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This is the concept behind the “screwdriver” antenna. The coil is wound with uninsulated wire along a spiral groove to keep the wires separated. A spring-loaded contact ring contacts the wire. The outer sheath containing the contact ring is driven up and down the coil by a reversible motor (originally an electric screwdriver – thus the name).
Do a google search on “screwdriver antenna” to see what is available to hams. There is even at least one model (I think) made for 160 meters (about 1800kHz) that could possibly work at the high end of the AM band. These antennas are intended for mobile use, so are small and within part 15 limits.
A major advantage for us would be the remote tuning capability. After mounting it high up, you can fine-tune it from the comfort of your easy chair.
The disadvantage of the standard offerings is that the coil tends to be very long with respect to the antenna length. This allows a wide tuning range at the expense of antenna length.
This would be a great opportunity for someone to design a version targeted to part 15 AM. I envision a shorter, possibly larger diameter coil with a longer antenna (keeping within the 3 meter limit). It should tune 1500-1700kHz.
The original screwdriver antenna plans for home construction were complicated (the plans are on the web somewhere). A strip of bronze finger contact stock was formed into a ring for the coil contact. You see this stuff along the edges of electronic cabinets for EMI shielding. One very important hurdle is to make the whole coil assembly absolutely waterproof. This requires a rubber boot or some such over the coil and contact sheath assembly.
This is a fun technical idea, but I think it would be overkill for part 15ers. We don’t change frequencies all the time as the hams do. Nevertheless, the remote tuning capability is really attractive when the antenna is mounted waaay up on a tower!