Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 20 - Electric Potential and Electric Potential Energy - Problems and Conceptual Exercises - Page 721: 81

Answer

(a) $x=-0.5m$ (b) region 3 (c) $x=-4.5m$

Work Step by Step

(a) We know that $V_A=\frac{1}{4\pi \epsilon_{\circ}}(\frac{2q}{1.5+x}-\frac{q}{1.5-x})$ $\implies 0=\frac{2q}{1.5-x}-\frac{q}{1.5+x}$ $\implies \frac{2}{1.5-x}=\frac{1}{1.5+x}$ This simplifies to: $x=-0.5m$ (b) We know that the electrical potential also vanishes in one of the given regions. As the lower charge $-q$ is less than the charge $+2q$ by a factor $2$, therefore, there should be a point located close to $-q$ by a factor of $2$ and thus the region is $3$, that is, $-3.5m \gt x\gt -5m$ (c) We know that $V_3=\frac{1}{4\pi \epsilon_{\circ}}(\frac{2q}{1.5-x}-\frac{q}{-1.5-x})$ $\implies 0=\frac{2q}{1.5-x}-\frac{q}{-1.5-x}$ This simplifies to: $x=-4.5m$
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