A 100-kW radio station emits EM waves in all directions from an antenna on top of a mountain. What is the intensity of the signal at a distance of 10 km? A) 8 × 10−⁵ W/m² B) 8 × 10−⁶ W/m² C) 3 × 10−³ W/m² D) 0.8 W/m² E) 2.5 × 10−⁵ W/m²

Question

Quizplus · Accepted Answer

The intensity of a spherical wave is given by $I = \frac{P}{4\pi r^2}$, where $P$ is the power (100 kW or $100 \times 10^3$ W) and $r$ is the distance (10 km or $10 \times 10^3$ m). Substituting the given values, $I = \frac{100 \times 10^3}{4\pi (10 \times 10^3)^2} = \frac{100}{4\pi 10^2} \approx 8 \times 10^{-4} \, \text{W/m}^2$.

A 100-KW Radio Station Emits EM Waves in All Directions