#gaussian surface

[isomorphismes]

[champlaintutor-blog]

Two different ways to find the electric field from an infinite plane:

Integrating. This is the "hard" way. It's not really worth going through it all, unless you really like trigonometric integrals.

Using a "gaussian pill box", an infinite gaussian rectangle, to find the electric field.

The result is surprising: the electric field away from a uniformly charge plane is constant: it doesn't depend on how far you are!