Gauss's law for curvilinear coordinates

Gauss's law states that the total electric flux passing through a closed surface equals the enclosed electric charge divided by the permittivity of free space. In curvilinear coordinates, which involve flexible, curved surfaces, this principle still holds but requires adjusting the way we measure the surface area using specific mathematical factors called scale factors. Essentially, Gauss's law relates electric fields and charges regardless of the surface shape, allowing us to calculate electric flux through complex, curved surfaces by accounting for their geometry. This helps in analyzing electric fields in diverse, real-world scenarios with non-uniform shapes.