NationMaster - Encyclopedia: Gauss' law

In physics, Gauss's law gives the relation between the electric flux flowing out a closed surface and the charge enclosed in the surface. Its integral form is: Physics (from the Greek, φυσικός (phusikos), natural, and φύσις (phusis), nature) is the science of nature in the broadest sense. ... This article is in need of attention. ... Electric charge is a fundamental property of some subatomic particles, which determines their electromagnetic interactions. ...

where is the electric field, is the area of a differential square on the surface A with an outward facing surface normal defining its direction, $Q A$ is the charge enclosed by the surface, $ε 0$ is the permittivity of free space and is the integral over the surface A. A surface normal, or just normal to a flat surface is a three-dimensional vector which is perpendicular to that surface. ... This article is in need of attention. ...

Its partial differential form is: In mathematics, and in particular analysis, a partial differential equation (PDE) is an equation involving partial derivatives of an unknown function. ...

where is the divergence, D is the electric displacement field (in units of C/m²), and ρ is the free electric charge density (in units of C/m³), not including dipole charges bound in a material In vector calculus, the divergence is an operator that measures a vector fields tendency to originate from or converge upon a given point. ... In physics, the electric displacement field is a vector-valued field that appears in Maxwells equations and that generalizes the electric field. ... A dipole ( Greek: dyo = two and polos = pivot) is a pair of electric charges or magnetic poles of equal magnitude but opposite polarity (opposite electronic charges), separated by some (usually small) distance. ...

In linear materials, the equation becomes:

where $ε$ is the electrical permittivity This article is in need of attention. ...

In the special case of a spherical surface with a central charge, the electric field is perpendicular to the surface, with the same magnitude at all points of it, giving the simpler expression: In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ...

where E is the electric field strength at radius r, Q is the enclosed charge, and ε₀ is the permittivity of free space. Thus the familiar inverse-square law dependence of the electric field in Coulomb's law follows from Gauss' law. In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ... In physics, an inverse-square law is any physical law stating that some quantity is inversely proportional to the square of the distance from a point. ... In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrical force that one stationary, electrically charged substance of small volume (ideally, a point source) exerts on another. ...

Gauss's law can be used to demonstrate that there is no electric field inside a Faraday cage without electric charges. Gauss's law is the electrostatic equivalent of Ampère's law, which deals with magnetism. Both equations were later integrated into Maxwell's equations. The Faraday cage is an electrical apparatus designed to prevent the passage of electromagnetic waves, either containing them in or excluding them from its interior space. ... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ...

It was formulated by Carl Friedrich Gauss in 1835, but was not published until 1867. Because of the mathematical similarity, Gauss's law has application for other physical quantities governed by an inverse-square law such as gravitation or the intensity of radiation. See also divergence theorem. Johann Carl Friedrich Gauss Johann Carl Friedrich Gauss (Gauß) ( April 30, 1777 - February 23, 1855) was a legendary German mathematician, astronomer and physicist with a very wide range of contributions; he is considered to be one of the greatest mathematicians of all time. ... 1835 was a common year starting on Thursday (see link for calendar). ... 1867 was a common year starting on Tuesday (see link for calendar). ... In physics, an inverse-square law is any physical law stating that some quantity is inversely proportional to the square of the distance from a point. ... This article covers the physics of gravitation. ... In physics, intensity is a measure of the time-averaged energy flux. ... Radiation generally means the transmission of objects or information from a source into a surrounding medium or destination. ... In vector calculus, the divergence theorem, also known as Gauss theorem, Ostrogradskys theorem, or Ostrogradsky-Gauss theorem is a result that links the divergence of a vector field to the value of surface integrals of the flow defined by the field. ...