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 22 - Electric Charges and Forces - Stop to Think 22.6 - Page 621: 1

Answer

$\vec{E}_b > \vec{E}_a > \vec{E}_d > \vec{E}_c$

Work Step by Step

Recall that $\vec{E} = \displaystyle \frac{kq}{r^2} = \frac{1}{4\pi\epsilon_0}\frac{q}{r^2}$ We can calculate the electric field on each point as: a. $\displaystyle \vec{E} = \frac{k(q)}{(r)^2} = \frac{kq}{r^2} = \vec{E}$ b. $\displaystyle \vec{E} = \frac{k(2q)}{(r)^2} = 2\frac{kq}{r^2} = 2\vec{E}$ c. $\displaystyle \vec{E} = \frac{k(q)}{(2r)^2} = \frac{1}{4}\frac{kq}{r^2} = \frac{1}{4}\vec{E}$ d. $\displaystyle \vec{E} = \frac{k(2q)}{(2r)^2} = \frac{2}{4}\frac{kq}{r^2} = \frac{1}{2}\vec{E}$ So, from largest to smallest, the electric field at each point ranks $\vec{E}_b > \vec{E}_a > \vec{E}_d > \vec{E}_c$
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