ANSWERS: 3
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I saw an experimental device demonstrated on tv, one of those science shows, that lifted small non-metallic objects. I can't find anything about it on the net, but it might have been the Podkletnov device- spinning supercondutors that Podkletnov claims reduces gravity by 2%. I'm not sure that was it, as I remember that it may have been super high power magnetics (like a million volts), which lifted any kind of small object, even a living thing- I think it lifted a small mouse! What I can't exactly remember is the description of the device, but I do remember it was high powered and experimental. The impression I seem to remember is that high enough magnetism can lift normal non-metallic objects.
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Mike777 is right about the strength of the magnetic field. My understanding is that you cannot do this with all materials, but it works well on water, and things containing water. Water is slightly diamagnetic, meaning that it is very slightly repelled by a magnet. There was a demonstration of using a 16 Tesla field to levitate a frog. I would guess that the same strength field could levitate a human, but making an electromagnet with that strong of a field and as big as a human would be very expensive. Typical MRI machines have a field of about 5T (from memory), and they are already very expensive, much of the expense having to do with the magnet.
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Yes, there are powerful magnets made from ceramics and rare earth metals.
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