[rotorwrench]

It may have been attached as a way to match impedance on the antenna wire. Most of the antenna wire replacements I've seen for these don't include and impedance coil but you never know what they might have been trying to do with that. The EFV8 club has had a long running series about radio equipment used in the early fords this year and maybe part of last year. I'd have to go back and look at all that stuff to see if it mentions anything about a coil like that.

Do you know which radio make & model you have? There is info out there for the old Ford tube type radio sets.

As far as I'm aware, there is no way to "boost" a signal by applying DC power to the antenna. It just needs a mast or in this case a wire mesh to receive the signals. Impedance is important but putting any power back through the antenna lead might fry the input circuitry.