Why are electric guitar pickups designed the way they are?
An electric guitar pickup consists of a coil of fine wire wound around a permanent magnet, placed close to the steel strings. Because steel is a magnetic material, it disturbs the field around the permanent magnet as it vibrates, and this generates an electrical signal in the coil by electromagnetic induction (Wikipedia has more detail). Nylon strings don’t work with this kind of pickup; for a nylon stringed guitar you need to use an acoustic pickup (which is essentially a contact microphone). It’s the steel string’s magnetic properties, not its electrical conductivity, that makes a pickup work. If you wanted to use a wire coil pickup without a permanent magnet in it, you’d need another way to make the string vary a magnetic field as it vibrates. You suggest running a current through the strings, but unless my physics intuition fails me badly, to match a decent permanent m
Sure — for years you’ve always been able to find pickups with power–active pickups. And with an active pickup you can have an EQ and other on-board effects, but they do a few other things that passive pickups never do: they can run out of power during the middle of that kick-ass solo or if stored too long, spill battery guts inside your guitar.
Pickups already don’t work with nylon string guitars. Pickups are a bit like microphones. A microphone is a magnet wound with wire, with a vibrating diaphram. In the case of a guitar pickup, the string is the diaphram. Not only do strings have to be metal, they have to have some ferrous content. I think one of the prime difficulties might be that you’d be operating a semi-complex electrical system in a rather harsh environment, where the strings might be dirty, corroded, old, sweaty, etc. To the extent that all the string-bearing surfaces of my guitar have become worn with use I bet you’d be replacing and resoldering all the time.