Are you referring to the little coil in the antenna whip itself ?
It serves a number of functions but mostly it is for impedance matching, i.e. so the "load" seen by the radio/coax is correct (50 ohms ). With RF, unlike DC, the load is not purely resistive, but has capacitive and inductive elements. You'll notice the shorter 1/4 wave whip doesn't have that coil, because it is inherently a 50 ohm load.
The effective ground plane in those antennas is provided by the shiny tube at the base. If you can imagine the normal sheet of metal you'd mount the base on twisted up into a tube. ( well, in simple terms anyway ).
I think that's right, but I am trying to recall my radio theory from thirty years ago.


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