Question

An AM radio station broadcasts with a power of 25 kW at a

frequency of 920 kHz. Estimate the intensity of the radio wave at a point 10 km from the broadcast antenna.

Short answer

The intensity of the radio wave is$2\times {10}^{-5}W/m^2.$

Step-by-step solution

Given data

The AM radio station has a power of

$$\begin{gathered} P=25kW \\ P=25,000W \end{gathered}$$

The distance of the broadcast antenna from the particular point to measure intensity is,$r=10km=10,000m$

Determination of intensity

The intensity of wave at $10km$distant from the broadcast area is,

role="math" localid="1648918482527" $$\begin{gathered} I=\frac{P}{A} \\ I=\frac{P}{4\pi r^2} \\ I=\frac{25,000W}{\left(4\pi \right){(10,000m)}^2} \\ I=2\times {10}^{-5}W/m^2 \end{gathered}$$