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 [TemplateBox[{InterpretationBox[, 1], {"A", , "/", , {"m", ^, 2}}, amperes per meter squared, {{(, "Amperes", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]], 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 [TemplateBox[{InterpretationBox[, 1], "V", volts, "Volts"}, QuantityTF]] and independent variables in [TemplateBox[{InterpretationBox[, 1], "m", meters, "Meters"}, QuantityTF]].
  • 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 [TemplateBox[{InterpretationBox[, 1], {"A", , "/", , {"m", ^, 2}}, amperes per meter squared, {{(, "Amperes", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]], models:
  • with a unit normal.
  • ElectricCurrentDensityValue with a specified current [TemplateBox[{InterpretationBox[, 1], "A", amperes, "Amperes"}, QuantityTF]], normal to the boundary, models:
  • with [TemplateBox[{InterpretationBox[, 1], {{"m", ^, 2}}, meters squared, {"Meters", ^, 2}}, QuantityTF]] 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:
  • parameterdefaultsymbol
    "BoundaryUnitNormal"Automatic
    "Current", electric current in [TemplateBox[{InterpretationBox[, 1], "A", amperes, "Amperes"}, QuantityTF]]
    "CurrentDensity"
  • {0,...}
    		• , electric current density in [TemplateBox[{InterpretationBox[, 1], {"A", , "/", , {"m", ^, 2}}, amperes per meter squared, {{(, "Amperes", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]]
    "NormalCurrentDensity", normal electric current density in [TemplateBox[{InterpretationBox[, 1], {"A", , "/", , {"m", ^, 2}}, amperes per meter squared, {{(, "Amperes", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]]
    "Thickness"-, thickness in [TemplateBox[{InterpretationBox[, 1], "m", meters, "Meters"}, QuantityTF]]
  • 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 [TemplateBox[{InterpretationBox[, 1], "A", amperes, "Amperes"}, QuantityTF]] to [TemplateBox[{InterpretationBox[, 1], {"A", , "/", , {"m", ^, 2}}, amperes per meter squared, {{(, "Amperes", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]].
  • 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 typeapplicable
    Frequency responseYes
    StationaryYes
  • 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 all

Basic 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 [TemplateBox[{InterpretationBox[, 1], "A", amperes, "Amperes"}, QuantityTF]] 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 vars and pars:

Set up the equation:

Define the geometry of the wire:

Visualize the wire:

Specify ground potential at the lower-right boundary:

Specify an inward current flow at the lower-left boundary:

Solve the PDE:

Visualize the electric potential:

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 vars and pars:

Specify an inward current flow on the left boundary:

Specify a ground potential:

Solve the PDE:

Compute the current density vector:

Visualize the current density magnitude:

Frequency Analysis  (1)

Model a dielectric material of a cylindrical capacitor that is excited with an alternating current (AC ) of [TemplateBox[{InterpretationBox[, 1], "Hz", hertz, "Hertz"}, QuantityTF]], 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 vars:

Define the frequency and the period:

Set up a region :

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:

Set up the equation:

Solve the harmonic PDE for [TemplateBox[{InterpretationBox[, 1], "Hz", hertz, "Hertz"}, QuantityTF]]:

Transform the voltage at the upper boundary to the time domain:

Visualize the voltage at the upper plate of the capacitor:

Wolfram Research (2024), ElectricCurrentDensityValue, Wolfram Language function, https://reference.wolfram.com/language/ref/ElectricCurrentDensityValue.html.

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

BibTeX

@misc{reference.wolfram_2024_electriccurrentdensityvalue, author="Wolfram Research", title="{ElectricCurrentDensityValue}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/ElectricCurrentDensityValue.html}", note=[Accessed: 21-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_electriccurrentdensityvalue, organization={Wolfram Research}, title={ElectricCurrentDensityValue}, year={2024}, url={https://reference.wolfram.com/language/ref/ElectricCurrentDensityValue.html}, note=[Accessed: 21-November-2024 ]}