Question

If $\int \overrightarrow{E}.\overrightarrow{ds}=0$ over a closed 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. None of these.

Answer 1

The correct option is D None of these.

As $\int \overrightarrow{E}.\overrightarrow{ds}=\frac{q}{{ϵ}_0}$
Where q is charge enclosed by the surface.
when $\int \overrightarrow{E}.\overrightarrow{ds}=0,q=0$
i.e. net charge enclosed by the surface must be zero.
Therefore, charges may be inside the surface. Example: +q and -q.