Watt balance

From Wikipedia, the free encyclopedia

The NIST watt balance is a project of the U.S. Government to develop an “electronic kilogram.” The vacuum chamber dome, which lowers over the entire apparatus, is visible at top.

The watt balance is an experimental electromechanical apparatus that may one day provide a definition of the kilogram based on electronics.

[edit] Overview

The watt balance is a more accurate version of the ampere balance, in which the force between two current-carrying coils is measured and then used to calculate the magnitude of the current. The principle of the watt balance was proposed by B. P. Kibble of the UK National Physical Laboratory (NPL) in 1975.^[1] The main weakness of the ampere balance method is that the result depends on the accuracy with which the dimensions of the coils are measured. The watt balance method has an extra calibration step in which the effect of the geometry of the coils is eliminated, removing the main source of uncertainty. This extra step involves moving the force coil through a known magnetic flux at a known speed.

The present accuracy record is held by the U.S. National Institute of Standards and Technology (NIST) with a relative ucertainty of 3.6 × 10⁻⁸,^[2] and experiments are continuing towards a goal of 1 × 10⁻⁸. Apart from the watt balances at the NPL and NIST, similar experiments are also taking place at the Swiss Federal Office of Metrology and Accreditation (METAS) in Berne, the International Bureau of Weights and Measures (BIPM) near Paris and Laboratoire national de métrologie et d’essais (LNE) in Trappes, France.^[3] The long-term goal of these experiments is to produce a new definition of the kilogram based on fundamental physical constants, to replace the present definition based on the International Prototype Kilogram, a cylinder of platinum/iridium owned by the BIPM.

[edit] Principle

A conducting wire of length L which carries an electric current I perpendicular to a magnetic field of strength B will experience a force due to the Biot–Savart law equal to BLI. In the watt balance, the current is varied so that this force exactly counteracts the weight of a standard mass m, which is given by the mass multiplied by the gravitational acceleration g. This is also the principle behind the ampere balance.

Kibble's watt balance avoids the problems of measuring B and L with a second calibration step. The same wire (in practice a coil of wire) is moved through the same magnetic field at a known speed v. By Faraday's law of induction, a potential difference U is generated across the ends of the wire, which is equal to BLv. Hence the unknown quantities B and L can be eliminated from the equations to give

Both sides of the equation have the dimensions of power, measured in watts in the International System of Units, hence the name "watt balance".

[edit] Measurements

Accurate measurements of electric current and potential difference are made in conventional electrical units rather than SI units, which are based on fixed conventional values of the Josephson constant and the von Klitzing constant, K_J–90 and R_K–90 respectively. The current watt balance experiments are equivalent to measuring the value of the conventional watt in SI units. From the definition of the conventional watt, this is equivalent to measuring the value of the product K_J²R_K in SI units instead of its fixed value in conventional electrical units.

The importance of such measurements is that they are also a direct measurement of the Planck constant h:

The principle of the "electronic kilogram" would be to define the value of the Planck constant in the same way that the speed of light is defined by the definition of the meter. In this case, the electric current and the potential difference would be measured in SI units, and the watt balance would become an instrument to measure mass.

Any laboratory which had invested the (very considerable) time and money in a working watt balance would be able to measure masses to the same accuracy as they currently measure the Planck constant.

[edit] References

1. ^ Kibble, B. P. (1975), Sanders, J. H.; Wapstra, A. H., eds., Atomic Masses and Fundamental Constants 5, New York: Plenum, pp. 545–51 
2. ^ Steiner, R. L.;Williams, E. R.; Liu, R.; Newell, D. B. (2007), IEEE Trans. Instrum. Meas. 56 (2): 592 
3. ^ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006". Rev. Mod. Phys. 80: 633–730. doi:10.1103/RevModPhys.80.633. http://physics.nist.gov/cuu/Constants/codata.pdf. 

[edit] External links

• R. Steiner, E.R. Williams, D.B. Newell and R. Liu. "Towards an electronic kilogram: an improved measurement of the Planck constant and electron mass." Metrologia. (October 2005)
• Joshua P. Schwarz, Ruimin Liu, David B. Newell, Richard L. Steiner, Edwin R. Williams, Douglas Smith "Hysteresis and Related Error Mechanisms in the NIST Watt Balance Experiment" (August 2001)
• Bureau International des Poids et Mesures
• Swiss Federal Office of Metrology