Problem — Power from the flux density

Problem

A probe measures, at $r=50$ m, an average intensity $I=2$ W/m². Estimate the power emitted by the (isotropic) source using $P=4\pi r^2 I$. Compare it with a medium-power radio transmitter.

Solution

Radiated power. For an isotropic source, the total power is the intensity multiplied by the area of the sphere:

$P=4\pi r^2 I=4\pi\cdot 50^2\cdot 2=4\pi\cdot 5000\approx 6{,}3\cdot 10^4\ \text{W}$

$\ev{P\approx 6{,}3\cdot 10^4\ \text{W}\approx 63\ \text{kW}}$

Comparison. This is of the order of magnitude of a local radio transmitter (a few tens of kW), consistent with a medium-power installation.

Collegamenti

Argomenti: Onde elettromagnetiche Concetti: Intensità di un’onda