College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 22 - Problems - Page 864: 39

Answer

$\frac{1}{2}\epsilon_0~E^2 = \frac{1}{2~\mu_0}~B^2$ In an EM wave traveling in a vacuum, the electric and magnetic energy densities are equal.

Work Step by Step

We can show that the electric and magnetic energy densities are equal. $\frac{1}{2}\epsilon_0~E^2 = \frac{1}{2}\epsilon_0~(c~B)^2$ $\frac{1}{2}\epsilon_0~E^2 = \frac{1}{2}\epsilon_0~c^2~B^2$ $\frac{1}{2}\epsilon_0~E^2 = \frac{1}{2}\epsilon_0~(\frac{1}{\sqrt{\epsilon_0~\mu_0}})^2~B^2$ $\frac{1}{2}\epsilon_0~E^2 = \frac{1}{2}\epsilon_0~(\frac{1}{\epsilon_0~\mu_0})~B^2$ $\frac{1}{2}\epsilon_0~E^2 = \frac{1}{2~\mu_0}~B^2$
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