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 - Conceptual Questions - Page 832: 11

Answer

a) $V_b\gt V_a=V_c$ b) $V_a\gt V_b\gt V_c$

Work Step by Step

$$\color{blue}{\bf [a]}$$ We know that the electric potential is given by $$V=\dfrac{kq}{r}$$ The two charges are positive, so $$V_{a}=V_1+V_2 $$ $$V_a= \dfrac{kq}{r_1}+ \dfrac{kq}{r_2}$$ $$V_a= \dfrac{kq}{r_1}+ \dfrac{kq}{3r_1}=\dfrac{3kq+kq}{3r_1}$$ Let's assume that $r_1=1$ unit. $$V_a= \dfrac{4kq }{3r_1}=\boxed{1.3kq}$$ By the same approach, $$V_c= \dfrac{4kq }{3r_1}=\boxed{1.3kq}$$ And $$V_b=\dfrac{kq}{1}+ \dfrac{kq}{1}=\boxed{2kq}$$ Therefore, $$\boxed{V_b\gt V_a=V_c}$$ $$\color{blue}{\bf [b]}$$ $$V_{a}=V_1+V_2 $$ $$V_a= \dfrac{kq}{r_1}+ \dfrac{-kq}{r_2}$$ $$V_a= \dfrac{kq}{r_1}+ \dfrac{-kq}{3r_1}=\dfrac{3kq-kq}{3r_1}$$ Let's assume that $r_1=1$ unit. $$V_a= \dfrac{2kq }{3r_1}=\boxed{0.67kq}$$ $$V_a= \dfrac{kq}{3r_1}+ \dfrac{-kq}{r_1}=\dfrac{kq-3kq}{3r_1}$$ $$V_c= \dfrac{4kq }{3r_1}=\boxed{-0.67kq}$$ And $$V_b=\dfrac{kq}{r_1}- \dfrac{kq}{r_1}=\boxed{0}$$ Therefore, $$\boxed{V_a\gt V_b\gt V_c}$$
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