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Basically, any magnetism is caused by moving electrical charges - that is, by electrical currents.

In an electromagnet, a current is made to flow through a conductor. This causes magnetism, but when the current is switched off, there is no more magnetism.

In a permanent magnet, the magnetism is caused by the electrons spinning around the atoms. In some materials, like iron, it is possible for atoms to become aligned, in the sense that more will have their axis of rotation point in one direction than in the other. These atoms cause the magnetism, then. In a regular material, every atom is a tiny magnet, but due to the random positions of the individual atoms, these tend to cancel each other on a large scale.

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