Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 22 - Electromagnetic Waves - General Problems - Page 643: 61

Answer

35 kW

Work Step by Step

The average intensity is given by equation 22–8. $$\overline{I}=\frac{1}{2}\epsilon_ocE_o^2$$ $$=\frac{1}{2}(8.85\times10^{-12}C^2/(N \cdot m^2)) (3.00\times10^8m/s)(0.12V/m)^2$$ $$=1.9116\times10^{-5}\frac{W}{m^2}$$ Assume that the radio station radiates uniformly. Imagine a sphere, centered at the station, whose radius is 12 km. The $1.9116\times10^{-5}\frac{W}{m^2}$ is the average intensity. This is equal to the radio station’s total power, distributed over the surface of the imaginary sphere. $$I=\frac{P}{A}$$ $$P=IA=(1.9116\times10^{-5}\frac{W}{m^2})4\pi(12\times10^{3}m)^2=35kW$$
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