How Is Field Strength Calculated at a Distance from an Antenna?

[erece]

The current at the base of an earthed antenna 30 metres high is 20 amperes at a frequency of 1MHz. Calculate the field strength at a distance of 10 Km.Now in this question do we have to consider that field generated from the antenna and field at the distance 10 Km are same ??

I solved like this...
power generated from monopole ( as given in question that antenna is earthed)
P = 80[∏xI]^{2}[l/λ]^{2}
where l = 2h
and h=30 m
l=60 m
I=20 A
λ=c/f = 300 m
So P=37.86KW
Power density at a distance of 10 Km =P/(4∏[10000]^{2}
= 30.14uW/[m][/2]
=[E]^{2}/120∏
From this i am getting E=106.5mV/m
But the answer is 4.8μV/m
I THINK I AM TOTALLY WRONG...
Please tell where i am wrong...

 

[jbsteele]

The main mistake you have made is that you have assumed that the field strength at the distance of 10 Km is equal to the power density at the distance of 10 Km. That is not correct. The field strength at a distance of 10 Km is proportional to the power density at the distance of 10 Km, but it is not equal to it. The field strength at a distance of 10 Km is given by:E = (120πP)/(4π × (10^4)^2)where P is the power generated from the monopole.Substituting the values given in the question, we getE = 4.8 μV/m