I feel really stupid that I can't solve this problem, but here goes...(adsbygoogle = window.adsbygoogle || []).push({});

The force on a magnetic moment [tex]\mu_z[/tex] in a nonuniform magenetic field [tex]B_z[/tex] is given by

[tex]F_z=\mu_z \frac{dB_z}{dz}[/tex]

If a beam of silver atoms travels a horizontal distance of 1 m through such a field and each atom has a speed of 100 m/s, how strong must the field gradient [tex]dB_z / dz[/tex] be in order to deflect the beam 1 mm?

I guess I am not really sure where to start. I would have used potential energy to solve this, and I don't know how forces are going to make sense because even with the force gradient it doesn't seem like I can come up how far the beam should deflect. The force of gravity and the force of the moment will be in equilibrium and will have to equal each other. So my thought would be that I could just say:

[tex]\frac{mg}{\mu_z}= \frac{dB_z}{dz}[/tex]

That doesn't incorperate any of the information given though, so I must be missing something.

Another thing I am not really sure about is extracting the quantum numbers out of silver. n=4 so l=3,2,1,0 and [tex]m_l[/tex]=3,2,1,0,-1,-2,-3

Since

[tex]\mu_z = \frac{-e}{2m_e} L_z = \frac{-e \hbar}{2m_e}m_l[/tex]

Which value of [tex]m_l[/tex] would I use?

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# Homework Help: Force of magnetic moment

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