One approach that has been used to compute an approximation of the
voltage at the end of a dipole is to look at the impedance of a full
wavelength antenna fed in the center.
The assumption is that the "feed point voltage" will be twice what the
"voltage relative to ground" is (whatever you want to consider "ground"
as being)
You can compare the current at the 1/2 way out point on one half (sort
of the "feed point) to get a scaling rule.
The tricky thing is that the impedance of a full wavelength dipole is
VERY dependent on the length/diameter ratio of the elements (unlike for
a regular half wave, where it's not real strongly dependent).
And, of course, there is the interaction between the two halves.
But, to take a simple example, assume a 20 meter long dipole at 7.15 Mhz
that is 2 cm diameter - the impedance is 71.5-j2 ohms.
if we make it 40 meters long, the feedpoint impedance is 2122-j1109
(about 520V for 100W)
The current at the midpoint is about 119-j708mA (compared to a
"feedpoint" current of 192+j101 mA
The current at the end is zero - that's because even though you have
some current at the feedpoint (how else could you put power into the
system) you can't have current at the end - there's also power radiated
all the way along the element- this is why the "take the full wave
dipole and divide by 2" isn't valid.
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