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

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SUMMARY

The Stern-Gerlach experiment demonstrates that a magnetic dipole experiences a force in a nonuniform magnetic field, specifically in the z-direction. The force is defined by the equation F = -∇(μ * B), where μ represents the magnetic moment and B the magnetic field. The absence of x or y components in the gradient is due to the specific design of the apparatus, which is oriented to create a gradient solely along the z-axis. This orientation is arbitrary, but it is crucial for the experiment's outcome.

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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?
 
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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.
 

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