Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 23 - The Electric Field - Stop to Think 23.4 - Page 643: 1

Answer

$\vec{E}_a = \vec{E}_b = \vec{E}_c = \vec{E}_d = \vec{E}_e$

Work Step by Step

At first, you might be tempted to say that since points $b, c, d,$ and $e$ are all the same distance away that the magnitude of the electric field vectors at those points are equal and that since point $a $ is further away from the other points that point $a$ is the weakest and all of the other ones are of equal magnitude. You would be correct if we were dealing with an infinite line charge, but the question sneakily states that we're dealing with a $ $ $PLANE$ $ $ of charge rather than an infinite line charge despite the given picture showing something that really depicts a line of charge rather than a surface. From here, all you need to know is that since the electric field vector points away from the plane (all horizontal components cancel at every point in space), that the equation for the electric field vector is $\vec{E} = \displaystyle \frac{\eta}{2\epsilon_0}$. We see here that distance from the plane does not at all affect the magnitude of $\vec{E}$. Therefore, the magnitude of the electric field vector is the same at all points in space: $\vec{E}_a = \vec{E}_b = \vec{E}_c = \vec{E}_d = \vec{E}_e$
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