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Question:

If copper moves through a magnetic field, will electrical energy be produced?

I am unsure as to whether or not the metal that moves within said field must be ferromagnetic.

Answer:

Yes. Your imagination is 100% correct. When any metal moves through a magnetic field, the electrical energy will be produced.
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It needn't be ferromagnetic. The changing magnetic field will produce an electrical current in the copper. Feromagnetism is the metal being brought near the magnetic field taking on a strong magnetic field.
Copper works better being a better conductor. We are dealing with induction here rather than just magnetism. Moving wire (any material) + magnetic field makes electricity.

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