If I have a metal instrument made of nickel titanium of length .001 m and very small diameter stuck, a tight tube, Can I apply a force using maglev?

If I have a metal instrument (0.001m long and very small diameter) made of nickel titanium and stuck in a rigid tube, I need to exert magnetic force on this instrument using magnetic levitation concept. i am thinking of approaching an AC electromagnet, that will induce eddy currents in the instrument(as it is made of an electrically conductive material), thus this Eddy current will produce magnetic field opposing the magnetic field of the AC electromagnet, can I get enough repulsive force to vibrate this instrument?

If i increase the strength of the electromagnet, can I get enough repulsive force to vibrate this instrument, if the electromagnet is 10 cm away from the instrument?

What if I dip the nickel titanium instrument in a liquid nitrogen, will the strength of the Eddy current increase thus the repulsive force will increase ? what if i switch the nickel titanium with stainless steel ?

$$1$$ mm is very small. Eddy currents will not flow significantly unless the frequency is very high. I doubt this approach will work. See Wire-grid polarizers on this page for a different example of how induced currents are important and size of the conductor matters.