Why is there no voltage induced into the secondary winding (in high-voltage step-up transformer) when the ignition switch is closed (OFF). When the current flows in the primary winding of the coil a magnetic field is generated. This interacts with the flux from the magnet. Assuming that the ignition switch is closed, the flow of alternating current created by the interaction of the two magnetic fields will flow to the ground. Will the flow of alternating current in the primary (while the ignition switch is closed, OFF position) induce a current in the secondary? If it does not, why not?
I assume you're talking about an aircraft mag. Mags are never really OFF off. Instead of ON/OFF, it's more like ON, and "on but not on enough to work".
With the ignition switch OFF, grounding out the primary, the alternating current generated in the primary as the mag spins flows to ground, and it does induce a voltage in the secondary as the current alternates, but this voltage is much too low to be able to jump a plug gap. So the mag is effectively off if not totally off.
To get a spark, the flow of alternating current in the primary needs to be fully cut off by the opening of the points within the primary to create a field collapse strong enough to generate sufficient high voltage to be induced in the secondary.