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 833: 5

Answer

$-2.23\times10^{-19}\;\rm J$

Work Step by Step

We know that the electric potential energy is given by $$U_e=qV\tag 1$$ So we have to find the net electric potential at the proton. $$V=V_1+V_2=\dfrac{kq_1}{r_1}+\dfrac{kq_2}{r_2}$$ The distance between the upper electron and the proton is equal to the distance between the lower electron and the proton. So $r_1=r_2=r$. And $q_1=q_2=-q$ $$V =\dfrac{-kq}{r }+\dfrac{-kq}{r }=\dfrac{-2kq}{r }$$ Plug into (1), $$U_e=q\dfrac{-2kq}{r }=\dfrac{-2kq^2}{r }$$ Plug the known and note, from the given graph, that $r=\sqrt{x^2+y^2}=\sqrt{(0.5^2+2^2)\times 10^{-9}}$ $$U_e= \dfrac{-2(9\times 10^9)(1.6\times 10^{-19})^2}{\sqrt{(0.5^2+2^2)\times (10^{-9})^2} }$$ $$U_2=\color{red}{\bf -2.23\times10^{-19}}\;\rm J$$
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