# Why can infinite planes be approximated as Gaussian surfaces?

A little background: I'm an undergraduate studying Electrodynamics, currently in Chapter 8 of Griffiths.

A question I came across (8.4 part a for those curious) asks for a calculation of the force exerted by one point particle on another point particle of equal charge. This is meant to be done through means of:

$$\oint_S \bar{T} \cdot d \vec{a}$$

$$\bar{T}$$ being the Maxwell stress tensor.

I'd expect that you'd have to create a closed surface around one of the point charges, but this question explicitly wants the surface integral to be done over the plane. Easy enough, but my question is why would this be a viable closed surface?

The explanation I've been given so far from the lecturing professor (and wikipedia) is that the plane is an approximation of a closed surface. It seems that as the "bubble" (see the below cross-section illustration) extends to infinite size, its function becomes negligible and what ultimately matters is the infinite plane.

This explanation makes intuitive sense, but I feel is a little hand-wavey. Why is this the case? Does it work for all systems of particles (continuous and not continuous), or just for a point particle. My intuition would tell me that if you zoomed in on the very edge of a sphere, it would start to look like a plane (but again this explanation is not very mathematical).

Any insight would be greatly appreciated.