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This is a common point of confusion. In an idealized scenario, where we hypothetically observe the behavior of pure 1H nuclei with no gradients of magnetic susceptibility, the case described by what you “have seen elsewhere” would pertain. In biological tissues, which are diamagnetic (i.e., magnetic susceptibility is less than 0), however, the case is actually as I explain it. I take this approach as it reflects the reality of clinical MRI. In any case, this is really an esoteric point that should not matter much to your understanding of MRI.
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