The sign problem

For an open surface we can choose the direction of S-vector two different ways
- to the left or to the right
- what we call flux would be different these two ways
- different by a minus sign

left

For a closed surface we can choose the direction of S-vector two different ways
- pointing “in” or “out”
- define “out” to be correct
- integral of EdS over a closed surface gives net flux “out”, but can be +or-

For an open surface we can choose the direction of S-vector two different ways