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arXiv · 1512.08359

A discussion of $Bl$ conservation on a two dimensional magnetic field plane in watt balances

Shisong Li·Wei Zhao·Songling Huang
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Abstract

The watt balance is an experiment being pursued in national metrology institutes for precision determination of the Planck constant $h$. In watt balances, the $1/r$ magnetic field, expected to generate a geometrical factor $Bl$ independent to any coil horizontal displacement, can be created by a strict two dimensional, symmetric (horizontal $r$ and vertical $z$) construction of the magnet system. In this paper, we present an analytical understanding of magnetic field distribution when the $r$ symmetry of the magnet is broken and the establishment of the $Bl$ conservation is shown. By using either Gauss's law on magnetism with monopoles or conformal transformations, we extend the $Bl$ conservation to arbitrary two dimensional magnetic planes where the vertical magnetic field component equals zero. The generalized $Bl$ conservation allows a relaxed physical alignment criteria for watt balance magnet systems.

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Shisong Li, Wei Zhao, Songling Huang. 2015-12-28. A discussion of $Bl$ conservation on a two dimensional magnetic field plane in watt balances. https://doi.org/10.1088/0957-0233%2F27%2F5%2F051001

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