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 [] and independent variables in [].
Stationary variables vars are vars={V[x₁,…,x_n],{x₁,…,x_n}}.
Frequency-dependent variables vars are vars={V[x₁,…,x_n],ω,{x₁,…,x_n}}.
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 [], 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:

parameter	default	symbol
"BoundaryUnitNormal"	Automatic
"Current"		, electric current in []
"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 []

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 [ $TemplateBox[{InterpretationBox[, 1], {"A", , "/", , {"m", ^, 2}}, amperes per meter squared, {{(, "Amperes", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]$ ].
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 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 …,keyp_i…,p_iv_i,…], the parameters are replaced with .

Examples

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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 [] 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 :

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 and :

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 [], 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.