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In physics (specifically electromagnetism), Gauss's law, also known as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations. It is an application of the divergence theorem , and it relates the distribution of electric charge to the resulting electric field .
Gauss's law, in physics, gives the relation between the electric flux flowing out a closed surface and the charge enclosed in the surface. It was formulated by Carl Friedrich Gauss. See also Gauss's law for gravity, and Gauss's law for magnetism.
It is impossible to mathematically prove Newton's law from Gauss's law alone, because Gauss's law specifies the divergence of g but does not contain any information regarding the curl of g (see Helmholtz decomposition). In addition to Gauss's law, the assumption is used that g is irrotational (has zero curl), as gravity is a conservative force:
It is an arbitrary closed surface S = ∂V (the boundary of a 3-dimensional region V) used in conjunction with Gauss's law for the corresponding field (Gauss's law, Gauss's law for magnetism, or Gauss's law for gravity) by performing a surface integral, in order to calculate the total amount of the source quantity enclosed; e.g., amount of ...
The source equations (Gauss' law for electricity and the Maxwell-Ampère law) are =. while the other two (Gauss' law for magnetism and Faraday's law) are obtained from the fact that F is the 4-curl of A, or, in other words, from the fact that the Bianchi identity holds for the electromagnetic field tensor.
Gauss's law Gauss's law for magnetism Gauss's principle of least constraint Gauss's digamma theorem Gauss's hypergeometric theorem Gaussian function See also: List of things named after Carl Friedrich Gauss: Mathematics, Physics: Johann Carl Friedrich Gauss: Gay-Lussac's law: Chemistry: Joseph Louis Gay-Lussac: Gibbs–Helmholtz equation ...
Gauss's law for magnetism thus states that the net magnetic flux through a closed surface equals zero. The integral and differential forms of Gauss's law for magnetism are mathematically equivalent, due to the divergence theorem. That said, one or the other might be more convenient to use in a particular computation.
Benford's law, which describes the frequency of the first digit of many naturally occurring data. The ideal and robust soliton distributions. Zipf's law or the Zipf distribution. A discrete power-law distribution, the most famous example of which is the description of the frequency of words in the English language.