Why is the electric intensity equal to charge density over 2*epsilon?

Question

Why is the electric intensity for a positive sheet of infinite extent given by:

Consider a sheet of infinite extent.To find electric intensity at a point P from the sheet.Imagine a Guassian surface in the form of a cylinder whose flat ends contain the point P on both sides of the sheet.The cylinder passes through the sheet so both flat ends are at a distance P from the sheet.Now while calculating the electric flux using the formula Φ = E.A=EAcosθ the flux through the curved surface of the cylinder is zero because they run parallel to the electric field lines.And the flux through the flat ends is given by: Φ = E.Acosθ = EA (since θ = 0).Now this was for one flat end we do the same for the other end and add the both of them.

Now my question is why do we add the both of them?Doesn't it give us twice the electric filed intensity than there really is at the point P from the sheet.

Adding the both of them leads to the following:

Φ = σ/2∈

Why shouldn't it be:

Φ = σ/∈

∈ = charge density.

Answer 1