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Tony
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It's called induction heating, and is actually a standard way of heating Al in the metallurgy industry. An electrical current is generated in the coil, which forms an opposing current in the metal called an Eddy current. The opposing forces cause a net force upwards strong enough to counteract gravity. The electrical resistance in the metal means that the Eddy current generates heat, which is why it melts

 

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Question

1: Why doesn't the coil melt

2: When melted why did the object fall, it wasn't any heavier

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The eddy currents that generate heat are focused at the centre of the coil, not in the helix of the coil itself. So a block of material at the centre of the coil is heated by induction but the coil is, in general terms, not. Nevertheless, a great deal of heat flows to the coil from stray currents and by radiation and conduction so the coil is normally hollow and cooled by flowing water.

 

The furnaces that I have seen always use a crucible to contain the molten metal, so I have never seen the material fall through in the way that it does in the demonstration. I can't think of any good reason why it should fall spontaneously and I would guess that in the demo it results from switching off the current at the end of the show? If it was an effect of liquefaction I would expect to see drips initially, rather than a sudden dumping of the whole charge.

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