When the electric flux associated with closed surface becomes positive, zero or negative ?

Explanation

If electric flux associated with area s due to electric field E is `vecE`, then
`phi = vecE. vecS`
`therefore vecphi = ES cos theta`……(1)
Where `theta` is angle between `vecE` and `vecS`.
(i) If `vecS bot vecE` means surface is parallel to `vecE` then, `theta = 90^(@)`
`therefore` from equation (1)
`phi = ES cos 0^(@)=0`
`therefore` Flux associated with surface is zero.
(ii) If `theta lt 90^(@)`, then `cos theta gt 0` (negative) hence flux is positive.
(iii) If `theta gt 90^(@)`, then `cos theta lt 0`. (negative) hence flux is negative.
All three are shown in figure (a), (b) and (c) respectively.