**By R. Belmans**

## Symmetric geometry and field

**If at the axis of symmetry** of a model on both sides the same material is defined, the same sources are in both parts present and the same boundary conditions are applied, the field and geometry are symmetrical according to the line. Considering a magnetic field, the flux crosses this line orthogonally. The symmetric part can be omitted and replaced by a homogenous Neumann boundary condition (Fig. 9.6). The same idea can be followed in a three-dimensional model (Fig. 9.7).

**Fig. 9.5. Electrostatic micro motor and entire three-dimensional model.**

**Fig. 9.6. The Neumann boundary condition represents a line of symmetry.**

## Periodic geometry and field

**If the geometry,** the applied sources and the boundary conditions are periodic with a given spatial period, the field is also periodic. The smallest common symmetry has to be modelled. The spatial connections are replaced by binary boundary conditions (Fig. 9.8). In Fig. 9.8 the field is periodic with one pole pitch. This is the smallest common symmetry with respect to the field and geometry.