Gauss’s law relates electric flux through a closed surface to the electric charge enclosed by that surface.
In its integral form, the total electric flux through a closed surface equals the enclosed charge divided by the permittivity of free space. The law is one of Maxwell’s equations and is especially useful when a charge distribution has high symmetry, such as spherical, cylindrical, or planar symmetry.
The law is named after German mathematician and physicist Carl Friedrich Gauss. It does not say that electric field is always uniform across a surface; instead, it connects the net flux to the total enclosed charge.
Charges outside a chosen closed surface can affect the electric field at points on the surface, but their net contribution to total electric flux through it is zero. This distinction often causes confusion when applying the law.