Derive an expression for electric field due to two parallel charged infinite sheets.

Explanation

Electric field due to two parallel charged infinite sheets:

Let us consider two infinitely large charged plane sheets with equal and opposite charge densities `+sigma` and `-sigma` which are placed parallel to each other as shown in the figure.
The electric field between the plates outside the plates is found using Gauss law. The magnitude of the electric field due to an infinite charged plane sheet is `sigma/(2epsilon_0)` ans it points perpendicularly outward if `sigma gt 0` and points inward of `sigma lt 0`.
At the points `P_2` and `P_3`, the electric field due to both plates are equal in magnitude and opposite in direction (Figure). Hence the electric field at a point outside the plates is zero. But inside the plate, electric fields are in same direction i.e., towards the right, the total electric field at a point `P_1`
`E_("electric") = sigma/(2epsilon_0)+sigma/(2epsilon_0) = sigma/epsilon_0`
The direction of the electric field inside the plates is directed from positively charged plate to negtively charged plate and is uniform everywhere inside the plate.