This is actually a pretty cool little experiment. I used such circuits for many, many years. We wrapped a coil on a nylon form with a steel bolt running through the core, no laminations, just a steel bolt. This part we secured to the outside of the stator windings on a very large and very unusual AC type motor. These motors ran at a very low AC frequency, typically sub 1 Hz. The coil was part of what we called a "pole slip detector". We could watch the stator magnetic field during normal run and monitor for any pole slips during running. Generally a pole slip or pole slipping is associated with a generator but in the case of some very special and unusual motors there is a need to detect pole slips.
If a special motor is driving a lead screw and the screw bottoms out or reaches a bottom or top stop the motor will begin to pole slip. The normal waveform picked up by the coil will show spikes in amplitude. So my signal from my coil can be amplified and passed along to a level detector (comparator) and when the spikes start to happen (pole slips) I can count them. I know I am at a top or bottom stop of the lead screw I am driving. I could for example allow 3 (or any number) of pole slips to occur then reverse two phases to my 3 phase motor and reverse the direction of my motor. Something else I could do is while my motor is running I could suddenly change the frequency to my motor which should result in a change to my motor's speed. A good motor should not have any pole slips happen when the speed is changed. A test of the motors ability to respond to speed changes while the motor is under a load.
So again a cool little experiment that has some very real world applications. While I did over all those years try many times to improve this test method using all sorts of hall effect sensors I could never seem to beat the method of the coil of wire and steel bolt. Simple and very, very effective.
Keep everyone up on how it goes and your observations.
Ron