My opinion is:
The statement that 'magnetic fields do no work' *only* applies to classical, freely moving point charges. This means quantum mechanical effects, such as what ‘force’ holds an electron in place in an atom, can’t be taken into account.
There are many situation where 2 magnetic field can interact and do work, e.g. 2 bar magnets being attracted). That situation is not comparable in any way to a freely moving point charge in a magnetic field.
Just my opinion though.
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Markus Imhof say: Nope - motion relative to an electric field doesn't create a magnetic field. At least not that simply. Rather, the voltage induced in a closed circuit is proportional to the rate of change of the magnetic flux it encloses (can't post the formulas here, so check them out in the source below) - and vice versa. The important thing here is that it's about change, and a closed circuit loop.
As for the magnetic field doing work - yes, after a fashion. Unfortunately (for the perpetuum mobile builders, mostly - not so much for people building or using all kinds of electric motors or generators), that work is almost 100% recoverable. Meaning, you can't get any work out a magnetic field that you didn't put into it at some place.
In the case of one magnet pulling up a second magnet (slightly different from your example), the work is done by reducing the energy in the combined magnetic field of these two magnets - and you have to put it back into the field when you pull the two magnets apart.
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Robert J say: You have the first bit backwards:
Currents are caused in a conductor by motion relative to a magnetic field.
Magnetic fields do not require motion.
Your example of using one magnet to lift another also has a misconception.
You are joining two items together - the fact that it is by magnetism rather than bolting them is irrelevant - it is then YOU that provide the energy / work to lift the lower object, just as if it were mechanically fixed to the top one.
The difference with two stuck-together magnets is that then you have to pull them apart, rather than simply removing a fixing.
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