Q: If the world is a giant magnet, how come we can’t build a repelling magnet that can float?
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Earth’s magnetic field is on the order of 1 ten thousandth as strong at its surface. If you had an electromagnet with the strength of the Earth’s magnetic field, you’d barely be able to pick up paper clips with it. But a magnetic field is a magnetic field; there’s nothing special about the field in any given place. Generally speaking, the level curves of the Earth’s magnetic field (the surfaces where it has constant strength) intersect the surface. Given the methods we have for magnetic levitation, the Earth’s magnetic field is severely lacking.