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  direction, which implies that the electric field is tangential to the rz-plane.