# Why do we conclude that an electric field is null if the flux is null?

Gauss's Law states that the flux is equal to the charge inside divided by a constant. and is also equal to the surface integral of the electric field. So, if there is no charge inside the closed surface, the flux is null but why do we deduct that the electric field is null at all points inside the surface? It doesn't make sense.

• Who are we? We who? Jan 18, 2021 at 17:17
• It is not true that zero flux through a closed surface implies the field is zero. Jan 18, 2021 at 18:04

Yes, you are right; it does not make sense. It does not make sense because it is just false. Take a point charge at the origin. The field extends everywhere, i.e., the field is $$\neq 0$$ everywhere. However, the total flux over a closed surface not including the origin is null.