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Electric-current easily cause shock to human body. But magnetic fluxs through human body do-not cause any perceptible change, as-well no invisible-impacts/ health impacts are well-known. We, when hold-in-hand a strong bar-magnet, or a big loudspeaker-magnet; we feel nothing about the magnetic field.

Even in MRI-machine, which produce immense magnetic field, do no perceptible change in human body (though it causes change in the atoms including the electrons such as electrons of benzene-rings).

Why does-it happen?

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    $\begingroup$ If you have been in an MRI scanner, then you may have experienced the induction currents caused by the gradient coils. They tingle, and not just a little. It's really just a question of the strength of the field. For AC fields it doesn't take much to be felt, or to even become damaging (you certainly wouldn't want to be exposed to the AC field inside your microwave), but one can probably estimate fairly well at which point even a DC field would do damage to human physiology. Whether we can generate such a field in the lab is questionable, though. $\endgroup$ – CuriousOne Jul 7 '16 at 18:57
  • $\begingroup$ Btw just found Wikipedia mentions in a place, some researchers humans can perceive magnetic field (en.wikipedia.org/wiki/Magnetite#Biological_occurrences), links to sciencemag.org/news/2016/06/… , though I don't know the source is how-much reliable. $\endgroup$ – Always Confused Jul 7 '16 at 19:14
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    $\begingroup$ It's obvious that at some point fields will be felt (a frog that is being diamagnetically levitated definitely feels that), whether these experiments are statistically meaningful... that I would have serious doubts about. Humans are not orienting themselves by magnetic fields (just look at all the news about people getting lost in the wild), so we definitely don't have a "sense". Our neural nets may be sensitive, to some extent, but those are two different things altogether. $\endgroup$ – CuriousOne Jul 7 '16 at 19:19
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    $\begingroup$ Yes, you would definitely feel the forces in a large scale diamagnetic levitation experiment (there is little hope that we could make such a field technically, and if we could, it might actually be already dangerous to humans). One could speculate and analyze if it would feel similar to floating in water or more similar to being in a zero-g environment. In water the force of buoyancy is caused by the pressure differential at different depths, so it doesn't act, directly, on the inside of the body. In magnetic levitation it's a volume effect because the field goes trough the body. $\endgroup$ – CuriousOne Jul 7 '16 at 19:27
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    $\begingroup$ The indiction takes place inside the tissue, well, it takes place in the entire volume of the magnetic field. Time dependent magnetic fields cause electric fields, and that is what we are feeling. The levitation, on the other hand, that's diamagnetism, i.e. it's a quantum mechanical effect on atoms and molecules. $\endgroup$ – CuriousOne Jul 7 '16 at 19:30

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