Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 34 - Electromagnetic Fields and Waves - Exercises and Problems - Page 1031: 49

Answer

$\bf Yes.$

Work Step by Step

To find out if the manufacturer’s claims are true or not, we need to find the electric field amplitude $E_0$ at $r=42$ m. We know that the radio wave is an electromagnetic wave, so its intensity is given by $$I =\dfrac{P}{A}=\dfrac{c\epsilon_0 E_0^2}{2}$$ Solving for $E_0$; $$E_0=\sqrt{\dfrac{2P}{c\epsilon_0 A}}$$ $$E_0=\sqrt{\dfrac{2P}{c\epsilon_0 (4\pi r^2)}}$$ where $A$ is the area of a sphere since the transmitting unit radiates in all directions. Plug the known; $$E_0=\sqrt{\dfrac{2(250\times 10^{-3})}{4(3\times 10^8)(8.85\times 10^{-12}) \pi (42)^2}}=\bf 0.092\;\rm V/m$$ This means that the claims of the manufacturer are true since a few steps before 42 m the field strength was 0.1 V/m.
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