How to prove that a electric field is constant

[Edwan]

I know mathematicly how to prove that a electric field is constant on an infinite plane, but how physicly I could prove that a electric field is constant ( i.e without mathematical equation) on an infinite plane, which means that the electric field don't change because of the radius like in a normal charge ( where the electric field change by 1/r².

Thank you!






P.S. Its not an homework question!

 

[Defennder]

Intuitively, you can visualise that the closer you get to the infinite plane, fewer of the direction vectors originating from the plane to the point remain orthogonal to the plane. Which means that the E-field contributions from those parts of the plane decrease, whereas the E-field contribution from the point on the plane directly underneath the point increases. The decrease from the other parts of the plane = increase due to that point on the plane directly underneath that point. So it sorts of cancels out.

Granted this is a very hand-waving type of explanation, but it's the best you can come up without working through the equations.