Question

If ${\oint }_s\overrightarrow{E}.\overrightarrow{d}s=0$ over surface, then

• A. the electric field inside the surface and on it is zero
• B. the electric field inside the surface is necessarily uniform
• C. all charges must necessarily be outside the surface
• D. all of these

Answer 1

The correct option is C all charges must necessarily be outside the surface

As $\oint \overrightarrow{E}.d\overrightarrow{s}=\frac{q}{{\epsilon }_0}$
where $q$ is charge enclosed by the surface
when $\oint \overrightarrow{E}.d\overrightarrow{s}=0,q=0$
i.e., net charge enclosed by the surface must be zero. Therefore, all other charges must be outside the surface. This is because charges outside the surface do not contribute to the electric flux.