Why do we need a coil to make a magnetic field?

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Why do electromagnets always need a coil to generate a magnetic field, and why do you need a AC current to generate inductance?

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You actually do not need a coil. A straight piece of wire will also work. But the magnetic field will be weaker with only a wire. A coil is a way to have more wire in a single place so you can focus the magnetic field. Electromagnets do work with DC. But a magnetic field does not induce current in a wire, for that you need a changing magnetic field.

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