University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 32 - Electromagnetic Waves - Problems - Exercises - Page 1077: 32.56

Answer

Choice B.

Work Step by Step

From the information given earlier the electric field limit limits the intensity. $$ I= \frac{1}{2}\epsilon_0 cE^2_{max}$$ $$ I_{max,E}= \frac{1}{2}\epsilon_0 c(\frac{350}{f})^2$$ Now express the intensity in terms of the magnetic field. $$ I= \frac{1}{2}\epsilon_0 cE^2_{max}$$ $$ I_{max,B}= \frac{1}{2}\epsilon_0 c(c^2)B^2_{max}$$ $$ I_{max,B}= \frac{1}{2}\epsilon_0 c^3(\frac{5}{f})^2$$ Take the ratio of the two intensities. $$\frac{ I_{max,E}}{ I_{max,B}}=\frac{1}{c^2}\frac{350^2}{5^2}=5.4\times10^{-14}$$ The allowed intensity using the electric field guideline is much smaller than the allowed intensity using the magnetic field guideline.
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