The value of total electric flux coming out of a closed surface is equal to the total charge enclosed by the surface.

The electric flux through a closed surface is a measure of the total electric field passing through that surface. It is given by the surface integral of the dot product of the electric field vector and the surface area vector.

Electric Flux Formula:
The electric flux (Φ) through a closed surface is given by the formula:
Φ = ∫∫ E · dA

where E is the electric field vector and dA is an infinitesimal area vector. The dot product of E and dA gives the component of the electric field that is normal to the surface.

Gauss's Law:
Gauss's law states that the total electric flux through a closed surface is equal to the total charge enclosed by the surface divided by the permittivity of the medium.

Φ = Q / ε₀

where Q is the total charge enclosed by the surface and ε₀ is the permittivity of free space.

Explanation:
When a closed surface encloses a charge, the electric field lines originating from the charge will pass through the surface and contribute to the electric flux. Therefore, the total electric flux passing through the closed surface will be proportional to the total charge enclosed by the surface.

If the total charge enclosed by the surface is zero (option A), then there will be no electric flux passing through the surface. This is because there are no electric field lines originating from or terminating on the enclosed charge.

If the electric flux is equal to the volume charge density (option B), it would imply that the electric field is constant throughout the entire volume enclosed by the surface. However, in most cases, the electric field will vary within the volume, so this option is not correct.

If the electric flux is equal to the surface charge density (option D), it would imply that the electric field is only present at the surface and does not penetrate into the volume. This is not generally the case, as the electric field can extend beyond the surface.

Therefore, the correct answer is option C, which states that the value of total electric flux coming out of a closed surface is equal to the total charge enclosed by the surface.