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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.
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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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