Physics Model

The first Maxwell equation is solved \[ div(\vec{D}) = \rho \] \[ \vec{E} = -grad(U) \] \[ \vec{D} = {\epsilon} \vec{E} \] with material equation. If the material is an-isotropic, then the $\epsilon$ is a tensor, generally $\epsilon$ is 3×3 matrix.

User Interface

Electrostatics Physics Modul Interface

In user interface for the electrostatics physics module the user can predefine potential values on the surface, or field values. Charge density can be defined in the domains.

Material Properties

Isotropic Material parameters
Name Dimension Definition Internal variable name
e_r 1 Relative dielectric constant e_r11_INTERNAL, e_r22_INTERNAL, e_r33_INTERNAL
Anisotropic Material parameters
Name Dimension Definition Internal variable name
er_11 1 Relative dielectric constant tensor 11 component e_r11_INTERNAL
er_12 1 Relative dielectric constant tensor 12 component e_r12_INTERNAL
er_13 1 Relative dielectric constant tensor 13 component e_r13_INTERNAL
er_21 1 Relative dielectric constant tensor 21 component e_r21_INTERNAL
er_22 1 Relative dielectric constant tensor 22 component e_r22_INTERNAL
er_23 1 Relative dielectric constant tensor 23 component e_r23_INTERNAL
er_31 1 Relative dielectric constant tensor 31 component e_r31_INTERNAL
er_32 1 Relative dielectric constant tensor 32 component e_r32_INTERNAL
er_33 1 Relative dielectric constant tensor 33 component e_r33_INTERNAL

Examples

2D Simulations

Low permittivity dielectric

High permittivity dielectric

Charged sphere close to grounded plane