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 29 - Potential and Field - Exercises and Problems - Page 864: 41

Answer

$3750\;\rm V/m$ downward, $7500\;\rm V/m$ upward.

Work Step by Step

We know that the electric field is given by $$E=-\dfrac{dV}{ds}$$ which means that the electric field is the negative of the slope of the $V-s$ graph. From the given graph, it seems that the potential surfaces are uniformly spaced along the $y$-axis above and below the origin point. At point 1, which lies between two potential surfaces of 25 V and 100 V. Whereas the distance between them, on the $y$-axis and above the origin, is 2 cm. Thus, $$E_1=-\dfrac{\Delta V}{\Delta y}=\dfrac{100-25}{0.02}$$ $$\vec E_1=-(\color{red}{\bf 3750}\;{\rm V/m})\;\hat j$$ It is pointing downward. At point 2, which lies between two potential surfaces of 25 V and 100 V. Whereas the distance between them, on the $y$-axis and below the origin, is 1 cm. Thus, $$E_2=-\dfrac{\Delta V}{\Delta y}=\dfrac{100-25}{-0.01}$$ $$\vec E_2= (\color{red}{\bf 7500}\;{\rm V/m})\;\hat j$$ It is pointing upward.
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