34 AWG in my experience takes up to much space, and can handle far more current than we push threw the coil.

38 is small enugh that when we make a 32 ohm coil it dosent end up being way larger than the little magnet we are moving.
We only push 100 mA thru the coil and the magnet we are moving is very small so when we use a very small wire we get a coil who's windings all fit inside the field of the small magnet.

The copper wire isnt bare its has a thin varnish coating.

Do you have a coil winder machine built? if so post pics!