Why Does the Stern-Gerlach Experiment Only Have a Gradient in the Z Direction?

[PsychonautQQ]

I'm confused.So a dipole needs a nonuniform field for the net force to not equal zero, cool.

My question is how do they go from
F = -∇(μ * B) = ((μ_z)(dB/dz))*(z unit vector)
how come the gradient has no x or y parts?

 

[Simon Bridge]

how come the gradient has no x or y parts?

... because they [messrs Stern and Gerlach] set up the apparatus that way.
The label "z" for the orientation is arbitrary.