Gauss theorem is directly derived from Coulomb's law by Gauss, and it completely depends on the quadratic inverse ratio law of the force between charges. When Gauss theorem is applied to the metal conductor with electrostatic balance, it can be concluded that there is no net charge inside the conductor, so it is an important method to test Coulomb law to determine whether there is net charge inside the conductor.

Gauss law is also called Gauss flux theorem, or divergence theorem, Gauss divergence theorem, Gauss-Ostrogradski formula, Auschwitz theorem or Gauss formula (usually Gauss theorem refers to this theorem, and there are other theorems with the same name).

Extended data:

In electrostatics, the relationship between the sum of charges on a closed surface and the electric flux integral of the electric field generated on the closed surface is shown.

gauss's law

Law) shows the relationship between the charge distribution in a closed surface and the generated electric field. Gauss's law of electrostatic field is similar to Ampere's law of magnetic field, and both of them are concentrated in Maxwell's equations. Because of the mathematical similarity, Gauss's law can also be applied to other physical quantities determined by inverse square law, such as gravity or irradiance.

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.

References:

Baidu encyclopedia-gauss theorem