The total
flux f  through the surface is  f = f1 + f2 + f3, where f1 and f2 represent
the flux through the surfaces 1 and 2 (of circular cross-section) of the
cylinder and f3 is the flux through the curved cylindrical part of the
closed surface Now the normal to the surface 3 at every point is
perpendicular to E, so by definition of flux, f3 = 0 Further, the outward
normal to 2 is along E while the outward normal to 1 is opposite to E Therefore,
f1 = –E S1,     f2 = +E S2
S1 = S2 = S
where S is the area of circular cross-section