In the Stern-Gerlach experiment an image for the $z$ measurement is often shown (although the decision to call this orientation $z$ is arbitrary)
It would seem that to make a measurement in the the $x$ direction that another apparatus would have to be placed and be turned $\pi/2$ around the axis of the beam.
However, the problem I've had with this line of reasoning is, what is this analogous to for the $y$ direction. Is the system rotated around an axis perpendicular to the beam?
It feels that this orientation would not deflect the particle. Some orientations may even have the particle not pass through the apparatus at all.
Question: Relative to the initial Stern-Gerlach, how is a $y$ orientation setup.