Can the Magnetic Field Be Determined Using Biot-Savart Law Superposition?

[LeoJakob]

For the following conductor loop, determine the magnetic field along the $z$-axis, which passes through the center of the conductor loop and is perpendicular to it.
The conductor loop consists of an infinitely long wire through which a constant current $I$ runs.
Is it possible to determine the magnetic fields in the different sections $\vec B_i$ with $i \in \{ 1,2,3 \}$ and then calculate the total field by $\vec B= \sum \limits_{i=1}^3 \vec B_i$?

 

[Baluncore]

Yes.
Is this homework ?

... determine the magnetic field along the z-axis, ...

At all points on the z-axis, or at the origin in the direction of the z-axis ?

Segments 1 and 3 are in line with the z-axis. Apply the right-hand rule.
What direction will the field from segments 1 and 3 be on the z-axis ?

What is the field on the central axis of a circle ?
What is the field on the central axis of a semicircle ?

 

[LeoJakob]

Thank you ! :)

It is an exercise to solve for the upcoming exams:

-segment 1 and 2 produce the same magnetic field at a point on the z axis
- a whole circle on the central x-axis would create a magnetic field that points only in the z-direction because of the radial symmetry
- a semicircle
on the central x-axis would create a magnetic field that points only in the z- and y-direction because the contributions on the x-axis cancel out