# Inductive sensor - How does it work?

I can't understand how the system sketched here physically works:

4 = permanent magnet, with residual magnetization $B_r$

6 = ferromagnetic core with a coil around it

7 = ferromagnetic toothed wheel

It's an inductive sensor that measures the speed of the wheel.

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I have thought that the Permanent Magnet induces an EMF in the coil, due to the magnetic field produced by it. (Faraday-Neumann law) (expecially at the beginning... when the coil is mounted on the permanent magnet). It should produce a current through the coil. Then, when a tooth passes near the coil, the magnetic flux through the coil changes again and it should produce another EMF and I can observe it.

Maybe all this reasoning is wrong... I have some difficulties in understanding the role of the PM and of its residual magnetization.. How can the wheel influence the magnetic field 'felt' by the coil if it is only a ferromagnetic material and it it not a permanent magnet? Is it due to the fact that the permanent magnet induces a FEM in the tooth and a field resisting to the flux variation thought the tooth that produces a variation in the field 'felt' by the coil, resulting in an induced EMF?

Please, let me know if something is not clear. Thanks.

When a tooth is near the core of the coil, the magnetic flux through the core will greatly increase ,because the tooth (and the wheel) helps lowering the reluctance of the magnetic circuit generated by the permanent magnet. That increase in the core flux is picked up by the coil.

As the wheel is in motion the permanent magnet will induce a current in the wheel due to it being ferromagnetic, which will change the magnetisation of the wheel which will then cause the magnetic field to vary in the core which will then create an EMF in the coil. Remember that a ferromagnetic material is indeed what they use to make permanent magnets.