Question

If the flux of the electric field through a closed surface is zero,
(a) the electric field must be zero everywhere on the surface
(b) the electric field may be zero everywhere on the surface
(c) the charge inside the surface must be zero
(d) the charge in the vicinity of the surface must be zero

Answer 1

(b) the electric field may be zero everywhere on the surface
(c) the charge inside the surface must be zero

As the flux is zero through the surface, the charge enclosed must be zero. But the electric field is not necessarily zero everywhere on the surface. For example, in the case of a dipole enclosed by the surface, the electric field through the surface is not zero but has some value. So, the correct answers are (b) and (c).