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Permanent magnets with high-permeability yokes have been widely used in wattbalances for supplying a robust and strong magnetic field at the coil position.Subjected to the mechanical realization, only several $B_r(z)$ (radial magneticfield along the vertical direction) profiles can be measured by coils for fieldcharacterization. In this article, we present an algorithm that can constructthe global magnetic field of the air gap based on $N(N\geq1)$ additionalmeasurements of $B_r(z)$ profiles. The proposed algorithm is realized bypolynomially estimating the $B_z(r)$ function with analysis of basic relationsbetween two magnetic components in air gap, i.e., $B_r(r,z)$ and $B_z(r,z)$,following the Maxwell's equations. The algorithm, verified by FEM simulations,can characterize the three-dimensional contribution of the magnetic field for awatt balance magnet with acceptable accuracy, which would supply basic fieldparameters for alignment and misalignment corrections.

Field representation of a watt balance magnet by partial profile measurements