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: 23

Answer

a) $27.1\;\rm V$ b) $-4.34\times 10^{-18}\;\rm J$

Work Step by Step

$$\color{blue}{\bf [a]}$$ The proton is assumed to be a point charge, so its electric potential at the electron's position is given by $$V=\dfrac{1}{4\pi \epsilon}\dfrac{q_e}{r}\tag 1$$ Plug the known; $$V=(8.99\times 10^9)\dfrac{1.6\times 10^{-19}}{0.053\times 10^{-9}}$$ $$V=\color{red}{\bf 27.1}\;\rm V$$ $$\color{blue}{\bf [b]}$$ The electric potential energy of the electron is then given by $$U_e=(-q_e)V$$ Plug from (1), $$U_e=\dfrac{1}{4\pi \epsilon}\dfrac{-q_e^2}{r} $$ Plug the known; $$U_e=(8.99\times 10^9)\dfrac{-(1.6\times 10^{-19})^2}{0.053\times 10^{-9}}$$ $$U_e=\color{red}{\bf -4.34\times 10^{-18}}\;\rm J$$
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