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 net charge inside the surface must be 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 net charge inside the surface must be zero

Using Gauss's law the flux of the electric field through closed surface is $\varphi =\oint \overrightarrow{E}.\overrightarrow{ds}=\frac{Q_{enclosed}}{{ϵ}_0}$
So if the electric field is zero everywhere, then the flux may be zero.
if charge inside the closed surface is zero, then flux must be zero.