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Question
Two infinitely large plane thin parallel sheets having surface charge densities σ1 and σ2 (σ1 > σ2) are shown in the figure. Write the magnitudes and directions of the net fields in the regions marked II and III.
Solution
In region II
The electric field due to the sheet of charge A will be from left to right (along the positive direction) and that due to the sheet of charge B will be from right to left (along the negative direction). Therefore, on region II, we have:
\[E = \frac{\sigma_1}{\epsilon_0} + \left( - \frac{\sigma_2}{\epsilon_0} \right)\]
\[ \Rightarrow E = \frac{1}{\epsilon_0}\left( \sigma_1 - \sigma_2 \right)\]
In region III
The electric fields due to both the charged sheets will be from left to right, i.e., along the positive direction. Therefore, in region III, we have:
\[E = \frac{\sigma_1}{\epsilon_0} + \frac{\sigma_2}{\epsilon_0}\]
\[ \Rightarrow E = \frac{1}{\epsilon_0}\left( \sigma_1 + \sigma_2 \right)\]
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