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For a given closed surface, Gauss's law gives the surface integral of E.dA = 0. From this alone we can conclude that:

1. The net electric flux through the surface is zero
2. E is necessarily zero everywhere on the surface
3. E is perpendicular to the surface at every point
4. The electric field only points outward through the surface

Correct answer: The net electric flux through the surface is zero

Solution

The closed surface integral of E.dA equals the net electric flux, which by Gauss's law equals q_enclosed / epsilon0. If this integral is zero, the only valid conclusion is that the net flux (and hence enclosed charge) is zero. The field E need not be zero on the surface, need not be perpendicular, and field lines may both enter and leave the surface.

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