Is computer memory based on the presence or non-presence of a magnetic "charge"?

You can Google it, but here is one good site: https://www.explainthatstuff.com/how-computer-memory-works.html

Only old computers, like those used in the Apollo spacecraft used magnetic memory.

It was called toroidal memory back in the earliest computing days. You ran current through a coil wrapped around a ferromagnetic core to magnetize it giving you a “1” you reversed the current to write a “0.” Later floppy discs used magnetic tape and then finally hard drives used magnetic platters. Only recently has modern solid state memory used something other than magnetic storage. Unless your PC has a solid state drive you are using magnetic memory right now when you access data stored on your hard drive. Your “RAM” is volatile silicon based memory. It used to be so expensive that at one time it was literally worth more than its weight in gold. It’s dirt cheap now.