The magnetic field is along the z axis in a Stern-Gerlach experiment. The force it exerts on a magnetic dipole with dipole moment is proportional to: B) B² C) dB/dz D) d²B/dz² E) $\int$B dz

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The force exerted by a magnetic field on a magnetic dipole is given by F = -d(U)/dz, where U is the potential energy of the dipole in the magnetic field. This potential energy is proportional to the dot product of the dipole moment and the magnetic field, which gives -μBcosθ. Taking the derivative of this with respect to z gives -μB(d(cosθ)/dz). Since the magnetic field is along the z axis, the angle between the field and dipole is constant, so cosθ is constant and d(cosθ)/dz = 0, leaving only the factor of the magnetic field strength B. Therefore, the force is proportional to dB/dz.

The Magnetic Field Is Along the Z Axis in a Stern-Gerlach