Gauss’s law

Gauss’s law, either of two statements describing electric and magnetic fluxes. Gauss’s law for electricity states that the electric flux Φ across any closed surface is proportional to the net electric charge q enclosed by the surface; that is, Φ = q/ε₀, where ε₀ is the electric permittivity of free space and has a value of 8.854 × 10^–12 square coulombs per newton per square metre. The law implies that isolated electric charges exist and that like charges repel one another while unlike charges attract. Gauss’s law for magnetism states that the magnetic flux B across any closed surface is zero; that is, div B = 0, where div is the divergence operator. This law is consistent with the observation that isolated magnetic poles (monopoles) do not exist.

Mathematical formulations for these two laws—together with Ampère’s law (concerning the magnetic effect of a changing electric field or current) and Faraday’s law of induction (concerning the electric effect of a changing magnetic field)—are collected in a set that is known as Maxwell’s equations, which provide the foundation of unified electromagnetic theory.