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Electrodynamics Feb 8, 2018
Quiz-III–Alternative Version
Two planes parallel to \(X-Z\) plane and two plane parallel to \(Y-Z\) plane
carry uniform charge densities as shown in figure below. Find the components of
the electric field in the nine regions I-IX listed below.
| Region | \(E_x\) | \(E_y\) |
| I | \(\dfrac{-\sigma_1-\sigma_2}{2\epsilon_0}\) | \(\dfrac{\sigma_3+\sigma_4}{2\epsilon_0}\) |
| II | \(\dfrac{\sigma_1-\sigma_2}{2\epsilon_0} \) | \(\dfrac{\sigma_3+\sigma_4}{2\epsilon_0}\) |
| III | \(\dfrac{\sigma_1+\sigma_2}{2\epsilon_0}\) | \(\dfrac{\sigma_3+\sigma_4}{2\epsilon_0}\) |
| IV | \(\dfrac{-\sigma_1-\sigma_2}{2\epsilon_0}\) | \(\dfrac{-\sigma_3+\sigma_4}{2\epsilon_0}\) |
| V | \(\dfrac{\sigma_1-\sigma_2}{2\epsilon_0} \) | \(\dfrac{-\sigma_3+\sigma_4}{2\epsilon_0}\) |
| VI | \(\dfrac{\sigma_1+\sigma_2}{2\epsilon_0}\) | \(\dfrac{-\sigma_3+\sigma_4}{2\epsilon_0}\) |
| VII | \(\dfrac{-\sigma_1-\sigma_2}{2\epsilon_0}\) | \(\dfrac{-\sigma_3-\sigma_3}{2\epsilon_0}\) |
| VIII | \(\dfrac{\sigma_1-\sigma_2}{2\epsilon_0} \) | \(\dfrac{-\sigma_3-\sigma_3}{2\epsilon_0}\) |
| IX | \(\dfrac{\sigma_1+\sigma_2}{2\epsilon_0}\) | \(\dfrac{-\sigma_3-\sigma_3}{2\epsilon_0}\) |
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