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`

.

The function must be of the form:

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:

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

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, 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`

.

`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 or time dependent by passing `NaN`

state values and looking for returned `NaN`

values.