Gauss's law

In integral form, Gauss's Law is expressed as the electric flux (Φ) through a closed surface equaling the enclosed charge (Q) divided by the permittivity of free space (ε₀). This fundamental physics concept demonstrates that the total flux is directly proportional to the charge inside. It is one of the four core equations of electromagnetism formulated by James Clerk Maxwell.

Gauss's law is primarily used to calculate the electric field of complex charge distributions with high symmetry, such as spheres, infinite cylinders, and flat sheets. By conceptualizing a "Gaussian surface" around the charge, engineers can determine the flux without doing complex calculus. It is much faster and simpler than using Coulomb's law for these specific, symmetric shapes.

The permittivity of free space, denoted as ε₀, is a fundamental physical constant that represents how an electric field affects, and is affected by, a vacuum. In Gauss's Law, it serves as the proportional constant that relates electric flux to the enclosed electric charge. The approximate value of this constant is 8.85 x 10^-12 farads per meter.

The law is named after the German mathematician Carl Friedrich Gauss, who formulated it in 1835, though it was not published until later. It established a crucial link between electric charge and electric flux. Gauss's work laid the groundwork for James Clerk Maxwell's later unification of electromagnetism in the 1860s.