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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.
In three dimensions, the derivative has a special structure allowing the introduction of a cross product: = + = + from which it is easily seen that Gauss's law is the scalar part, the Ampère–Maxwell law is the vector part, Faraday's law is the pseudovector part, and Gauss's law for magnetism is the pseudoscalar part of the equation.
Electric field from positive to negative charges. Gauss's law describes the relationship between an electric field and electric charges: an electric field points away from positive charges and towards negative charges, and the net outflow of the electric field through a closed surface is proportional to the enclosed charge, including bound charge due to polarization of material.
Gauss's law for electricity; Gauss's law for gravity; Gauss's law for magnetism; Gibbs–Helmholtz equation; Gross–Pitaevskii equation; Hamilton–Jacobi–Bellman equation; Helmholtz equation; Karplus equation; Kepler's equation; Kepler's laws of planetary motion; Kirchhoff's diffraction formula; Klein–Gordon equation; Korteweg–de Vries ...
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 ...
Informally, the case of a point charge in an arbitrary static electric field is a simple consequence of Gauss's law.For a particle to be in a stable equilibrium, small perturbations ("pushes") on the particle in any direction should not break the equilibrium; the particle should "fall back" to its previous position.
The fixed value of k = 0.01720209895 [rad] was taken to be the one set by Gauss (converted from degrees to radian), so that a = 4 π 2:(k 2 P 2 M) ≈ 1. [5] Gauss's 1809 value of the constant was thus used as an authoritative reference value for the orbital mechanics of the Solar System for two centuries.