Current Density¶

Current density $\v{j}$ is a vector field in the same direction as current $\v{I}$ but with magnitude of current per area. It may also be represented as $\v{j} = \rho \v{v_d}$ , where $\rho$ is charge density (i.e. charge per volume) and $\v{v_d}$ is the drift velocity of charged particles. Current density is related to electric field via $\v{j} = \sigma \v{E}$ via the conductivity constant $\sigma$ of the material. See Wikipedia:Current_density for background.

SIMION specific¶

SIMION in its poisson solver (in Early Access Mode) can solve for current density throughout space when given a conductivity ( $\sigma$ ) throughout space and boundary conditions on electric potential. The governing Poisson Equation is

$\div (\sigma \grad \phi) = 0$

which is the same as equation used in dielectrics problems $\div (\epsilon \grad \phi) = 0$ but with the dielectric constant $\epsilon$ replaced with $\sigma$ .

SIMION Early Access Mode can also utilize a known distribution of current density for calculating (vector) Magnetic Potential and hence magnetic fields. (See Magnetic Potential for details.)

Note

See these additional sections in this topic in the offline SIMION 8.1.0 help file:

SIMION Modeling Details - Calculating current density from conductivity
Plotting current density vector fields

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Current Density¶

SIMION specific¶

See Also¶

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