# Electromagnetic waves

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?

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, im having difficulties understanding where factor 1/2 comes from, i think ill have to consider S as average energy flux density and then yes, there is 1/2 factor also, is this thought correct?