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 27 - Gauss's Law - Exercises and Problems - Page 808: 47

Answer

See the detailed answer below.

Work Step by Step

We know that the electric field of an infinite plane of charge is given by $$E=\dfrac{\eta}{2\epsilon_0}$$ From the figure below, we can see that, $\bullet$ At region 1: $$E_{net,1}=E_B-E_C-E_A=\dfrac{\eta}{2\epsilon_0}-\dfrac{\eta}{4\epsilon_0}-\dfrac{\eta}{4\epsilon_0}$$ $$\boxed{\vec E_{net,1}=\bf 0\;\rm N/C}$$ $\bullet\bullet$ At region 2: $$E_{net,2}=E_B+E_A-E_C=\dfrac{\eta}{2\epsilon_0}+\dfrac{\eta}{4\epsilon_0}-\dfrac{\eta}{4\epsilon_0}$$ $$\boxed{\vec E_{net,2}=\dfrac{\eta}{2\epsilon_0}\hat j}$$ $\bullet\bullet\bullet$ At region 3: $$E_{net,3}=E_A-E_B-E_C=\dfrac{\eta}{4\epsilon_0}-\dfrac{\eta}{2\epsilon_0}-\dfrac{\eta}{4\epsilon_0}$$ $$\boxed{\vec E_{net,3}=-\dfrac{\eta}{2\epsilon_0}\hat j}$$ $\bullet\bullet\bullet\bullet$ At region 4: $$E_{net,4}=E_C+E_A-E_B=\dfrac{\eta}{4\epsilon_0}+\dfrac{\eta}{4\epsilon_0}-\dfrac{\eta}{2\epsilon_0}$$ $$\boxed{\vec E_{net,4}=\bf 0\;\rm N/C}$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.