Roy Lewallen wrote:
"The problem is that you`re looking for a single voltage between two
points in space. There is no single value for that voltage."

Keith Henney in his 1950 "Radio Engineering Handbook on page 638 wrote:
"A thin-wire dipole gives an end potential of about 3,900 volts for 1000
watts antenna input for a height of 1/4-wave. It will be higher for
smaller heights, and falls to a minimum of about 1700 volts as height
increases to 3/4-wave; beyond this point it settles down to the
free-space value of about 3000 volts. Potentials vary as the square root
of the power ratio and as the inverse square root of the capacitance per
unit length. For a potential of 3900 volts on a wire 0.101 in. in
diameter (No.10 B&S), the radial gradient is of the order of 31 kv per
cm."

At frequencies where the antenna has high reactance and low resistance,
a few watts of power produce very high potentials. At high altitudes,
high potentials can easily produce corona and flashover. Apply more
watts and produce corona and flashover at sea level.

One way to measure the voltage at the end of a dipole might be to
increase input to the dipole until orona cccurs and then scale that to
the power of interest.

Best regards, Richard Harrison, KB5WZI