Basically neodymium magnets are like imaginary copper coils carrying tremendous amps. like on the order of one million amp turns per meter.
However the magnet is the same as air magnetically, (it also conducts electricity). because it is as air, it takes 1 million amp turns per meter to generate 1 tesla.
An iron core with copper wire wrapped around it only requires approximately 1/10,000 or 1/3000th as many amp turns to generate the same flux.
this is why a thousand turns carrying 2 amps can saturate your car's alternator with the stock claw pole.
however, the amps generated in the stator coils, oppose the amps flowing in the rotor.
there is also an air gap in the alternator. the rotor coil has to pass enough current to magnetize that air as well, and this takes a lot of magnetic mmf, or amp turns.
In most motors, we concentrate the flux in the teeth as high as is practical, for two reasons:
1 so that the flux lines do not travel through the copper coil, but rather around it.
2 so as to allow for more copper to be installed in the machine.
car alternators have relatively thin "back iron"
which means the back iron will saturate before the teeth do.
i'm not sure if this is by design but i wouldn't be surprised if it is.
in any case because the magnet spans nearly 3 teeth, the flux density through the air gap is about half the flux density in the thinnest part of the iron.
iron has non linear permeability and its practically impossible to get cheap motor laminations past 1.5T.
so you don't need real strong magnets.
with regard to the volume of magnet required, the amp turns flowing out of the machine demagnetize the magnets. the question is, how much.
these sorts of calculations used to be done by hand.. now we have computers.