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So now we can go ahead, and first of all, I want to define the current density.

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So we already defined you, the prefecture, and I told you that this is basically constant.

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So what we can do now is I could ride an if statement, for example, if the X coordinates of our vector

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aren't positioned Vector Square plus our one square and then the square root and P Dot Square roads

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is larger than zero, then it would be zero.

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So then we return an array, which is just zero.

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And in the other case, where opposition matter is at a point which has a radius smaller than zero,

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then we would return an array which only has a Z component and the Z component is then j0.

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However, I basically will make the problem here a bit more simple, and I will clean up the code more

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because I already told you, according to this equation, we would have to integrate the our dash over

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the whole space, and this will take a lot of time.

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However, we know that our current density is only non-zero in the wire, so we will only integrate

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over the z axis here.

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So basically, we we don't even consider the other points in space that are far away from two C axes.

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So this is why we will not not even have to use this if statement here we can just straight up return.

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That's the current density.

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Looks like this because we consider archeology only the wire.

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OK, but it wouldn't be a problem if you would include these three lines of code here, it would just

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make the code a tiny bit slower.

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OK.

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So what happens is when we call now our function for position vector on the z axis, for example, zero

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zero five, then we get our own because I didn't run the zone and now it works, OK.

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So if we are to position zero zero five, then our current density will be zero zero one, just as we

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programmed to.

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Now we must integrate.

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So to do this, we must first prepare some lists.

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And first I will prepare a coordinate list so the coordinates will be Kautz is equal to and p dot,

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right?

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So it will be an array, of course, and we can use know the mesh grid commands.

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This is something that we used already for plotting, for example, when we plotted a density plot where

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we had an x axis y axis and then the value for the z axis, which was a color.

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And to generate the array for the X and Y coordinates we have used and mesh grids.

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So now we can just define basically the lists for the values on the axes and then it will mesh and will

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fill, then the whole space.

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So we write, we mesh here.

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Be like this and total in space, and we start from minus cordone at Max.

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We go to cordon off Max and we have a certain number of points.

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So you see, I program this year in a flexible way so that we can adjust these values later on.

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And here I tested this before so that our code doesn't run forever and that we still get a nice convergence

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for the integral later on.

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So I choose these values here, and this is just the list for the x axis.

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Now we need another list for the y axis and we need another list for the z axis.

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However, I told you that we will only consider the X Y plane, so basically Z equals zero.

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So this means we don't need this here.

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We could, of course, use it to get a more accurate result for our particular problem, but I will

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only calculate it for the X y plane.

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So this is why I'm using here and zeroes one.

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So this will be just a array with a single value at zero.

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OK, so now we are finished with the coordinates and we can now test something, for example,

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codes and these arrays will have no many indices and I can show you what they do.

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First of all, these will be the coordinates X, Y and Z.

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So I want to plot all of them here and then we can write in some points.

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For example, divided by two.

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So here's a problem this is a marked down, so I would go to the next cell instead.

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No points divide it by two and then for the other index, also non-point, divided by two.

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And then for the Z value, we'll just take the only index that we have.

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Zero.

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So this will be the output for this particular point.

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So the index in this case would be 25 25 zero.

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And for the first index, we take all three, so basically going zero, one and two.

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And this is the output.

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The X coordinate that corresponds to this value is zero point one zero point one zero.

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It c.

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When we change this index, we get an arrow because we only have a single point in the Z direction.

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And here we can, for example, subtract one along the X direction and you see that there is a problem,

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but you see that this value here goes from plus zero point one to minus 0.1.

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However, here's a problem because actually I wanted to change here the X coordinate.

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However, the Y coordinate changed, and this is something that's very odd about and mesh grid, because

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if you take just two lists here, it will First Order or the the indexing will first be the y axis and

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then the x axis.

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And then when you take another one, then comes the z axis.

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So that's actually a very, very odd.

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So I can write down here so that you remember standard indexing is for whatever reason, I cannot tell

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you it makes no sense in my eyes.

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So not indexing is first.

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Why then x stanza?

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It makes no sense.

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However, we can fix this.

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Fixed by using

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indexing is equal to I.J.

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That's also something that I had to look up because I run into problems here because the indexing was

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incorrect so we can write it down like this.

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And now I know it should work.

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Yes.

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So for example, we can now write, print this one and then print another, output

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this one.

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And you see, these are our numbers.

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First output is minus zero point one zero point one zero and then zero point one zero point one zero.

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So this maybe also explains to you why I've chosen these values here.

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I explicitly wanted to exclude the values zero for X and zero for Y, and the reason is we will integrate

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our dash over the z axis were X and Y are both zero.

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So if we would consider X0 and y0 for our, then we would have the case where we divide by zero.

93
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And that's something you really have to avoid.

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And this is why I have not included Devalues zero.

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Here, so I'm going here in steps of two, as I'm sorry of 0.2, and we have a nicely dense array here

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of coordinates, but we exclude the point zero zero.

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Now we do the same thing for the vector potential.

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So first, we start with an empty array or empty list, and we can actually just copy this here and

99
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just give it a different name.

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A, for example.

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So now we have empty lists for the coordinates and as no, not not empty list for the coordinates,

102
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but these or any of these values of the coordinates.

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And for a actually, we don't need the same as for the coordinates, but we need an empty list.

104
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So instead of this one, I will write, I will write and peter the zeros and then number of points.

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This will be a list of length nom points where the values are all zeros at the same for the Y coordinates.

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And here, let's make this a bit nicer.

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Don't know what happened here?

108
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And here we go.

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OK, now we have it, and now we can, for example, check what we right here A and E.

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We should get three zeros in both cases because we haven't calculated a yet.

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OK, so now we have everything set up.

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Now we can do the integration.