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 642: 55

Answer

61 km.

Work Step by Step

The energy per unit area per unit time is the magnitude of the average intensity, which we can relate to the electric field amplitude using equation 22–8. The intensity of the radio station at a given distance is assumed to be the radiated power, divided by the surface area of a sphere. $$\overline{I}=\frac{P}{4\pi r^2}=\frac{1}{2}\epsilon_ocE_o^2$$ Solve for the radius. $$r=\sqrt{\frac{P}{2\pi\epsilon_ocE_o^2 }}$$ $$r=\sqrt{\frac{25000W}{2\pi( 8.85\times10^{-12} C^2/(N\cdot m^2))(3.00\times10^8m/s)(0.020V/m)^2 }}$$ $$\approx 61\times10^{3} m$$
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