Question

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

• A. Yes; zero field everywhere means zero flux everywhere.
• B. Yes; zero electric field means that there are no charges of any kind in the region.
• C. No; there may be some positive and some negative charges enclosed within the surface.
• D. No; zero field could be caused by charges outside of the surface as well as inside the surface.
• E. No; it is impossible for charges to exist and yet electric field to be zero everywhere.

Answer 1

The correct option is A Yes; zero field everywhere means zero flux everywhere.

Gauss's theorem states if a closed surface encloses a charge , then surface integral of the electric field over the closed surface is $1/{\epsilon }_0$ times of the charge enclosed by the surface ,

$\oint \overrightarrow{E}.\overrightarrow{dS}=Q/{\epsilon }_0$

it is clear that if $\overrightarrow{E}$ (charge enclosed) is zero then $Q=0$