Current density is a vector field in the same direction as current but with magnitude of current per area. It may also be represented as , where is charge density (i.e. charge per volume) and is the drift velocity of charged particles. Current density is related to electric field via via the conductivity constant of the material. See Wikipedia:Current_density for background.
SIMION in its poisson solver (SIMION 8.1) can solve for current density throughout space when given a conductivity () throughout space and boundary conditions on electric potential. The governing Poisson Equation is
which is the same as equation used in dielectrics problems but with the dielectric constant replaced with .
NoteThis page is abridged from the full SIMION "Supplemental Documentation" (Help file). The following additional sections can be found in the full version of this page accessible via the "Help > Supplemental Documentation" menu in SIMION 8.1.1 or above:
- SIMION Modeling Details - Calculating current density from conductivity
- Plotting current density vector fields