What is the relationship between total electric flux and enclosed charge according to Gauss's law?

The correct answer is that total electric flux is directly proportional to the enclosed charge according to Gauss's law. This law states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space (ε₀). Mathematically, this relationship is expressed as:

[ \Phi_E = \frac{Q_{\text{enc}}}{\varepsilon_0} ]

Where (\Phi_E) is the electric flux, (Q_{\text{enc}}) is the net charge enclosed within the surface, and (\varepsilon_0) is the permittivity of free space. This equation clearly indicates that as the enclosed charge increases, the total electric flux through the surface will also increase in direct proportion, illustrating a straightforward and fundamental relationship in electromagnetism.

In contrast, the other options do not pertain to this fundamental relationship outlined by Gauss's law. For instance, the proportionality of flux to surface area, voltage, or resistance involves different principles in physics and does not accurately represent the relationship defined by Gauss's law. Understanding this direct proportionality is crucial for analyzing electric fields and their behavior around charges in both theoretical and practical applications.