Who says a mag field does no work? Who? Mag fields store energy then transfer said energy to the form of electric, electromagnetic, thermal, kinetic, and/or chemical energy domain(s). Have you studied physics or EE extensively? Just curious why you make such sweeping generalizations such as a mag field doing no work, as if it were undisputed gospel? Nothing personal but what is the basis for saying mag fields do no work?
The only reason some give are the Lorentz force relations where mag force acts normal to a charge carrier's velocity. In this case the mag Lorentz force, Fm = quXB, is indeed not doing work on the charge carrier. But E & B fields are mutual & interdependent so that one of them, or both, can do work on dipoles, motors, etc. Also, if an inductor de-energizes into a passive network loop, the time varying B field includes an E field which does work on the charges. B transferred its energy to E which can do work on charges.
This is a topic which cannot be explained in a few posts. I will elaborate if needed.