In a field effect transistor they use a polarity to control to vary the electricity flowing through it. What is the maximum distance such a polarity can be projected over longer distances? I.E. one foot, one yard or one mile?

I think you need to read up on what a FET is, how it works and what it does.
It uses a small signal to the gate terminal to control the amperage from the source terminal to the drain terminal. It does not project anything.

https://en.wikipedia.org/wiki/Field-effect_transistor