<math> \mathbf{E(r)} = - \nabla \Phi(\mathbf{r}) = \frac{1}{4\pi\epsilon} \int\int\int_V \frac{\mathbf{r - r^{\prime}} }{ | \mathbf{r - r^{\prime}} |^3 } \rho(\mathbf{r^{\prime}}) dv^{\prime} </math>
== Static Field Arising from Steady-State Conduction Currents ==
In an Ohmic conductor, the current density is related to the electric field as follows:
<math> \mathbf{J(r)} = \sigma \mathbf{E(r)}</math>
where σ is the electric conductivity. In addition, the continuity equation for a stationary current in a closed region requires that
<math> \nabla \mathbf{J(r)} = 0 </math>
These equations lead to the Laplace equation inside an Ohmic conductor medium:
== Magnetostatics Analysis==