Gaußian pillbox

The Gaußian pillbox provides a technique for deriving the electric field around a charged surface using Gauß’s law. At a given point $⃗ 𝐫$ on a surface $Σ$ with normal $ˆ 𝐧$ , we let $G (𝑎, 𝜖)$ denote a rectangular prism with faces of area $𝑎 2$ parallel to $Σ$ at $⃗ 𝐫$ and with height $𝜖$ .