Question

If the flux of the electric field through a closed surface is zero, then (more than option may be correct)

• 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 is zero.
• D. the charge in the vicinity of the surface must be zero

Answer 1

Answer: (B), (C)

The correct options are
B the electric field may be zero everywhere on the surface
C the charge inside the surface is zero.

If the flux of the electric field through a closed surface is zero, according to Gauss's law the inside the surface must be zero. $(\varphi =\frac{Q_{en}}{{ϵ}_0})$
Thus the flux through a surface depends only on the charge which is inside the surface. So the charge in the vicinity of the surface may not zero.
The electric field is the resultant field effect due to all charge. So It must not be zero but sometimes it may zero on the surafce depend on the charge distribution.