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

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.

5pages, 6 figures, submitted to MST

References in corpus (6)

• Magnetic monopole field exposed by electrons
• Determination of the Planck constant using a watt balance with a superconducting magnet system at the National Institute of Standards and Technology
• Construction, Measurement, Shimming, and Performance of the NIST-4 Magnet System
• A nonlinearity in permanent-magnet systems used in watt balances
• Field representation of a watt balance magnet by partial profile measurements
• Magnetic monopoles and dyons revisited: A useful contribution to the study of classical mechanics

Cited by in corpus (1)

• The irony of the magnet system for Kibble balances -- a review