ElectricCurrentDensityValue
ElectricCurrentDensityValue[pred,vars,pars]
represents a current density boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
ElectricCurrentDensityValue[pred,vars,pars,lkey]
represents a current density boundary condition with local parameters specified in pars[lkey].
Details
- ElectricCurrentDensityValue specifies a boundary condition for ElectricCurrentPDEComponent and is used as part of the modeling equation:
- ElectricCurrentDensityValue is typically used to model an electric current density , normal to the boundary, in units of [], that enters or leaves through a boundary.
- A positive value denotes an inward electric flow, and a negative value denotes an outward flow.
- ElectricCurrentDensityValue models an electric current density , normal to the boundary, with dependent variable in volts [] and independent variables in [].
- Stationary variables vars are vars={V[x1,…,xn],{x1,…,xn}}.
- Frequency-dependent variables vars are vars={V[x1,…,xn],ω,{x1,…,xn}}.
- ElectricCurrentDensityValue with a specified scalar electric current density , normal to the boundary, models:
- ElectricCurrentDensityValue with a specified electric current density vector [], models:
- with a unit normal.
- ElectricCurrentDensityValue with a specified current [], normal to the boundary, models:
- with [] the boundary area. Currents are automatically converted to a normal electric current density .
- Model parameters pars are specified as for ElectricCurrentPDEComponent.
- The following additional model parameters pars can be given:
-
parameter default symbol "BoundaryUnitNormal" Automatic "Current" , electric current in [] "CurrentDensity" - {0,...}
, electric current density in [] "NormalCurrentDensity" , normal electric current density in [] "Thickness" - , thickness in [] - All model parameters may depend on the spatial variables .
- In two dimensions, the parameter "Thickness" is taken into account to convert the current from units [] to [].
- To localize model parameters, a key lkey can be specified and values from association pars[lkey] are used for model parameters.
- A prescribed electric current density boundary condition can be used with:
-
analysis type applicable Frequency response Yes Stationary Yes - ElectricCurrentDensityValue evaluates to a NeumannValue.
- The boundary predicate pred can be specified as in NeumannValue.
- If the ElectricCurrentDensityValue depends on parameters that are specified in the association pars as …,keypi…,pivi,…], the parameters are replaced with .
Examples
open allclose allBasic Examples (3)
Set up a symbolic electric current density boundary condition:
Set up a symbolic electric current density boundary condition with a current density:
Model a copper wire that is excited with a direct current (DC) of [] with a current density boundary condition at the lower-left boundary and with a zero electric potential condition at the lower-right boundary.
Set up the stationary current PDE model variables and :
Define the geometry of the wire:
Specify ground potential at the lower-right boundary:
Scope (6)
Create an electric current density boundary condition:
Create an electric current density boundary condition with a boundary unit normal :
Create an electric current density boundary condition with :
Create an electric current density boundary condition with a current :
Create an electric current density boundary condition in 2D with a current and a thickness :
Create a parametric-frequency electric current density boundary condition:
Applications (2)
3D Stationary Analysis (1)
Model a copper spiral inductor that is excited with a current density normal to the left boundary and has a zero electric potential boundary condition at the right boundary.
Define the spiral inductor geometry:
Set up the stationary current PDE model variables and :
Specify an inward current flow on the left boundary:
Frequency Analysis (1)
Model a dielectric material of a cylindrical capacitor that is excited with an alternating current (AC ) of [], with a current density boundary condition at the upper boundary, which represents one of the capacitor electrodes, and with a zero electric potential boundary condition at the lower boundary.
Set up the frequency current PDE model variables :
Define the frequency and the period:
Specify an electrical conductivity and a relative permittivity :
Specify the ground potential at the lower boundary:
Specify an inward current flow at the upper boundary:
Solve the harmonic PDE for []:
Transform the voltage at the upper boundary to the time domain:
Text
Wolfram Research (2024), ElectricCurrentDensityValue, Wolfram Language function, https://reference.wolfram.com/language/ref/ElectricCurrentDensityValue.html.
CMS
Wolfram Language. 2024. "ElectricCurrentDensityValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ElectricCurrentDensityValue.html.
APA
Wolfram Language. (2024). ElectricCurrentDensityValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ElectricCurrentDensityValue.html