Dictionary:Gauss’s theorem

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Warning: Display title "Dictionary:Gauss’s theorem" overrides earlier display title "Dictionary:Gauss’s theorem".


The total flux through any closed surface is equal to times the source strength m enclosed by the surface

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Here, ds is a vector surface element and dv a volume element. (The is often deleted in the mks system.) k is a constant that depends on the units of measure. This can also be expressed in terms of the flux density or field strength g, the source density , and the potential U. may be electrical flux if m is electrical charge. In the mks system, is in webers if m is in coulombs and , or may be gravitational flux if m is mass, in which case , where is the gravitational constant. Or may be magnetic flux if m is magnetic pole strength.

Also called Gauss's law: The equality between the surface and volume integrals involving g is also called the divergence theorem (q.v.). This theorem postulates the inherent nonuniqueness of potential fields.