Editing Magnetic flux (section)

== Magnetic flux through a closed surface ==

[[File:SurfacesWithAndWithoutBoundary.svg|right|thumb|200px|Some examples of [[closed surface]]s (left) and [[open surface]]s (right). Left: Surface of a sphere, surface of a [[torus]], surface of a cube. Right: [[Disk (mathematics)|Disk surface]], square surface, surface of a hemisphere. (The surface is blue, the boundary is red.)]]

{{main|Gauss's law for magnetism}}

[[Gauss's law for magnetism]], which is one of the four [[Maxwell's equations]], states that the total magnetic flux through a [[closed surface]] is equal to zero. (A "closed surface" is a surface that completely encloses a volume(s) with no holes.) This law is a consequence of the empirical observation that [[magnetic monopole]]s have never been found.

In other words, Gauss's law for magnetism is the statement:

:{{oiint
| preintegral = <math>\Phi_B=\,\!</math>
| intsubscpt = <math>\scriptstyle S</math>
| integrand = <math>\mathbf{B} \cdot d\mathbf S = 0</math>}}

for any [[closed surface]] ''S''.