The mathematical formula of gauss theorem is ∮ f ds = ∫ (▽ f) dv. Gauss's law shows the relationship between the charge distribution on a closed surface and the generated electric field. Let an empty space be a bounded closed region ω, and its boundary ω is a piecewise smooth closed surface. Functions P(x, y, z), Q(x, y, z). R(x, y, z) and its first-order partial derivative are continuous on ω, where the positive side of ω is the outer side, and cosα, cosβ and cosγ are the direction cosines of the outer normal vector of ω.

Gauss theorem concept

Gauss theorem shows the relationship between the charge distribution on a closed surface and the generated electric field. Gauss theorem is similar to ampere's law applied in magnetic field under electrostatic field, both of which are concentrated in Maxwell's equations. Because of the mathematical similarity, Gauss theorem can also be applied to other physical quantities determined by inverse square law, such as gravity or irradiance. The content of the theorem is a bounded closed region of space, and its boundary is a piecewise smooth closed surface.