Gauss' law (magnetism)

Gauss’ law for magnetism states that the total magnetic flux through a closed surface is always zero.

Differential form

$$\nabla \cdot \mathbf{B}=0$$

where
$\mathbf{B}(\mathbf{x},t)$	magnetic field (or magnetic flux density), measured in tesla $\text{T}$
$\mathbf{x}$	position vector in three-dimensional space, typically expressed as $\mathbf{x}=(x,y,z)$ and measured in meters $\text{m}$
$t$	time, measured in seconds $\text{s}$
$\nabla \cdot$	divergence operator, which measures the net flux of a field out of an infinitesimal volume, and which when applied to $\mathbf{B}$ is: $\nabla \cdot \mathbf{B}=\frac{\partial }{\partial x}{B}_x+\frac{\partial }{\partial y}{B}_y+\frac{\partial }{\partial z}{B}_z.$

Integral form

$${\oint }_S\mathbf{B}\cdot d\mathbf{A}=0$$

where
$S$	closed surface in three-dimensional space
${\oint }_S$	surface integral which sums the contribution of the field $\mathbf{B}$ over the entire surface $S$
$d\mathbf{A}$	differential surface element that represents an infinitesimally small patch of the surface $S$