Why is the electric field of an infinite sheet of charges independent of r

#electrodynamics #sayphysics #griffiths
What makes the electric field of an infinite charged sheet unaffected by distance?
Why does the electric field from an infinite charge plane stay constant regardless of distance?
What causes the electric field of an endless charge surface to remain constant irrespective of distance?
How does the electric field of an infinite charge distribution remain constant with distance?
What factors ensure the electric field of an infinite charge sheet remains independent of distance?"
Consider Gauss's law, which states that the electric flux through a closed surface is proportional to the enclosed electric charge. When you apply Gauss's law to a flat sheet, you choose a Gaussian surface that is also flat and perpendicular to the sheet. This results in a uniform electric field passing through the Gaussian surface. Since the electric field is uniform and perpendicular to the surface at every point, the flux through the surface is constant.
Since the flux is independent of the distance from the sheet, by Gauss's law, the electric field strength must also be independent of the distance. This is true regardless of how far away you are from the sheet, hence why the electric field of an infinite sheet of charges is independent of the distance from the sheet.
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"Constant electric field distance"
"Infinite charge plane field independence"
"Electric field endless charge surface"
"Charge distribution distance invariant"
"Electric field infinite charge distribution"
"Charge sheet field unaffected by distance"
"Electric field constant regardless of distance"
"Infinite charge surface field stability"
"Electric field distance-invariant property"