<math>\Delta\varPhi(\mathbf{r}) = \nabla^2 \varPhi(\mathbf{r}) = -\frac{\varrho(\mathbf{r})}{\varepsilon}</math>
where Φ(<b>r</b>) is the electric scalar potential, ρ(<b>r</b>) is the volume charge density, and ε is the permittivity of the medium.
EM.Ferma also solves the Poisson equation for the magnetic vector potential subject to specified boundary conditions:
<math>\Delta \mathbf{A} (\mathbf{r}) = \nabla^2 \mathbf{A}(\mathbf{r}) = - \varmu mu \mathbf{J}(\mathbf{r}) </math>
where <b>A(r)</b> is the magnetic vector potential, <b>J(r)</b> is the volume current density, and μ is the permeability of the medium. The magnetic Poisson equation is vectorial in nature and involves a system of three scalar differential equations corresponding to the three components of <b>A(r)</b>.