Calculating Amplitude of Electromagnetic Waves 100 km from Earth

[vabamyyr]

i have a problem i have been wrestling for past day. Radiowave transmitter on Earth radiates sinusoidal waves with whole power of 50kW. we have to presume that radiation is equally distributed to upper surface. And i have to find amplitude of E and B 100 km from earth.

I derived equation that involves P and E. P = E^2 * sigma0 * c
But that P is probably power of one wave. And to get power of one wave I thought it is logical to divide whole P with semisphere with radii of 100 km.
and after that calculated E and got 3*10^-5 V/m, but book has different answer, after getting E it is easy to calculate B because B = E/c. any suggestions?

 

[drbaer]

I assume your sigma0 is the permittivity of free space (I know it as epsilon0).
In any case your formula is missing a factor 1/2 (for the average power).
You can also write S=E^2/(2*Z0), Z0 being the impedance of the vacuum, 377 Ohm (That number is simply easier to remember).
S is the power flux density (power flowing through a certain area), S=P/(2*pi*R^2).
I get S= 800 nW/m^2 and then E=0.024 V/m.

 

[vabamyyr]

u have the correct answer, I understand that on one hand S = P/2pii*R^w
but on the other hand S = E*H where S is called poynting vector, also i found out where 377 comes from Em/Hm = sqrt(myy0/epsilon0) = 120 pii = 377 and H is therefore E/377 and when i plug it into S equation i get S = E^2/377, i`m having difficulties understanding where factor 1/2 comes from, i think i`ll have to consider S as average energy flux density and then yes, there is 1/2 factor also, is this thought correct?