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Radiofrequencies are usually used to flip polarized nuclei in a magnetic field in NMR and MRI. These RF correspond to the Larmor frequency of those nuclei. Since the effect from the RF is usually due to the magnetic component of the electromagnetic wave, would an oscillating magnetic field be able to also flip nuclei? In resonant inductive coupling, magnetic fields can oscillate to create "magnetic waves" (if that's even a term) - https://en.wikipedia.org/wiki/Resonant_inductive_coupling. If this oscillated at the Larmor frequency, would it be able to flip polarized nuclei?

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Yes, my understanding is that MRI and NMR are performed with resonant coils. Both are near field. Typically the trick in NMR and MRI is getting the field strong enough to actually flip a nuclei, not getting it to resonate at the Larmour frequency. For MRI this is on the order of a few Tesla, which is huge.

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