Say there’s an iron nail sitting on the table and I bring a permanent magnet close enough above it that the nail comes off the table and sticks to the magnet. Now it appears a force has been exerted on the nail to move it over a distance (the definition of work, measured in units of energy). Where did the energy come from?
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It’s basically like gravity but with magnetism. Say there’s a ball on my balcony and I push it gently and it falls down. Where did the energy come from to make it fall down?
Answer: It started with energy because it was on the balcony instead of on the ground. And your nail started with energy because it wasn’t stuck to a magnet.
Actually for calculations it’s easier to go the other way around: we say that a nail by itself with no magnets nearby has 0 energy, and when it’s stuck to a magnet it has negative (-) energy. That’s fine – since we can’t measure potential energy, just potential energy difference, we can say 0 is wherever we like.
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