Ermi Roos said:
The mathematical formula for finding the radiated power from an electrically-short vertical monopole over a perfectly-conducting flat ground plane for a particular electric field intensity at a particular distance is....
I haven't investigated why our answers disagree, but below is a paste from my spreadsheet exercise based on an equation from an engineering reference, that is applicable to this situation.
The term
dBi (below) refers to the h-plane antenna system gain in decibels relative to an isotropic radiator, and which includes the effect on radiation resistance of a 10-meter, unfiltered/unchoked, vertical "ground" conductor attached to the r-f ground terminal of the elevated transmitter with a 3-m whip attached to its antenna connector.
NEC-2 was used to calculate the radiation resistance of the elevated whip and 10-meter ground conductor, which along with the other ohmic losses in the antenna system resulted in the antenna system
net gains in dBi cited below.
EQUATION:
Field Intensity in mV/m = 1000 / Distance(m) * SQRT(30 * Power(watts)) * 10 ^ (dBi / 20)
30 Distance, meters
-2.66 Antenna System Gain, dBi
0.3015 Power, watts (about 300 milliwatts)
Ans. 73.80453203 mV/m, which is about 73,800 microvolts/meter.
That ~300 mW value of radiated power needed is significantly higher than that posted using the equation Pr = 1.111(10^-11)[(Ed)^2].
For confidence, below is the calculation using that same spreadsheet for the h-plane field for 1 kW radiated by a perfect 1/4-wave monopole driven against a perfect ground plane:
1000 Distance, meters
5.15 Antenna Gain, dBi
1000 Power, watts
Ans. 313.372316 mV/m
That ~313 mV/m value is the value for such a configuration shown in standard antenna engineering textbooks.
And of course, none of this is sufficient to determine the input power of the transmitter needed to
produce that radiated power for any specific "Part 15" AM system -- which necessarily includes all of the unknown factors given in my post in this thread of today (18 Apr 2010) at 11:20:47 CDST.
RF