College Physics (4th Edition)

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

Chapter 22 - Problems - Page 864: 40


The equation $~~I = ~\lt u \gt c~~$ is dimensionally consistent.

Work Step by Step

$I$ is intensity in units of $W~m^{-2}$ $\lt u \gt$ is energy density in units of $J~m^{-3}$ $c$ is the speed of light in units of $m~s^{-1}$ We can verify the units of the term $\lt u\gt ~c$: $(J~m^{-3})~(m~s^{-1}) = J~s^{-1}~m^{-2} = W~m^{-2}$ We can see that both sides of the equation $~~I = \lt u \gt c~~$ have units of $\frac{W}{m^2}$ Therefore the equation $~~I = ~\lt u \gt c~~$ is dimensionally consistent.
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