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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 for gravity is often more convenient to work from than Newton's law. [1] The form of Gauss's law for gravity is mathematically similar to Gauss's law for electrostatics, one of Maxwell's equations. Gauss's law for gravity has the same mathematical relation to Newton's law that Gauss's law for electrostatics bears to Coulomb's law.
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 ...
Any inverse-square law can instead be written in a Gauss's law-type form (with a differential and integral form, as described above). Two examples are Gauss's law (in electrostatics), which follows from the inverse-square Coulomb's law, and Gauss's law for gravity, which follows from the inverse-square Newton's law of universal gravitation. The ...
Gauss's law: first described by Joseph Louis Lagrange in 1773, over half a century before Gauss. [22] [23] Gauss's theorem: first proved by Ostrogradsky in 1831. Gaussian distribution: the normal distribution was introduced by Abraham de Moivre in 1733, but named after Carl Friedrich Gauss who began using it in 1794.
While Gauss's law holds for all situations, it is most useful for "by hand" calculations when high degrees of symmetry exist in the electric field. Examples include spherical and cylindrical symmetry. The SI unit of electric flux is the volt-meter (V·m), or, equivalently, newton-meter squared per coulomb (N·m 2 ·C −1).
By the divergence theorem, Gauss's law for the field P can be stated in differential form as: =, where ∇ · P is the divergence of the field P through a given surface containing the bound charge density .
The extension of the above considerations confirms that where B is to H, and where J is to ρ, then it necessarily follows from Gauss's law and from the equation of continuity of charge that E is to D i.e. B parallels with E, whereas H parallels with D. Engineering diagram of Boltzmann's Bicykel. Boltzmann's Bicykel model of electromagnetic ...