The divergence theorem, also known as Gauss's theorem, is a fundamental theorem in vector calculus that relates the flux of a vector field through a closed surface to the divergence of the vector field within the volume enclosed by the surface. It is a powerful tool in electromagnetism as it allows us to relate the behavior of electric and magnetic fields to the distribution of charges and currents.

The theorem states that the flux of a vector field through a closed surface is equal to the volume integral of the divergence of the field over the enclosed volume. Mathematically, it can be expressed as:

∮S F · dA = ∫∫∫V ∇ · F dV

where ∮S denotes the surface integral over the closed surface S, F is the vector field, dA is the differential area vector, ∫∫∫V represents the volume integral over the enclosed volume V, and ∇ · F is the divergence of the vector field F.

Now, let's analyze the options given in the question:

a) Field intensity: Field intensity is a measure of the strength of an electric or magnetic field at a point. The divergence theorem does not directly evaluate field intensity.

b) Field density: Field density is not a well-defined concept in electromagnetism. It is not directly related to the divergence theorem.

c) Potential: Potential refers to the electric potential or scalar potential in electromagnetism. The divergence theorem does not directly evaluate potential.

d) Charge and flux: The divergence theorem relates the flux of a vector field through a closed surface to the divergence of the field within the enclosed volume. In the context of electromagnetism, the vector field can represent the electric field or the magnetic field. The flux of the electric field through a closed surface is directly related to the total charge enclosed by the surface. Similarly, the flux of the magnetic field through a closed surface is related to the total current enclosed by the surface. Therefore, the ultimate result of the divergence theorem evaluates the charge and flux, making option 'D' the correct answer.

In summary, the divergence theorem relates the flux of a vector field through a closed surface to the divergence of the field within the enclosed volume. It is a fundamental tool in electromagnetism and allows us to evaluate the charge and flux.