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 806: 19

Answer

$2q,q,-3q$

Work Step by Step

We know that the net electric flux through the closed surface is given by $$\Phi=\dfrac{Q_{in}}{\epsilon_0}$$ And from the given figures, we can see that $$Q_{in,A}=q_1+q_3=-q$$ $$q_1+q_3=-q\tag 1$$ $$Q_{in,B}=q_1+q_2=3q$$ $$q_1+q_2=3q\tag 2$$ $$Q_{in,C}=q_2+q_3=-2q$$ $$q_2+q_3=-2q\tag 3$$\ From (2), $q_2=3q-q_1$ Plug that into (3), $$(3q-q_1)+q_3=-2q$$ Hence, $$ -q_1+q_3=-5q$$ Add this to (1), $$q_1+q_3+(-q_1+q_3)=-q+(-5q)=-6q$$ Hence, $$\boxed{q_3=-3q}$$ Plug into (2) to find $q_2$, and into (1) to find $q_1$ $$q_2-3q=-2q$$ Hence, $$\boxed{q_2= q}$$ $$q_1-3q=-q$$ Hence, $$\boxed{q_1= 2q}$$
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