<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>
== 2D Quasi-Static Solution of TEM Transmission Line Structures ==
At lower microwave frequencies (f < 10GHz), multi-conductor transmission line structures usually support either a dominant transverse electromagnetic (TEM) propagating mode or a dominant quasi-TEM propagating mode. These modes are almost non-dispersive, and their behavior can be regarded as frequency-independent. As a result, it is usually possible to perform a 2D electrostatic analysis of a transmission line structure and compute its characteristics impedance Z<sub>0</sub> and effective permittivity ε<sub>eff</sub>. The "quasi-static approach" to modeling of a TEM transmission line involves two steps:
<math> \beta = k_0\sqrt{\epsilon_{eff}} = \frac{2\pi f}{c}\sqrt{\epsilon_{eff}} </math>
where c is the speed of light in the free space.
== Magnetostatics Analysis==