This is a direct consequence of Gauss's Law, which states:
* The total electric flux through any closed surface is proportional to the enclosed electric charge.
Mathematically, this is expressed as:
```
Φ = ∮ E ⋅ dA = Q_enclosed / ε₀
```
where:
* Φ is the electric flux
* E is the electric field
* dA is an infinitesimal area element of the closed surface
* Q_enclosed is the total charge enclosed by the surface
* ε₀ is the permittivity of free space
Since Q_enclosed = 0 in this case, the electric flux Φ will also be zero.
Intuitively:
Imagine the electric field lines emanating from a charge. If there is no charge inside a closed surface, then no electric field lines will originate from within the surface and pass through it. Therefore, the total electric flux through the surface will be zero.
