A radio transmitter is operating at an average power of $4.00 \mathrm {~kW}$ and is radiating uniformly in all directions.What is the average intensity of the signal $8.00 \mathrm {~km}$ from the transmitter? A)4.97 μW/m² B)2.49 μW/m² C)0.00497 W/m² D)0.00249 W/m²

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Quizplus · Accepted Answer

The intensity of the signal is given by the power divided by the area of a sphere with radius $8.00 \mathrm {~km}$. The area of a sphere is $4\pi r^2$, so the intensity is:$$I = \frac{P}{4\pi r^2} = \frac{4.00 \mathrm {~kW}}{4\pi (8.00 \mathrm {~km})^2} = 4.97 \mu\mathrm {W/m^2}$$

A Radio Transmitter Is Operating at an Average Power Of 4.00