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 - Problems - Page 642: 42

Answer

1.7 V/m.

Work Step by Step

The intensity is the power per unit area. The satellite’s microwave power is distributed uniformly over the circular area specified in the problem. The energy per unit area per unit time is the magnitude of the average intensity, equation 22–8. Find the rms value of the electric field. $$\overline{I}=\frac{P}{A}=\frac{1}{2}\epsilon_ocE_o^2=\frac{1}{2}\epsilon_oc(\sqrt{2}E_{rms})^2=\epsilon_ocE_{rms}^2$$ $$E_{rms}=\sqrt{\frac{\overline{I}}{\epsilon_oc }}=\sqrt{\frac{P}{A\epsilon_oc }}$$ $$E_{rms}=\sqrt{\frac{13\times10^3 W }{(\pi (750m)^2) (8.85\times10^{-12} C^2/(N\cdot m^2))(3.00\times10^8m/s) }}$$ $$\approx 1.7V/m$$
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