[[Gauß's law]]
# 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 $\vab r$ on a surface $\Sigma$ with normal $\unitv n$,
we let $\mathcal{G}(a,\epsilon)$ denote a rectangular prism with faces of area $a^2$ parallel to $\Sigma$ at $\vab r$
and with height $\epsilon$.
![[Gaußian pillbox.png]]

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