Whoever said magnets do not do work is wrong. Magnets can totally do work. Usually, you need to couple this with other kinds of motion to make it useful (a magnet just sitting there isn’t going to be moving mountains!), but it is totally possible for magnets to do work.
That’s one of the ways magnets can wear out, actually. By doing work against an opposing magnetic field, some of the atoms inside the magnet (which are what give the magnet its magnetic field!) get pushed, so they no longer nicely line up with all of their neighbors. This effect is very small in most cases, so it takes a lot of wear to wear out a magnet–but no so-called “permanent” magnet actually stays permanently magnetic forever.
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