Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 22 - Electric Fields - Problems - Page 656: 48d

Answer

The term $(1 - \frac{z}{\sqrt{z^2+R^2}})$ is slightly less than 1 and it does not increase very much as the release point is moved closer to the disk. As a result, the magnitude of the acceleration only increases slightly as the release point is moved closer to the disk.

Work Step by Step

We can use Equation (22-26) to write an expression for the magnitude of the electric field: $E = \frac{\sigma}{2\epsilon_0}(1 - \frac{z}{\sqrt{z^2+R^2}})$ The term $(1 - \frac{z}{\sqrt{z^2+R^2}})$ is slightly less than 1 and it does not increase very much as the release point is moved closer to the disk. Therefore the magnitude of the electric field only increases slightly as the release point is moved closer to the disk. As a result, the magnitude of the acceleration only increases slightly as the release point is moved closer to the disk.
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