Consider a metallic rod hung by two springs (symmetrically), a magnetic field exists out of the plane of our system. At t = 0, we switch on a battery which produces current in wire (left to right in the rod) so now, a force of magnetic origin acts on the rod to pull it down and extend the springs thus magnetic force appears to do work in this case.
So is the fact that magnetic forces don't do work incorrect? Because I don't think that some other force can do work on the system
Assume the rod and springs to be massless.