Research On Inductive Proximity Sensors

The short machinedesign.com article is a good introduction. In short, inductive proximity sensors are circuits that maintain a oscillating magnetic fields while sensing the reluctance of the circuit through the voltage amplitude of the oscillation. The magnetic fields induce eddy currents in proximate ferrous materials. These eddy currents create their own magnetic fields, opposing the one created by the sensor and increasing sensor circuit (coil) reluctance.

LJ12A3-4-Z/BX

This is the sensor model supplied by Folgertech here.