Finding an electric field from a radio station

[Noone1982]

If a radio station transmits at 500 kW, how does one find the electric field 25 kM away?

 

[clive]

The energy emitted by the source in $$dt$$ is $$Pdt$$
where $$P=500\,kW$$. At $$R=25\,km$$ from the source this energy will be uniformly distributed in a spherical shell of radii $$R$$ and $$R+dR$$. The volume of this shell equals
$$dV=\pi R^2 c dt$$
where $$c$$ is the speed of light. Now you have to know that the energy density of an electromagnetic wave can be written as
$$w=\frac{1}{2}\epsilon_0 E^2$$
with $$E$$ the elecric field amplitude. So
$$P dt=w\cdot dV$$
... and you find E!