In addition, the boundary condition at a conductor-dielectric interface requires a vanishing normal derivative of the electric potential:
<math> \frac{\partial \Phi}{\partial n} = 0 = 0</math>
At the interface between two contiguous conductors, the normal component of the current density must be continuous.
<math> \hat{\mathbf{n}} . [ \mathbf{J_2(r)} - \mathbf{J_1(r)} ] = 0 </math>
which can be written as:
<math> \sigma_1 \hat{\mathbf{n}} . \mathbf{J_1(r)} = \sigma_2 \hat{\mathbf{n}} . \mathbf{J_2(r)} </math>
== Magnetostatics Analysis==