Gauss divergence theorem
Posted on: Tue Feb 20 2024 05:30:00 GMT+0530 (India Standard Time)
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Divergence theorem / Gauss divergence theorem / Gauss’ theorem / Ostrogradsky’s theorem / Gauss-Ostrogradsky theorem
The divergence theorem relates an integral over a volume to an integral over the surface bounding that volume. The divergence theorem states that the integral of the divergence of a vector field over a volume is equal to the flux of that field through the surface bounding that volume.
$$ \int_{\mathcal V} \left( \nabla \cdot {\bf A} \right) dv = \oint_{\mathcal S} {\bf A}\cdot d{\bf s} $$