Given a closed surface 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 again. We can use a similar definition of inside and outside of . on the right hand side of Gauss' law is simply the total charge inside .
We have a line of alternating charges on the -axis at with a positive charge at the origin. What is the total charge inside a sphere of radius , i.e. what is ?