Two simple modifications to improve the magnetic field profile in radial magnetic systems

All present watt balances employ permanent magnet systems using a yoke with high permeability as flux return. Very often these systems are built with vertical and azimuthal symmetries. In its simplest form, the air gap is defined as the radial distance between an inner and outer yoke with the same height. This design leads to sloped field lines away from the plane of vertical symmetry. In order to suppress this vertical magnetic field, we propose two modified magnet constructions: (1) adding a permanent magnet in the outer yoke, and (2) decreasing the height of the outer yoke. Finite element method simulations show that, with reasonable optimization, either proposal can lower the vertical magnetic field by about one order of magnitude.