Cauchy-Gauss theorem

The Cauchy-Gauss theorem, also known as the Divergence Theorem, states that the total flow (or flux) of a vector field through a closed surface equals the total amount of the source or sink inside the volume enclosed. In simpler terms, it links the behavior of a field on the boundary of a region to what’s happening inside that region. For example, if you think of a fluid flowing through a container, the theorem relates how much fluid crosses the container’s surface to how much fluid is being added or removed inside.