 Volume conductor

A volume conductor is a conducting three-dimensional medium through which electric currents flow. In the quasistatic bioelectric model, the total current density is $\mathbf{J}={\mathbf{J}}^p-\sigma \nabla u$, comprising an impressed source current and its Ohmic return current. Electric charge conservation gives $\nabla \cdot (\sigma \nabla u)=\nabla \cdot {\mathbf{J}}^p$. An insulating boundary has zero normal total current.