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where <math>\vec{E}^i</math> is an incident electric field, <math>\vec{J}</math> is a current density, <math>\vec{A}</math> is the magnetic vector potential, <math>\phi</math> is the scalar electric potential, and <math>\sigma</math> the electrical conductivity all at observation point <math>\vec{r}</math>. In the figures on the right, an orthogonal metal strip with 3 nodes and 2 cells, and the corresponding PEEC circuit are shown.
By using the definitions of the scalar and vector potentials, the current- and charge-densities are discretized by defining pulse basis functions for the conductors and dielectric materials. Pulse functions are also used for the weighting functions resulting in a Galerkin type solution. By defining a suitable inner product, a weighted volume integral over the cells, the field equation can be interpreted as Kirchhoff's voltage law over a PEEC cell consisting of partial self inductances between the nodes and partial mutual inductances representing the magnetic field coupling in the equivalent circuit. The partial inductances are defined as
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