Given an air-core coil of known inductance and a given frequency of applied voltage, you can predict the coil reactance, the current, and the voltage/current phase relationship.
What effect, if any, will a permanent magnet placed at one end of the coil have on the predicted properties of the coil?
Additionally, if the reactance for the given frequency is altered by the magnet, can the applied frequency be changed such that a new reactance (in the presence of the magnet) can be matched to the original reactance without the magnet.
The former paragraph is at the core of what I'm trying to get at, because I want to know if the magnet will have any kind of transformer effect (parasitic or otherwise) on the oscillating coil. Will the presence of a magnet simply change the inductance of the coil, or will it cause other behaviors (similar to those seen when two coils share mutual inductance)? Or is there something else altogether I am missing?
The arrangement of coil and magnet is end-to-end as the field polarities would be aligned along their axes like this:
coil <--> magnet _//////_ [N | S]
The arrangement would also allow for the magnet to slide into the coil, thereby creating a sort of magnet-core coil.