Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 24 - Electric Potential - Problems - Page 713: 56

Answer

The charge of particle 3 is $~~-5.7~\mu C$

Work Step by Step

We can write a general expression for the electric potential energy of a system of charged particles: $U = \frac{1}{4\pi~\epsilon_0}~\sum \frac{q_i~q_j}{r_{ij}}$ We can see that $U=0$ when the x coordinate of particle 3 is $x = 10~cm$ We can find $q_3$, the charge of particle 3: $U = \frac{1}{4\pi~\epsilon_0}~(\frac{q_1~q_2}{4.0}+\frac{q_1~q_3}{14}+\frac{q_2~q_3}{10}) = 0$ $\frac{q_1~q_2}{4.0}+\frac{q_1~q_3}{14}+\frac{q_2~q_3}{10} = 0$ $35q_1~q_2+10q_1~q_3+14q_2~q_3 = 0$ $q_3~(10q_1+14q_2) = -35q_1~q_2$ $q_3 = -\frac{35q_1~q_2}{10q_1+14q_2}$ $q_3 = -\frac{(35)(5.0~\mu C)(3.0~\mu C)}{(10)(5.0~\mu C)+(14)(3.0~\mu C)}$ $q_3 = -5.7~\mu C$ The charge of particle 3 is $~~-5.7~\mu C$.
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