Question

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

• 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. both options $\left(b\right)$ and $\left(c\right)$.

Answer 1

The correct option is D both options $\left(b\right)$ and $\left(c\right)$.

We know that, by Gauss's law, electric flux through any closed surface is given by,

$\varphi =\oint \overrightarrow{E}.\overrightarrow{dA}=\frac{q_{\text{enclosed}}}{{\in }_0}$

If $q_{\text{enclosed}}=0$ then $\varphi =0$ but electric field may or may not be equal to zero as the electric field may be due to external charges or source.
Thus, option $\left(b\right)$ and $\left(c\right)$ are appropriately explaining the concept.

Thus, option $\left(d\right)$ is correct.