Consider two plane parallel infinite sheets with equal and opposite charge densities +σ and –σ as shown in Fig.
Fig. Electric field due to two thin infinite parallel sheets of charge
The magnitude of electric field on either side of a plane sheet of charge is E = σ/2εo and acts perpendicular to the sheet, directed outward (if the charge is positive) or inward (if the charge is negative).
Case 1. When the point P1 is in between the sheets, the field due to two sheets will be equal in magnitude and in the same direction. The resultant field at P1 is,
E = E1 + E2 = σ/2εo + σ/2εo = σ/εo (towards the right)
Case 2. At a point P2 outside the sheets, the electric field will be equal in magnitude and opposite in direction. The resultant field at P2 is,
E = E1 – E2 = σ/2εo - σ/2εo = 0
