Gauss Law in a plane sheet, and thick sheet (Infinite)

[Prannoy Mehta]

We have learned the below formula for a plane sheet of charge with thickness.

E=σ/ϵ

and the one below for with no thickness (negligible)

E=σ/2ϵ

The problem, I am facing is digesting the derived equations. It is one thing for sure that these formulas must be right. But then the fact that E is proportional to the square of the distance between the test charge (Or any other charge, taken from columbs law.) is disobeyed by it (Atleast that's what I think.) I have seen alternate derivations with the same expression. Why is this not obeyed, or is it obeyed over here.

Thank you.

 

[Jilang]

The contribution from each individual charge does obey the inverse square law, but the geometry of the situation leads to the result.
This might help
http://mlg.eng.cam.ac.uk/mchutchon/chargedPlanes.pdf
Notice that the sin θ term increases with the distance from the plate and this counteracts the inverse square relationship.

 

[Prannoy Mehta]

Thanks a tonne :D