Gauss's law

Gauss's Law is one of Maxwell's four fundamental equations of electromagnetism. It states that the total electric flux out of any closed surface is directly proportional to the total electric charge enclosed within that surface, divided by the permittivity of free space.

Physicists apply Gauss's Law to easily calculate electric fields for highly symmetrical charge distributions, such as spheres or infinite planes. By using a hypothetical 'Gaussian surface' that matches the symmetry of the charge, complex integral calculus problems become simple algebraic ones.

Gauss's Law and Coulomb's Law are essentially mathematically equivalent ways of describing the electrostatic interaction between charges. In fact, you can directly derive Coulomb's Law by applying Gauss's Law to a single point charge surrounded by a spherical Gaussian surface.

In the context of Gauss's Law, the permittivity of free space, represented by epsilon zero, is a fundamental physical constant. It has an exact value of approximately 8.854 x 10^-12 farads per meter.