how the sum of the divergences within a volume equates to the net flux passing through the outer boundary of that volume

The Divergence Theorem, or Gauss's Theorem, connects the flux of a vector field through a closed surface to the divergence of the field inside the volume. The demonstration shows this through two views: a Volume Decomposition View and a Flux Cancellation View. The first view illustrates how a large volume can be broken down into many small cubes, while the second view highlights how the flux between adjacent, internal cubes cancels out. This cancellation means that the total flux only depends on the net flow through the outer boundary of the entire volume, visually proving that summing the divergences within the volume is equivalent to calculating the flux through its outer surface.

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