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 26 - The Electric Field - Conceptual Questions - Page 775: 14

Answer

a) $1$ b) Less than 1.

Work Step by Step

$$\color{blue}{\bf [a]}$$ We know that the force exerted on a charge by a uniform electric field is given by $$F=qE$$ And we know that the amount of charge $q$ in an electron and a proton is equal. We also know that the electric field inside an ideal capacitor is constant and is given by $$E=\dfrac{\eta}{\epsilon_0}$$ This means that since the amount of charge $q$ is the same for a proton and an electron, and $E$ is constant, the force exerted on the electron and the proton is equal. The only difference here is the force direction. Thus, $$\dfrac{F_{\rm p}}{F_{\rm e}}=\color{red}{\bf 1}$$ $$\color{blue}{\bf [b]}$$ The acceleration here depends on mass since the force exerted on both is the same. According to Newton's second law, $$a=\dfrac{F}{m}$$ The mass of the electron is indeed less than the mass of the proton, and according to Newton's second law of motion, the acceleration is inversely proportional to the mass. Therefore, with the same force applied, the electron will experience a greater acceleration compared to the proton. $$\dfrac{a_{\rm p}}{a_{\rm e}} \color{red}{\bf\lt 1}$$
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