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 27 - Gauss's Law - Exercises and Problems - Page 807: 33

Answer

$188\;\rm N\cdot m^2/C$

Work Step by Step

We know that the net electric flux through a closed surface is given by $$\Phi=\dfrac{Q_{in}}{\epsilon_0}$$ And we have a box of 6 identical surfaces that contains a charge of 10 nC at its center. Thus the flux will be divided on these 6 surfaces equally. Thus, $$\Phi_{\rm surface}=\dfrac{Q_{in}}{6\epsilon_0}$$ Plug the known; $$\Phi_{\rm surface}=\dfrac{10\times 10^{-9}}{6(8.85\times 10^{-12})}$$ $$\Phi_{\rm surface}=\color{red}{\bf 188}\;\rm N\cdot m^2/C$$
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