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Now let us consider a horizontal conductor[a thin rod for our example] moving in a vertical magnetic field,perpendicular to its own length.As the electrons move axially, work performed on unit charge is BLV[which is indeed the induced emf]

Here,

B: Magnetic field

L: Length of the conductor

V:Speed of the moving conductor

Now the axial force on an electron is BeV. Again the axial motion invites a magnetic force perpendicular to the length of the conductor.This particular force gets continuously canceled by the surface forces. The total magnetic force is indeed a no-work force.But if a part of this "total magnetic force" gets canceled by some other force for example the surface forces the remaining part can indeed perform work!By this mechanism work done on unit charge is indeed BLV. So by this mechanism we can derive work from the magnetic forces.[You may consider my postings at sci.physics.foundations "Why don't we do that?" and "Power from Motional Emf----A simple Illustration"[Dated 1st March] ]

Can a reasoning of this type explain the work done by the magnetic forces in the example of the rotating magnet?

We can get work out of the magnetic forces . Would it be reasonable to modify Poynting's theorem in the view of this fact to make it more realistic? It is to be noted that the derivation of the Poynting theorem assumes that the magnetic forces are not capable of doing any work.