I'll take a stab at this. The force is proportional to current if we are talking magnetic brakes.
The other issues are the frictional forces. Static friction is usually larger than rolling friction. Rolling friction is probably RPM dependent.
With any frictional forces there will be heat. Heat will likely lower the friction. Heat also affects the coils.
In say a tension controller. I designed a simple one and made one mistake which was important because I was operating at low tension, very low speed and very low duty cycle. We didn't need it in the log run anyway because frictional forces were enough.
I did vary the current through the coil, but you have to allow some reversal. i.e. from -0.1 A to 1A. Usually an application would have a tension arm. I could not. The only purpose was to incrementally move a fixed amount of Teflon to expose a 4" window every minute or so.
as the magnetic field changes, current is induced. the faster the change, the more current is induced and more breaking action. it is used in many applications from damping for analog instruments to slowing down race cars.
Retarders on trucks produce a fairly constant braking torque, which means that energy absorbed will go up with speed.
Theres usually a 6 position switch so you can select how much braking you want.
Is it possible, I wonder, to reach magnetic saturation in a magnetic brake (like you do in a transformer). Would you eventually reach a point where you ceased to get any braking? Doesn't sound very feasible...
I suppose that a magnetic brake is really just a specialist type of generator, so maybe generator equations are what you need to look at for formal answer? Or look for data from a commercial product?