Under static conditions, the electric potential, V, is defined by the relationship:

Combining this equation with the constitutive relationship D = ε0E + P between the electric displacement D and the electric field E, it is possible to represent Gauss’ law as the following equation:

In this equation, the physical constant, ε0 (SI unit: F/m) is the permittivity of vacuum, P (SI unit: C/m2) is the electric polarization vector, and ρ (SI unit: C/m3) is a space charge density. This equation describes the electrostatic field in dielectric materials.

For in-plane 2D modeling, the Electrostatics interface assumes a symmetry where the electric potential varies only in the x and y directions and is constant in the z direction. This implies that the electric field, E, is tangential to the xy-plane. With this symmetry, the same equation is solved as in the 3D case. The physics interface solves the following equation where d is the thickness in the z direction:

The axisymmetric version of the physics interface considers the situation where the fields and geometry are axially symmetric. In this case, the electric potential is constant in the φ direction, which implies that the electric field is tangential to the rz-plane.