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: 59

Answer

About 60 billion watts.

Work Step by Step

Assume the radio waves are emitted equally in all directions, so the intensity at a given distance is the radiated power, divided by the surface area of a sphere. Relate the electric field amplitude to the average intensity, using equation 22–8. $$\overline{I}=\frac{P_0}{4\pi r^2}=\frac{1}{2}\epsilon_ocE_o^2$$ Solve for the power since we are given the electric field amplitude. $$P_0=4\pi r^2 \overline{I}=2\pi r^2 \epsilon_o c E_0^2$$ $$P_0=2\pi (0.65m)^2 (8.85\times10^{-12} C^2/(N\cdot m^2))(3.00\times10^8m/s)(3\times 10^6 V/m)^2$$ $$\approx 6\times10^{10}W$$ This is many thousands of times greater than the typical power output of a radio station.
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