So if a coils inside length was 3" with 50 turns of #16 vs. 6" with 50 turns of #16 (turns and size are just grabbed out of the air) would more copper give you more power?
Maybe.
Generic...
If the magnet was 3", then no.
The induced voltage would be the same, but 'power' means flowing amps, flowing amps means there is a resistance loss, and longer #16 wire means more resistance so less power comes out.
If the magnet is 6", then yes.
The larger diameter would 'catch more flux' (?), and make more power.
The area of the magnet compared to the length of the wire counts for a lot.
3x3" magnet is 9"sq, with 12" per turn.
6x6" magnet is 36"sq with 24" per turn. Twice the wire (and resistance) 'catches' 4x as much magnetic field.
G-