Magnetic field at (z) axis of square loop

[Siune]

Homework Statement

We have a square loop with side length 2a, at xy plane. Now we know ( I have calculated ) that the magnetic field at the center of the square loop to be

$H = \frac{2I}{\sqrt{2} \pi a}$

Now we want to know what is the magnetic field at point P, which is on the axis which goes through the center of loop.

Homework Equations

Biot-Savart.

The Attempt at a Solution

I know that I need to calculate contribution by one side-length to the total magnetic field and then multiply it with 4. But I'm lost which would be the best variable to use to get the integration done. Any hint what is the variable I should use to be most effective?

Sincerely yours, Siune.

 

[mfb]

I would simply integrate over the length of a side in Cartesian coordinates. If that does not work, try something else.