Question

If the net charge enclosed by a closed Gaussian surface is zero, does this mean that the electric field at all points on the surface is also zero?

• A. Yes; because $\oint \overrightarrow{E}\overrightarrow{dA}=\frac{Q_{enc}}{{ϵ}_0}$, if $Q_{enc}$ is zero, then $\overrightarrow{E}$ must be zero.
• B. Yes; electric field strength depends on how much net charge is present in a region.
• C. Yes; electric field can be cancelled out by charges outside the surface.
• D. No; It is not necessary that electric field should be zero but flux should be zero.
  
• E. No; there is no relationship between charge and electric field.

Answer 1

The correct option is D No; It is not necessary that electric field should be zero but flux should be zero.

It is not necessary that electric field should be zero because if net charge is zero. Then there may be possibility that only dot product of $E$ and $A$ will be zero. That doesn't mean that electric field will be zero.