<math> \mathbf{J(r)} = \sigma \mathbf{E(r)} = -\sigma \nabla \Phi(\mathbf{r}) </math>
where σ is the electric conductivity. In additionOn the other hand, the continuity equation for a stationary current in requires no charge buildup or decay inside a closed region requires . This means that
<math> \nabla . \mathbf{J(r)} = 0 </math>
These above two equations lead to the Laplace equation inside an Ohmic conductor medium:
<math>\nabla^2 \Phi(\mathbf{r}) = 0</math>