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# The Kibble balance

Formerly known as the watt balance, the Kibble balance was invented by Dr Bryan Kibble in 1975 and was renamed after his death in 2016. It is an instrument used for making extremely accurate measurements of a fundamental physical constant: the Planck constant.

Like a set of scales, the Kibble balance uses the force produced by a current-carrying wire in a magnetic field to balance the weight of a mass. By taking measurements of other experimentally-derived quantities, the Kibble balance can be used to accurately measure the Planck constant: a fundamental constant of nature.

Scientists are using the Kibble balance as part of their ongoing attempt to redefine the kilogram in terms of a fundamental physical constant. The kilogram is currently the last SI base unit to be defined by a physical object: the International Prototype Kilogram, a cylinder of platinum-iridium alloy kept in Sèvres, France.

The redefinition would allow for more accurate measurements of mass, which have potential implications in the study of many fields, from quantum mechanics to mechanical engineering.

## How does it work?

Drs Bryan Kibble and Ian Robinson working together
on the improved Kibble balance

A wire coil inside a magnetic field is suspended from the arm of a balance. A kilogram mass is also placed on this arm exerting a force downwards due to gravity. An electrical current is passed through the coil generating a force, the strength of which depends on the size of the current, the strength of the field and the length of the coil. The value of current is varied until the downward force from the mass is balanced by the force from the coil in the magnetic field.

The mass is then removed and the coil is moved in the field. This induces a voltage in the coil and from measurements of the velocity and voltage of the coil the relationship between the coil force and the current in the first part of the experiment can be derived.

By measuring the current and voltage using the Josephson and quantum Hall effects the Planck constant can be measured in terms of mass, length and time.

But what's this got to do with the kilogram?

The Planck constant is a fundamental constant of nature which sets a limit on the accuracy with which we can measure both the position and momentum of a physical system. It depends on the SI units of length, mass and time: the metre, kilogram and second, respectively. As the second and metre are defined by universal constants such as the speed of light, they can be used in conjunction with a fixed value of the Planck constant to redefine the kilogram. This would remove the need for the International Prototype Kilogram.

## The History

The predecessor of the Kibble balance was the current balance, used to measure the ampere, the SI unit of current. Measurements made using the current balance were limited in accuracy due to difficulties in measuring the equipment itself. For example, it was almost impossible to measure the position of the wires in the coil accurately.

In the early 1970s, Dr Kibble proposed a new method which would allow for very accurate measurements of the ampere. His proposal was brought to life in 1978, when the first Kibble balance was made.

Over the next 10 years it was used to make measurements which resulted in the setting of the 1990 conventional values of the von Klitzing and Josephson constants which are used throughout the world for voltage and resistance calibration.

By 1990, Dr Kibble and Dr Ian Robinson built the Mark II Kibble balance which used a circular coil and operated in vacuum conditions.

By 2014, Dr Kibble and Dr Robinson published new methods for building cheaper Kibble balances so that National Measurement Institutes across the world could have access to them. Later the same year, Canada's National Research Council used the Mark II Kibble balance, made at NPL, to measure the Planck constant with an accuracy of nineteen parts per billion: sufficient for the proposed redefinition of the kilogram.

## Agreement on the value of the Planck constant

After 2018, Kibble balances will be used throughout the world to realise the SI unit of mass using a fixed value of the Planck constant. But, prior to redefinition, it is important to have consensus on the value of the Planck constant which meets the requirements set by the scientific community. These state that three results, using two different techniques should agree within a required set of uncertainties. Research groups from around the world have achieved this already.

As of 2016, all the requirements have been met. The results come from two measurements made using Kibble balances: one at the US National Institute of Standards and Technology (NIST) America, and a second at the National Research Council (NRC) Laboratory in Canada. The latter measurement uses NPL's Mark II balance, which was transferred to NRC in 2009. The third result is obtained from measurements of the Avogadro constant made by the International Avogadro Coordination.

## So, what's next?

After consensus on the value of the Planck constant is reached, a formal redefinition of the kilogram in terms of this value will be made. After almost 130 years of use, the International Prototype Kilogram will be retired.

The redefinition will allow for a stable definition of the kilogram, which is independent of location or of a physical object.