Marty,
You are mistaking a magnet for magnetic field. Magnets have permanent magnetic fields around them but you can modify the flux lines (shape of magnetic field) by what materials you place close to the magnet...so the magnet and coil sensor do not have to move in order to induce current in a coil ...provided you change the field by moving something close to it.
An iron core is the same thing you have in a transformer - it concentrates magnetic flux lines and increases the magnetic field locally.
You are mistaking a magnet for magnetic field. Magnets have permanent magnetic fields around them but you can modify the flux lines (shape of magnetic field) by what materials you place close to the magnet...so the magnet and coil sensor do not have to move in order to induce current in a coil ...provided you change the field by moving something close to it.
An iron core is the same thing you have in a transformer - it concentrates magnetic flux lines and increases the magnetic field locally.