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electromagneticSource

Specify current density or charge density for electromagnetic model

    Description

    example

    electromagneticSource(emagmodel,"ChargeDensity",rho) specifies the charge density. The solver uses a charge density for an electrostatic analysis.

    example

    electromagneticSource(emagmodel,"CurrentDensity",J) specifies the current density. The solver uses a current density for magnetostatic or harmonic (time-harmonic) analyses.

    example

    electromagneticSource(___,RegionType,RegionID) specifies the charge or current density for the specified geometry region. Use this syntax with any of the input argument combinations in the previous syntaxes.

    example

    emagSource = electromagneticSource(___) returns the electromagnetic source object.

    Examples

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    Specify charge density on the entire geometry for an electrostatic analysis.

    emagmodel = createpde("electromagnetic","electrostatic");
    importGeometry(emagmodel,"PlateHoleSolid.stl");
    electromagneticSource(emagmodel,"ChargeDensity",10)
    ans = 
      ElectromagneticSourceAssignment with properties:
    
            RegionType: 'Cell'
              RegionID: 1
         ChargeDensity: 10
        CurrentDensity: []
    
    

    Specify current density on the entire geometry for harmonic analysis.

    Create an electromagnetic model for harmonic analysis.

    model = createpde("electromagnetic","harmonic");

    Include a square geometry in the model. Plot the geometry with the edge labels.

    geometryFromEdges(model,@squareg);
    pdegplot(model,"EdgeLabels","on")
    xlim([-1.1 1.1])
    ylim([-1.1 1.1])

    Figure contains an axes object. The axes object contains 5 objects of type line, text.

    Specify current density on the entire geometry. For a 2-D harmonic analysis model with the electric field type, the current density must be a column vector of two elements. When solving the model, the toolbox multiplies the specified current density value by -i and by frequency.

    electromagneticSource(model,"CurrentDensity",[1;0])
    ans = 
      ElectromagneticSourceAssignment with properties:
    
            RegionType: 'Face'
              RegionID: 1
         ChargeDensity: []
        CurrentDensity: [2x1 double]
    
    

    Specify charge density on individual faces in electrostatic analysis.

    Create an electromagnetic model for electrostatic analysis.

    emagmodel = createpde("electromagnetic","electrostatic");

    Create a 2-D geometry with two faces. First, import and plot a 2-D geometry representing a plate with a hole.

    gm = importGeometry(emagmodel,"PlateHolePlanar.stl");
    pdegplot(gm,"EdgeLabels","on","FaceLabels","on")

    Figure contains an axes object. The axes object contains an object of type line.

    Then, fill the hole by adding a face and plot the resulting geometry.

    gm = addFace(gm,5);
    pdegplot(gm,"FaceLabels","on")

    Figure contains an axes object. The axes object contains an object of type line.

    Specify charge density values separately for faces 1 and 2.

    sc1 = electromagneticSource(emagmodel,"Face",1,"ChargeDensity",0.3)
    sc1 = 
      ElectromagneticSourceAssignment with properties:
    
            RegionType: 'Face'
              RegionID: 1
         ChargeDensity: 0.3000
        CurrentDensity: []
    
    
    sc2 = electromagneticSource(emagmodel,"Face",2,"ChargeDensity",0.28)
    sc2 = 
      ElectromagneticSourceAssignment with properties:
    
            RegionType: 'Face'
              RegionID: 2
         ChargeDensity: 0.2800
        CurrentDensity: []
    
    

    Use a function handle to specify a charge density that depends on the coordinates.

    Create an electromagnetic model for electrostatic analysis.

    emagmodel = createpde("electromagnetic","electrostatic");

    Create a unit circle geometry and include it in the model.

    geometryFromEdges(emagmodel,@circleg);

    Specify the charge density as a function of the x- and y-coordinates, ρ=0.3x2+y2.

    rho = @(location,~)0.3.*sqrt(location.x.^2 + location.y.^2);
    electromagneticSource(emagmodel,"ChargeDensity",rho)
    ans = 
      ElectromagneticSourceAssignment with properties:
    
            RegionType: 'Face'
              RegionID: 1
         ChargeDensity: @(location,~)0.3.*sqrt(location.x.^2+location.y.^2)
        CurrentDensity: []
    
    

    Input Arguments

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    Electromagnetic model, specified as an ElectromagneticModel object. The model contains a geometry, a mesh, the electromagnetic properties of the material, the electromagnetic sources, and the boundary conditions.

    Charge density, specified as a real number or a function handle. Use a function handle to specify a charge density that depends on the coordinates. For details, see More About.

    Data Types: double | function_handle

    Current density, specified as a real number, a column vector, or a function handle. Use a function handle to specify a current density that depends on the coordinates.

    For magnetostatic analysis, the current density must be a real number for a 2-D model, a column vector of three elements for a 3-D model, or a function handle for a 2-D or 3-D model.

    For harmonic analysis with the electric field type, the current density must be a column vector of two elements for a 2-D model, a column vector of three elements for a 3-D model, or a function handle for a 2-D or 3-D model. The toolbox multiplies the specified current density by -i and by frequency.

    For harmonic analysis with the magnetic field type, the current density must be a scalar for a 2-D model, a column vector of three elements for a 3-D model, or a function handle for a 2-D or 3-D model. The toolbox uses the curl of the specified current density.

    For details, see More About.

    Data Types: double | function_handle

    Geometric region type, specified as "Face" for a 2-D model or "Cell" for a 3-D model.

    Data Types: char | string

    Region ID, specified as a vector of positive integers. Find the face or cell IDs by using pdegplot with the "FaceLabels" or "CellLabels" name-value argument set to "on".

    Example: electromagneticSource(emagmodel,"CurrentDensity",10,"Face",1:3)

    Data Types: double

    Output Arguments

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    Handle to the electromagnetic source, returned as an ElectromagneticSourceAssignment object. For more information, see ElectromagneticSourceAssignment Properties.

    More About

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    Specifying Nonconstant Parameters of Electromagnetic Model

    In Partial Differential Equation Toolbox™, use a function handle to specify these electromagnetic parameters when they depend on the coordinates and, for a harmonic analysis, on the frequency:

    • Relative permittivity of the material

    • Relative permeability of the material

    • Conductivity of the material

    • Charge density as source (can depend on space only)

    • Current density as source (can depend on space only)

    • Voltage on the boundary (can depend on space only)

    • Magnetic potential on the boundary (can depend on space only)

    • Electric field on the boundary (can depend on space only)

    • Magnetic field on the boundary (can depend on space only)

    For example, use function handles to specify the relative permittivity, charge density, and voltage on the boundary for emagmodel.

    electromagneticProperties(emagmodel, ...
                              "RelativePermittivity", ...
                              @myfunPermittivity)
    electromagneticSource(emagmodel, ...
                          "ChargeDensity",@myfunCharge, ...
                          "Face",2)
    electromagneticBC(emagmodel, ...
                      "Voltage",@myfunBC, ...
                      "Edge",2)

    The function must be of the form:

    function emagVal = myfun(location,state)

    The solver computes and populates the data in the location and state structure arrays and passes this data to your function. You can define your function so that its output depends on this data. You can use any names in place of location and state.

    If you call electromagneticBC with Vectorized set to "on", then location can contain several evaluation points. If you do not set Vectorized or set Vectorized to "off", then solvers passes just one evaluation point in each call.

    • location — A structure array containing these fields:

      • location.x — The x-coordinate of the point or points

      • location.y — The y-coordinate of the point or points

      • location.z — For a 3-D or an axisymmetric geometry, the z-coordinate of the point or points

      • location.r — For an axisymmetric geometry, the r-coordinate of the point or points

      Furthermore, for boundary conditions, the solver passes this data in the location structure:

      • location.nx — The x-component of the normal vector at the evaluation point or points

      • location.ny — The y-component of the normal vector at the evaluation point or points

      • location.nz — For a 3-D or an axisymmetric geometry, the z-component of the normal vector at the evaluation point or points

      • location.nr — For an axisymmetric geometry, the r-component of the normal vector at the evaluation point or points

    • state — A structure array containing this field for a harmonic electromagnetic problem:

      • state.frequency - Frequency at evaluation points

    Relative permittivity, relative permeability, and conductivity get this data from the solver:

    • location.x, location.y, location.z, location.r

    • state.frequency for a harmonic analysis

    • Subdomain ID

    Charge density, current density, electric or magnetic field on the boundary get this data from the solver:

    • location.x, location.y, location.z, location.r

    • Subdomain ID

    Voltage or magnetic potential on the boundary get these data from the solver:

    • location.x, location.y, location.z, location.r

    • location.nx, location.ny, location.nz, location.nr

    When you solve an electrostatic or magnetostatic problem, the output returned by the function handle must be of the following size. Here, Np = numel(location.x) is the number of points.

    • 1-by-Np if a function specifies the nonconstant relative permittivity, relative permeability, and charge density. For the charge density, the output can also be Np-by-1.

    • 1-by-Np for a 2-D model and 3-by-Np for a 3-D model if a function specifies the nonconstant current density and magnetic potential on the boundary. For the current density, the output can also be Np-by-1 or Np-by-3.

    When you solve a harmonic problem, the output returned by the function handle must be of the following size. Here, Np = numel(location.x) is the number of points.

    • 1-by-Np if a function specifies the nonconstant relative permittivity, relative permeability, and conductivity.

    • 2-by-Np for a 2-D problem and 3-by-Np for a 3-D problem if a function specifies the nonconstant electric or magnetic field.

    • 2-by-Np or Np-by-2 for a 2-D problem and 3-by-Np or Np-by-3 for a 3-D problem if a function specifies the nonconstant current density and the field type is electric.

    • 1-by-Np or Np-by-1 for a 2-D problem and 3-by-Np or Np-by-3 for a 3-D problem if a function specifies the nonconstant current density and the field type is magnetic.

    If relative permittivity, relative permeability, or conductivity for a harmonic analysis depends on the frequency, ensure that your function returns a matrix of NaN values of the correct size when state.frequency is NaN. Solvers check whether a problem is nonlinear or time dependent by passing NaN state values and looking for returned NaN values.

    Additional Arguments in Functions for Nonconstant Electromagnetic Parameters

    To use additional arguments in your function, wrap your function (that takes additional arguments) with an anonymous function that takes only the location and state arguments. For example:

    emagVal = @(location,state) myfunWithAdditionalArgs(location,arg1,arg2...)
    electromagneticBC(model,"Edge",3,"Voltage",emagVal)
    

    Version History

    Introduced in R2021a