To make it simple.
This article is about Gauss's law concerning the electric field. For an analogous law concerning the magnetic field, see Gauss's law for magnetism. For an analogous law concerning the gravitational field, see Gauss's law for gravity. For Gauss's theorem, a general theorem relevant to all of these laws, see Divergence theorem.
In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. Gauss's law states that:
The electric flux through any closed surface is proportional to the enclosed electric charge.
The law was formulated by Carl Friedrich Gauss in 1835, but was not published until 1867.[1] It is one of the four Maxwell's equations, which form the basis of classical electrodynamics. Gauss's law can be used to derive Coulomb's law,[2] and vice versa.
Gauss's law may be expressed in its integral form:
where the left-hand side of the equation is a surface integral denoting the electric flux through a closed surface S, and the right-hand side of the equation is the total charge enclosed by S divided by the electric constant.
Gauss's law also has a differential form:
where ? · E is the divergence of the electric field, and ? is the charge density.
The integral and differential forms are related by the divergence theorem, also called Gauss's theorem. Each of these forms can also be expressed two ways: In terms of a relation between the electric field E and the total electric charge, or in terms of the electric displacement field D and the free electric charge.
Gauss's law has a close mathematical similarity with a number of laws in other areas of physics. See, for example, Gauss's law for magnetism and Gauss's law for gravity. In fact, any "inverse-square law" can be formulated in a way similar to Gauss's law: For example, Gauss's law itself is essentially equivalent to the inverse-square Coulomb's law, and Gauss's law for gravity is essentially equivalent to the inverse-square Newton's law of gravity.
Gauss's law can be used to demonstrate that there is no electric field inside a Faraday cage with no electric charges. Gauss's law is something of an electrical analogue of Ampère's law, which deals with magnetism.
