I don't really understand what you mean by "main circuit"...[/b]
The main circuit from the battery to the car, just as in the drawings above.

I don't know what a field circuit is...[/b]
VERY basically put, alternators work on the concept of comparing a circuit in the car to what voltage it's putting out, always trying to keep them equal to its setting. In the case of a 12V car, that's about 13.5 volts. If that secondary circuit, the field circuit, gets low on voltage the alternator puts out more; if it gets high, less.

Therefore, with an alternator, if you cut off the battery only then as the field circuit voltage drops the alternator tries to out out more and more voltage. Eventually the field circuit voltage will drops too low and the alternator goes offline, but it's not instantaneous, and in the interim the alternator continues trying to charge pu the system to ~13.5V.

However, if you open this field circuit with a switch or relay then the alternator sees zero voltage and drops offline.

So, you can wire the car one of two ways: wire the kill switch's smaller secondary contacts such that it disconnects the field circuit and the alternator goes offline, system voltage drops to zero, and the car quits running due to lack of electrical power; or, you can wire the ignition through those secondary contacts so the car quits running and the alternaotr stops producing power due to lack of rotation.

Either way works fine, simply choose the method that is most convenient for your car and kill switch location. - GA