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.

Answer 1

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:

$$E=\frac{{\sigma }_1}{{ϵ}_0}+(-\frac{{\sigma }_2}{{ϵ}_0})$$

$$\Rightarrow E=\frac{1}{{ϵ}_0}({\sigma }_1-{\sigma }_2)$$

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:

$$E=\frac{{\sigma }_1}{{ϵ}_0}+\frac{{\sigma }_2}{{ϵ}_0}$$

$$\Rightarrow E=\frac{1}{{ϵ}_0}({\sigma }_1+{\sigma }_2)$$