Hope that this helps Grado Cartridge Structure. Click on the top tab marked "Cartidges"
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Thanks for the link, but the Grado explanation is that the moving iron element creates an increase in one flux gap and a decrease in another as it moves back and forth on the cantilever. I don't quite understand what that means or how it induces a current. If there were already a constant current, I think I understand how it could impede that as it moves, but I don't understand how it could induce current.
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.