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: 32

Answer

a) $-2Q/\epsilon_0$ b) $2Q/\epsilon_0$

Work Step by Step

$$\color{blue}{\bf [a]}$$ When the sphere of radius $R=2a$ is centered at the origin, the two charges $q_1$ and $q_2$, which are at $x=-a$ and at $x= a$ respectively, will be inside the sphere. Thus, the net electric flux through this sphere is given by $$\Phi_e=\dfrac{Q_{in}}{\epsilon_0}=\dfrac{q_1+q_2}{\epsilon_0}$$ Plugging the known; $$\Phi_e =\dfrac{-4Q+2Q}{\epsilon_0}$$ $$\boxed{\Phi_e =\dfrac{- 2Q}{\epsilon_0}}$$ $$\color{blue}{\bf [b]}$$ When the sphere of radius $R=2a$ is centered at $x=2a$, the charge $q_2$, which is at $x= a$, will be the only charge inside the sphere. Thus, the net electric flux through this sphere is given by $$\Phi_e=\dfrac{Q_{in}}{\epsilon_0}=\dfrac{ q_2}{\epsilon_0}$$ Plugging the known; $$\Phi_e =\dfrac{ 2Q}{\epsilon_0}$$ $$\boxed{\Phi_e =\dfrac{ 2Q}{\epsilon_0}}$$
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