Surface current density ($\mathbf{K}$)

A surface current density is electric current per unit transverse length confined to a surface. Integrating a thin layer's current density through its thickness gives $\mathbf{K}$.

A current sheet idealizes electric current as supported on a surface. It produces a jump in the tangential magnetic field.

For a surface current density $\mathbf{K}$ on an interface with unit normal $\mathbf{n}$, Ampère's law givesin Gaussian units, or ${\mu }_0\mathbf{K}$ in SI units.

Surface conductivity is the conductivity of a thin layer integrated through its thickness. The sheet form of Ohm's law is $\mathbf{K}=\Sigma {\mathbf{E}}_{\parallel }$.