Corrected entry: The way Sue is wrapping the wires around the door handle in order to make a magnet, would cause the current to go from left to right and return from right to left. This would create two equally powerful magnetic fields in opposite directions so the final sum would be zero magnetic field. The door handle shouldn't get magnetized.
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Correction: In actual fact, all electromagnets are wound from one end to the other, and back again. The only way to cancel the induced magnetism would be to wind it in the opposite direction (i.e. clockwise round the core, then anti-clockwise, the same number of turns).
airhead