Please give intuition without Gauss Law.

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    $\begingroup$ Why not Gauss law? $\endgroup$ Apr 10, 2020 at 12:25

1 Answer 1


The constant field is for an infinite sheet.

There are a few ways to think about this. Both of these will be pretty hand-wavy arguments because I think that's what you're asking for.

  1. Scaling.

Let's say you have some weird-shaped charge distribution, e.g. shaped like a 🐱 (let's say the cat has a diameter of $d$). When you're close to the cat ($r\ll d$), the electric field will have some complicated form because the cat is complex shape. But as you get very far away from the cat ($r\gg d$), it will look more and more like a point charge, and so the field should start to look like the inverse square law.

Now think about a $d\times d$ sheet a distance $r$ away. The same logic applies, when you're far away (relative to the size of the sheet), it will have to look like a point charge. When you make the sheet infinite, $d\to \infty$, then no matter how far away you go, $r \ll d$, the sheet still looks infinite. If the object looks the same (hand wave ahead) then it doesn't really matter how far away you are, it still looks like the same distance away.

  1. Electric field lines

If you think about an electric field line leaving the sheet, it starts out by going perpendicular to the sheet. As it gets further away, no matter what, the sheet looks the same in every direction, so it doesn't make sense for the field line to go any direction other than straight. Since electric field lines are all parallel and the density never changes the electric field is constant at any distance away. There's 'no room' for the inverse square law because there are too many other field lines.


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