Virtual Casing Principle in presence of sink/source currents

The possibility of describing the magnetic field due to currents within a finite control volume via an equivalent surface current distribution on the boundary of such volume is given by the well-known Virtual Casing Principle. This has been illustrated and implemented in the past for the case of solenoidal currents in the volume of interest, i.e. when the currents to represent have a null normal component to the boundary of the control volume. Here, we illustrate how to apply and implement the Virtual Casing Principle for the more general case where the currents to represent can cross the boundary.