Moving the magnetic field around a fixed conductor?

In this example:

and many others related to electromagnetic induction, the main component of motion would be the conductor perpendicular to a magnetic field.

I know it’s possible to have it the other way around, fixed conductor and move the magnetic field source (e.g., magnets, electromagnets), but I’m curious of the type of force the magnetic field source would experience when current flows.

In a typical generator (where the wire rotates around a fixed magnet(s)) there is an induced EMF ($vBL$) and current will flow to the load, and due to the induced EMF is opposing the change in magnetic field flux, the Lorentz force acting on the wire will oppose the applied motion ($v$). What about the case when the magnet rotates a fixed conductor? Will it experience an induced Lorentz force opposing the motion?