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!

 

[kyle8921]

To find the electric field from a radio station, we can use the formula E = P/(4πr^2), where E is the electric field, P is the power transmitted by the radio station, and r is the distance from the radio station.

In this case, the power transmitted by the radio station is 500 kW and the distance is 25 km (converted to 25000 m). Plugging these values into the formula, we get:

E = (500,000 W)/(4π(25000 m)^2) = 0.001 W/m^2

Therefore, the electric field from the radio station at a distance of 25 km is 0.001 W/m^2. This value may seem low, but it is important to note that the electric field decreases with distance from the source due to the inverse square law. Additionally, the electric field from a radio station is typically very small and poses no health risk to humans.