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I know three different types: unipolar switch - switching on when a magnetic field enough strong, bipolar switch - switcing on with magnet nordpole and off with southpole, hall-effect bridge with linear out - You can measure the magnetic field.
from what i know they are used to mesure current trough conductor by the magnetic field the current that passes trough them generates.
the devices are used usually when it is about high current and when putting a series reistor to mesure the voltage drop on it and get the current will mean a very big loss of energy so these sensors are best for industrial aplications....
there are some devices that are used to mesure the current trough the lines of copper on a pcb