When deriving the magnetic field due to a current carrying wire, if we choose a circular Amperian loop, we can state:
$$\oint \vec B \ \cdot d\vec s = \mu_0 \ I$$
But due to the symmetry of the Amperian loop, and the fact that the path is traversed counter-clockwise, we can state:
$$\oint B \ d s = \mu_0 \ I$$
$$B \oint ds = \mu_0 \ I$$
However, it is not obvious to me that the magnetic field is parallel to $d\vec s$ at all continuous summations. If $d\vec s$ points infinitesimally along the Amperian loop at every increment, it means the magnetic field at every point will have to be pointing in the exact same direction.
I know that the magnetic field around a wire coils around it, so having a circular Amperian loop might achieve this, but:
Say we drew an Amperian loop of an arbitrary radius. How do we know that this will align with a magnetic field loop of the current carrying wire so that $d\vec B$ and $d\vec S$ will still be parallel?
Perhaps this is possible, but I may or not understand why. If it's why, I'll illustrate why with a (poorly) drawn graphic I just made:
Where the red circles are lines of constant magnetic field strength and the black circle is the Amperian loop. As the loop is traversed, with each path element $d\vec S$, located at some value $\theta$ around the loop, the magnetic field vectors of all the magnetic field strength rings will be parallel to them since the Amperian loop is a circle. This would explain the need for an Amperian loop aligned this way in order to work out.
If this isn't the case, please clarify what is. If this makes some sense, some questions:
What happens if we don't use a circular Amperian loop? Could we accurately find the magnetic field? It would seem weird if we had to choose the correct loop shape
How do I know that $d\vec B$ in my graphic isn't going to be anti-parallel to $d\vec S$ at all points, rather than parallel?