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== Static Modeling Methods ==
<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>
which can be written as:
<math> \sigma_1 \hat{\mathbf{n}} . \mathbf{J_1E_1(r)} = \sigma_2 \hat{\mathbf{n}} . \mathbf{J_2E_2(r)} </math>
== Magnetostatics Analysis==
and its characteristic impedance is given by:
<math> Z_0 = \frac{\eta_0}{\sqrt{ \epsilon_{eff}}} = \eta_0 \sqrt{ \frac{C_a}{C} } </math>
where η<sub>0</sub> = 120π Ω is the intrinsic impedance of the free space.