iron rod penetrating field coil

Hi,
I'd like to measure the length of a rod (made of iron; diameter: a few millimetres; length: 5 cm) is extending into a field coil.
So I can imagine there is an exploring coil which detects the signal from the field coil. The signal in the measuring coil is changed depending on the length of the rod penetrating it.
Will that work ? What sort of excitation signal works best for that ? How sensitive could such a set-up be made ?
Thanks

Only an AC excitation signal will work. The response would probably be rather nonlinear.

You might be able to drop the rod from a specific height and sample the response as it goes through the coil.

ETA:
If the idea is to know how far the rod is extending into the coil, you will have to excite the coil with an ac signal - preferably sinusoidal - and measure the inductance. You will have to experiment to determine how the inductance changes with distance.

You have re-invented the LVDT, only without the differential part that makes it more accurate.