abstract
| - It is one of the four Maxwell's equations, which form the basis of classical electrodynamics, and is also closely related to Coulomb's law. The law was formulated by Carl Friedrich Gauss in 1835, but was not published until 1867. Gauss's law has two forms, an integral form and a differential form. They 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. (The former is given in sections 1 and 2, the latter in Section 3.) 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. See the article Divergence theorem for more detail. 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. Both equations were later incorporated into Maxwell's equations.
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