Gauss Law Infinite Plans of Surface Charge Densities

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1. Three infinite planes of surface charge densities of ρs = 2, -3, and 0.5μC/m2 lies parallel the xy plane as shown in Figure 1, each separated by a 1 mm air gap. Find the field at:
i. z = 0.2mm
ii. z = 1.2 mm
iii. z = 2.2mm
iv. z = -2.2mm

Figure 1 Three parallel infinite planes of charges. The lowest plane is in the xy plane at the origin.

According to Gauss' law, the electric flux through a closed surface is where is the charge enclosed within the closed surface and is the permittivity of free space.
The field strength at a point in the field is the flux per unit area normal to the surface.
The mathematical form of Gauss' law is given as

"Electric flux E emerges from a positive charge and terminates on a negative charge or goes to infinity."
( is the angle between the field and outward normal to the surface) gives the total flux coming out of the closed surface. If we consider a closed surface such that either the field is normal to the ...