\(Q_{enc}\)

Given a closed surface \(S\) there is always an outward pointing normal, where by outward pointing we mean that if I travel along the normal direction I can keep going forever without intersecting \(S\) again. We can use a similar definition of inside and outside of \(S\). \(Q_{enc}\) on the right hand side of Gauss' law is simply the total charge inside \(S\).

We have a line of alternating charges on the \(x\)-axis at \(x=...,-2,-1,0,1,2,....\) with a positive charge at the origin. What is the total charge inside a sphere of radius \(3.5\), i.e. what is \(Q_{enc}\)?

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