 10 to the minus six.
And so here they are, really added as arrows.
So an arrow after length 10 to the minus six.
This added to these points.
So of course, we do not see anything.
So we must scale them by some number.
And for this, I would just multiply all of the components with scale and then I will.
Right scale is, for example, something like like this 0.2 times 10 to the power of six.
And now we have some arrows here.
They look a bit a bit funny because we don't see anything here, but this is basically because our image
is just too small.
And to change this, it's possible to change the figures of all of the figures in the notebook by using
such a command here penalty that our rc params off figure and figure size.
So this means we are changing like the internal parameters of the notebook.
We are changing the standard figure size of all the following figures to this size 40 times 15.
So this depends not a lot on your display, on your browser, on your Zoom.
So I can show you what happens for me when I run both of these cells and we get such a large figure
now where we can really see what's going on.
And it could happen that in your case, you have a different resolution.
For example, you need to change these numbers and make them smaller, for example.
OK, so now we see that there aren't some arrows indeed.
But still, it looks a bit funny, to be honest.
And the reason is that the Z component only goes from minus 0.04 to + 0.04.
So I always like to set the Z limits, so this will be set underscore ceiling to minus one and one because
this is the range in which the arrows can point.
And you see now it looks much, much better.
So if you don't like the background here because it can be a bit confusing, we can also get rid of
this one.
So this would be background in visible.
We could work just right arrow dot dot axis and then Capital F falls.
And you see, this is now what we get.
So our so-called quiver plot has generated the magnetic fields.
And you see here does this really in real space, the setup of the magnetic field and you see it in
the middle, there would be the wire going from negative z to positive Z, and the magnetic field is
really circulating around the wire.
And this is exactly as in this scenario.
So you see, we have restored this very fundamental phenomenon or this very general observation that
you get told very early in school that the magnetic field around a charged by her is such a rotational
set up, such a toroidal set up where the magnetic fields rotates around the wire and using the methods
of derivatives and integrals, we have been able to restore this result.
So this was here an exercise for derivatives and multiple dimensions because we used here the kernel
and reprogram to curl forward the vector potential.
And it was also an exercise, of course, for integrals, because we have programmed also this equation,
which is an integral equation.