The mathematical formula of Gauss theorem is: ∮ f ds = ∫ (▽ f) dv. Gauss's law shows the relationship between the charge distribution in a closed surface and the generated electric field. Gauss theorem is also called Gauss flux theory, or divergence theorem, Gauss divergence theorem, Gauss-Ostrogradski formula, Auschwitz theorem or high-Austrian formula. Usually Gauss theorem refers to this theorem, and there are other theorems with the same name.

Introduction to gauss theorem

Gauss theorem points out that the electric flux passing through a closed surface is directly proportional to the amount of charge surrounded by the closed surface. In other words, the area fraction of the electric field intensity on the closed surface is directly proportional to the amount of charge surrounded by the closed surface.

It shows that the flux of electric field intensity to any closed surface depends only on the algebraic sum of charges in the closed surface, but has nothing to do with the position distribution of charges in the closed surface and charges outside the closed surface. In the case of vacuum, σ q is the algebraic sum of free charges in a closed surface. When there is a medium, σ q should be understood as the sum of closed free charge and polarized charge in a closed curved surface.