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: 43

Answer

$6.25\times10^{-4}V/m$, $1.04\times10^{-9}W/m^2$.

Work Step by Step

Find the electric field strength from the specified rms voltage, and the antenna’s length. $$E_{rms}=\frac{V_{rms}}{d}=\frac{0.00100V}{1.60m}=6.25\times10^{-4}V/m$$ Use that electric field to calculate the intensity. The energy per unit area per unit time is the magnitude of the average intensity, equation 22–8. $$\overline{I}=\frac{P}{A}=\frac{1}{2}\epsilon_ocE_o^2=\frac{1}{2}\epsilon_oc(\sqrt{2}E_{rms})^2$$ $$=\epsilon_ocE_{rms}^2=\epsilon_oc(\frac{V_{rms}}{d})^2$$ $$=(8.85\times10^{-12} C^2/(N\cdot m^2))(3.00\times10^8m/s) (\frac{0.00100V}{1.60m})^2$$ $$= 1.04\times10^{-9}W/m^2$$
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