According to Gauss's law, what does the total electric flux that passes out of a closed surface equal?

According to Gauss's law, the total electric flux passing out of a closed surface is directly proportional to the total charge enclosed within that surface. This relationship is mathematically represented by the equation:

Φ_E = Q_enc / ε₀

where Φ_E is the electric flux, Q_enc is the total charge enclosed within the surface, and ε₀ is the permittivity of free space. This fundamental principle highlights that only the charge within the closed surface contributes to the electric flux; charges outside the surface do not influence the flux through the surface itself.

Understanding this is crucial in electromagnetism because it establishes a direct link between electric fields and charge distributions. It signifies that when considering a closed surface, the net electric field due to the enclosed charge can be derived, which is essential in various applications, such as calculating electric fields around conductors and analyzing electrostatic conditions.

Other concepts, such as the total charge outside the surface or net electric field, do not contribute to the electric flux in the context of Gauss's law. Hence, the focus remains on the charge contained within the closed surface to determine the electric flux accurately.