Gauss' law

In physics, Gauss' law, also known as Gauss' flux theorem, is a law relating the distribution of electric charge to the resulting electric field.

The law was first formulated by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1813, both in the context of the attraction of ellipsoids. It is one of Maxwell's four equations, which form the basis of classical electrodynamics. Gauss' law can be used to derive Coulomb's law, and vice versa.

In words, Gauss' law states that:

Gauss' law has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss' law for magnetism and Gauss' law for gravity. In fact, any inverse-square law can be formulated in a way similar to Gauss' law: for example, Gauss' law itself is essentially equivalent to the inverse-square Coulomb's law, and Gauss' law for gravity is essentially equivalent to the inverse-square Newton's law of gravity.

The law can be expressed mathematically using vector calculus in integral form and differential form, both are equivalent since they are related by the divergence theorem, also called Gauss' theorem. Each of these forms in turn 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.

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