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Permanent magnets together with yokes to concentrate the magnetic flux into a cylindrical air-gap are widely employed in Kibble balances. These experiments require a uniform magnetic flux density along a vertical path, typically a substantial fraction of the length of the air-gap. Fringe fields that are present at both ends of the air-gap limit the region where the flux density does not change more than a certain relative fraction (here 5 × 10-4) of the flux density in the center of the magnet system. By simply adding an iron ring with