Question

If the flux of the electric field through a closed surface is zero.

• A. the electric field must be zero every where on the surface
• B. the electric field may be zero everywhere on the surface
• C. the charge inside the surface must not be zero
• D. the charge in the vicinity of the surface must be zero

Answer 1

Answer: (B)

Using Gauss's law the flux of the electric field through closed surface is $\varphi =$ $\oint \vec{E}\cdot \overrightarrow{ds}=\frac{Q_{\text{enclosed }}}{{ϵ}_0}$
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.