Electrostatics Material¶

ElectrostaticMaterial binds a Marker to the dielectric law used by the electrostatics model. The material is characterised by its electric permittivity $\varepsilon$ — the only property needed in the Poisson equation $\nabla\cdot(\varepsilon\nabla\phi) = -\rho$.

material = ElectrostaticMaterial(
    name=...,
    marker=...,
    electric_permittivity=...,  # method object, scalar, or None (-> vacuum)
)

Passing a float is auto-wrapped as a relative constant; passing None selects vacuum ($\varepsilon_r = 1$).

Typical applications¶

The general electrostatic material covers the regions most often encountered in HV / capacitor / MEMS / electron-optics studies:

Air, vacuum, and gases — defaults ($\varepsilon_r = 1$).
Solid dielectrics (oils, mineral / pressboard insulation, polymer films, ceramics) — constant relative permittivity from datasheet values.
Inhomogeneous insulators and graded dielectrics — use the function method with a coefficient that varies in space (or couples to temperature, humidity, etc.).
Semiconductor / piezoelectric layers when modelled as position-dependent permittivity.

Permittivity Methods¶

Electric Permittivity Methods
Name	Example	Description
Vacuum (default)	`my_eps = None` Equivalently: `my_eps = ElectricPermittivityMethodRelativeConstant( relative_electric_permittivity=1.0, )`	Vacuum permittivity $\varepsilon = \varepsilon_0$.
Relative Constant	`my_eps = 2.7` Equivalently: `my_eps = ElectricPermittivityMethodRelativeConstant( relative_electric_permittivity=2.7, )`	Constant relative permittivity: $\varepsilon = \varepsilon_0 \varepsilon_r$.
Function	`eps_r_field = mufem.CffExpressionScalar( "2.0 + 0.5 * exp(-z()^2)" ) my_eps = ElectricPermittivityMethodFunction( cff_scalar_variable=eps_r_field, )`	Spatially varying relative permittivity supplied through any scalar coefficient function — useful for graded dielectrics or coupling with other models.

Example¶

A simple air region:

from mufem.electromagnetics.electrostatics import ElectrostaticMaterial

air = ElectrostaticMaterial(name="Air", marker="Air" @ Vol)

An oil-filled HV bushing modelled with $\varepsilon_r = 2.2$:

oil = ElectrostaticMaterial(
    name="Oil",
    marker="Bushing" @ Vol,
    electric_permittivity=2.2,
)