It
has a small area of cross section d S and negligible height Just inside the surface, the electrostatic field is zero; just outside, the
field is normal to the surface with magnitude E Thus,
the contribution to the total flux through the pill box
comes only from the outside (circular) cross-section
of the pill box This equals  ± EdS (positive for s > 0,
negative for s < 0), since over the small area dS, E
may be considered constant and E and dS are parallel
or antiparallel