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 28 - The Electric Potential - Exercises and Problems - Page 834: 32

Answer

${\rm \color{black}{\bf -10}\; nC,\; and\;\; \color{black}{\bf +40}\; nC}$

Work Step by Step

We have two charges $q_1$ and $q_2$and we know that the net electric potential energy is -180 $\mu$J. Hence, $$U=\dfrac{1}{4\pi \epsilon_0}\dfrac{q_1q_2}{r}$$ Hence, $$q_1q_2=4\pi \epsilon_0 r U\tag 1$$ We are given that the net charge of both of them is about 30 nC, so $$q_1+q_2=30\;\rm nC=30\times 10^{-9}\;C\tag 2$$ Hence, $$q_1=(30\times 10^{-9})-q_2$$ Plug into (1), $$ [(30\times 10^{-9})-q_2]q_2=4\pi \epsilon_0 r U$$ Plug the known; $$ (30\times 10^{-9})q_2-q_2^2=\dfrac{1}{9\times 10^9} (2\times 10^{-2})(-180\times 10^{-6})$$ Hence, $q_2= \bf -10\;\rm nC$ or, $q_2=40\;\rm C$ Plug into (2), $q_1= \bf 40\;\rm nC$ or, $q_1=-10\;\rm C$ Therefore, the two charges are $$\boxed{\rm \color{red}{\bf -10}\; nC,\; and\;\; \color{red}{\bf +40}\; nC}$$
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