Charge conservation

Charge conservation is the principle that electric charge can neither be created or destroyed.

The equation of charge conservation

The net current into a volume is

$I=-\iint \limits _{S}\mathbf {J} \cdot d\mathbf {S}$

where S = ∂V is the boundary of V oriented by outward-pointing normals, and dS is shorthand for NdS, the outward pointing normal of the boundary ∂V.

From the Divergence theorem this can be written

$I=-\iiint \limits _{V}\left(\nabla \cdot \mathbf {J} \right)dV$.