Electric field due to infinite sheet

[kahwawashay1]

Ok so the electric field due to an infinitely large sheet of charge is the same at any distance from the sheet, as derived from Gauss' Law or calculus or whatnot. I was just wondering how well experimental data verifies this? I just find it kind of hard to believe that the electric field due to charged particles would not diminish with distance from them if the particles were arranged in a sheet

 

[Doc Al]

That result is for an infinite sheet of charge, which is a pretty good approximation in certain circumstances--such as if you are close enough to the surface. Of course real sheets of charge are finite and their electric field will diminish with distance if you move far enough away.

 

[phyphenomenon]

Why electric field is independent of distance

In the case of a point charge, the electric lines of force diverges as distance increases. But in the case of a charged infinite plane sheet the electric lines of forces are parallel. Since the lines are parallel, the number of electric lines of force through a certain area does not change in the case of plane sheet. So electric field is also independent of the distance.

 

[MikeGomez]

Ok so the electric field due to an infinitely large sheet of charge is the same at any distance from the sheet, as derived from Gauss' Law or calculus or whatnot. I was just wondering how well experimental data verifies this? I just find it kind of hard to believe that the electric field due to charged particles would not diminish with distance from them if the particles were arranged in a sheet

As distance from a point charge increases, the field strength falls off as $1/r^{2}$.

As distance from a line source (or cylinder) increases, the field strength falls off as $1/r$.

As distance from an infinite plane increases, the field strength remains the same.

What Phyphenomenon said regarding parallel lines of force is true. Imagine an ideal laser which produces a beam of light which is perfectly parallel. The intensity of the light is exactly the same at 1 meter distance as it is at 1 kilometer distance or further.

In the case of an infinite sheet there is a little more going on than parallel lines of force. However the non-parallel lines of force end up canceling out, regardless of distance. Explaining it is non-trivial, but professor Ramachandran does a fantastic job in this video. You can watch from 47:00 for the full explanation, or skip ahead to 55:00 for the answer.