# electromagneticSource

Specify current density, charge density, and magnetization for electromagnetic model

*Since R2021a*

## Syntax

## Description

`electromagneticSource(`

specifies the current density. The solver uses a current density for magnetostatic or
harmonic (time-harmonic) analyses.`emagmodel`

,"CurrentDensity",`J`

)

For a 3-D magnetostatic analysis, you can specify current density by using the DC
conduction results. See `ConductionResults`

.
The toolbox does not support conduction results as a source of current density for a 2-D
magnetostatic analysis, in which case current density must be a scalar or a function handle
returning a scalar that represents out-of-plane current.

`electromagneticSource(___,`

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.`RegionType`

,`RegionID`

)

returns the electromagnetic source object.`emagSource`

= electromagneticSource(___)

## Examples

### Specify Charge Density on Entire Geometry

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: [] Magnetization: []

### Specify Current Density on Entire Geometry

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])

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] Magnetization: []

### Specify Charge Density on Each Face

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")

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

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

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: [] Magnetization: []

sc2 = electromagneticSource(emagmodel,"Face",2,"ChargeDensity",0.28)

sc2 = ElectromagneticSourceAssignment with properties: RegionType: 'Face' RegionID: 2 ChargeDensity: 0.2800 CurrentDensity: [] Magnetization: []

### Specify Nonconstant Charge Density

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, $\rho =0.3\sqrt{{\mathit{x}}^{2}+{\mathit{y}}^{2}}$.

```
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: [] Magnetization: []

### Use DC Conduction Solution as Current Density

Use a solution obtained by performing DC conduction analysis to specify current density for a magnetostatic model.

Create an electromagnetic model for DC conduction analysis.

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

Import and plot a geometry representing a plate with a hole.

gm = importGeometry(emagmodel,"PlateHoleSolid.stl"); pdegplot(gm,"FaceLabels","on","FaceAlpha",0.3)

Specify the conductivity of the material.

`electromagneticProperties(emagmodel,"Conductivity",6e4);`

Apply the voltage boundary conditions on the left, right, and back faces of the plate.

electromagneticBC(emagmodel,"Voltage",0,"Face",[1 3 5]);

Specify the surface current density on the front face of the geometry and on the face bordering the hole.

electromagneticBC(emagmodel,"SurfaceCurrentDensity",100,"Face",[2 7]);

Generate the mesh.

generateMesh(emagmodel);

Solve the model.

R = solve(emagmodel);

Change the analysis type of the model to magnetostatic.

`emagmodel.AnalysisType = "magnetostatic";`

This model already has a quadratic mesh that you generated for the DC conduction analysis. For a 3-D magnetostatic model, the mesh must be linear. Generate a new linear mesh. The `generateMesh`

function creates a linear mesh by default if the model is 3-D and magnetostatic.

generateMesh(emagmodel);

Specify the current density for the entire geometry using the DC conduction solution.

`electromagneticSource(emagmodel,"CurrentDensity",R)`

ans = ElectromagneticSourceAssignment with properties: RegionType: 'Cell' RegionID: 1 ChargeDensity: [] CurrentDensity: [1x1 pde.ConductionResults] Magnetization: []

### Specify Magnetization

Specify magnetization on a face in a magnetostatic analysis.

Create a unit square geometry with a circle in its center. The circle represents a permanent magnet.

L = 0.8; r = 0.25; sq = [3 4 -L L L -L -L -L L L]'; circ = [1 0 0 r 0 0 0 0 0 0]'; gd = [sq,circ]; sf = "sq + circ"; ns = char('sq','circ'); ns = ns'; g = decsg(gd,sf,ns);

Plot the geometry with the face labels.

pdegplot(g,"FaceLabels","on")

Create a magnetostatic model and include the geometry in the model.

emagmodel = createpde("electromagnetic","magnetostatic"); geometryFromEdges(emagmodel,g);

Specify the magnetization magnitude.

M = 1;

To make the circle represent a permanent magnet, specify the uniform magnetization in the positive *x*-direction.

electromagneticSource(emagmodel,"Face",2,"Magnetization",M*[1;0])

ans = ElectromagneticSourceAssignment with properties: RegionType: 'Face' RegionID: 2 ChargeDensity: [] CurrentDensity: [] Magnetization: [2×1 double]

## Input Arguments

`emagmodel`

— Electromagnetic model

`ElectromagneticModel`

object

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.

`rho`

— Charge density

real number | function handle

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`

`J`

— Current density

real number | column vector | function handle | `ConductionResults`

object

Current density, specified as a real number, a column vector, a function handle, or
a `ConductionResults`

object. Use a function handle to specify a nonconstant current density.

For magnetostatic analysis, the current density must be

A real number or a function handle for a 2-D model. The toolbox does not support conduction results as a source of current density for a 2-D magnetostatic analysis.

A column vector of three elements, a

`ConductionResults`

object, or a function handle for a 3-D model.

For harmonic analysis with the electric field type, the toolbox multiplies the
specified current density by `-i`

and by frequency. The current density
must be

A column vector of two elements or a function handle that depends on the coordinates for a 2-D model.

A column vector of three elements or a function handle that depends on the coordinates for a 3-D model.

For harmonic analysis with the magnetic field type, the toolbox uses the curl of the specified current density. The current density must be

A scalar or a function handle that depends on the coordinates for a 2-D model.

A column vector of three elements or a function handle that depends on the coordinates for a 3-D model.

For details, see More About.

**Data Types: **`double`

| `function_handle`

`M`

— Magnetization

column vector | function handle

Magnetization, specified as 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. Use a function handle to specify a magnetization that depends on the coordinates. For details, see More About.

**Data Types: **`double`

| `function_handle`

`RegionType`

— Geometric region type

`"Face"`

for a 2-D model | `"Cell"`

for a 3-D model

Geometric region type, specified as `"Face"`

for a 2-D model or
`"Cell"`

for a 3-D model.

**Data Types: **`char`

| `string`

`RegionID`

— Region ID

vector of positive integers

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

`emagSource`

— Handle to electromagnetic source

`ElectromagneticSourceAssignment`

object

Handle to the electromagnetic source, returned as an
`ElectromagneticSourceAssignment`

object. For more information, see
ElectromagneticSourceAssignment Properties.

## More About

### 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)

Magnetization (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)

Surface current density 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 the solver 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 analysisSubdomain ID

Charge density, current density, magnetization, surface current density on the boundary, and 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, magnetostatic, or DC conduction 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, or 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`

.`2`

-by-`Np`

for a 2-D model and`3`

-by-`Np`

for a 3-D model if a function specifies the nonconstant magnetization or surface current density on the boundary.

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 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**

### R2023a: Nonlinear magnetostatics

Magnetization and current density can depend on the magnetic flux density, magnetic potential, and its gradients.

### R2022b: Magnetization value for permanent magnets

Magnetization can be specified to account for materials generating their own magnetic fields in a magnetostatic analysis workflow.

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