EM.Ferma solves the Poisson equation for the electric scalar potential subject to specified boundary conditions:
<math>\Delta\varphivarPhi(\mathbf{r}) = \nabla^2 \varphivarPhi(\mathbf{r}) = -\frac{\varrho(\mathbf{r})}{\varepsilon_0}</math>
where Φ(<b>r</b>) is the electric scalar potential and ρ(<b>r</b>) is the volume charge density.
In a source-free region, ρ(<b>r</b>) = 0, and Poisson's equation reduces to the Laplace equation: