---
title: "Kibble Balance Interactive Lab | Sandbox Physics"
description: "How do weighing and velocity measurements remove an unknown magnetic factor?"
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  zh-CN: "https://sandboxphysics.com/zh/labs/kibble-balance/"
last_modified: "2026-11-12"
---

IN36 · One coil, two experiments

# Kibble Balance

**How do weighing and velocity measurements remove an unknown magnetic factor?** Current supports the mass in weighing mode; motion induces voltage in velocity mode. The shared magnetic factor can then be eliminated. Different working positions need a measured correction, and changed magnetic history requires an independent consistency check before a mass is reported.

Move an open-circuit coil, then support a mass at null with current. Compare working positions, field gradients and optical alignment to find when a mass can be inferred.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Drag the copper coil to change the active working position. Save a new two-mode cycle to measure the changed apparatus.

Weighing position $0\,\mathrm{mm}$ Velocity scan center $0\,\mathrm{mm}$ Axial field gradient $0.18$ Coil speed $2\,\mathrm{mm\,s^{-1}}$ Optical axis tilt $0\,\mathrm{mrad}$

A simulated two-mode cycle and independent known-mass check are loaded.

Simulation source and magnetic history

Source mass / grams $100\,\mathrm{g}$ Mode-dependent factor change / ppm $0$

These values drive simulated observations. Source mass and the hidden factor shift never enter the mass reconstruction. A separate fifty-gram reference tests the mode comparison.

Model assumptions

One axisymmetric flux function and horizontal thin coil serve both modes. Weighing uses ideal null feedback; velocity mode samples constant-speed open-circuit strokes. External electrical, length, optical-angle and gravity references are frozen with each record. Josephson and quantum Hall standards supply calibration inputs. Mass uses raw channels and declared references; position correction interpolates only inside the measured velocity map. An independent known-mass check must pass. Turnaround acceleration, self-inductance, thermal expansion, buoyancy, vibration and detailed hysteresis dynamics are omitted. Field and performance parameters are teaching assumptions; the cutaway is not a manufactured magnet design. The conditional error budget is not a certified kilogram realization.

Retained simulated measurements

## Two experiments meet at the weighing position

Retained two-mode cycle

Conditional reconstructed mass $100\,\mathrm{g}$

Measured factor at weighing $24.9\,\mathrm{T\,m}$

Retained weighing current $39.4\,\mathrm{mA}$

Independent mass check $0\,\mathrm{ppm}$

> Measured factor map and weighing location; numerical results and limits are described below.

> Raw voltage, current and projected velocity, each with its own labelled scale.

Correction and conditional error budget

The budget combines declared independent standard uncertainties, a twenty-five-ppm interpolation allowance and the observed reference-mass residual in quadrature. It is conditional on an affine factor within this teaching model. It omits correlated errors, drift between checks, buoyancy, thermal effects and detailed hysteresis. It is not a coverage interval or certified uncertainty. A spatially uniform map appears flat by design in its named demo.

Frozen external references and raw replay

Replay exported JSON or CSV

Raw channels retain nominal amperes, volts, metres, projected metres per second, null error, gravity input, magnetic-history state and elapsed seconds. Electrical scale and zero corrections, length and velocity scales, optical angle, gravity and the independent known mass are declared external metrology inputs. Josephson and quantum Hall standards label their calibration origin; their devices are not simulated. CSV embeds the complete reference metadata; CSV and JSON both reproduce the same raw-only reconstruction. Earlier observations and references remain frozen after controls or Reset change the apparatus.

Virtual power, geometry and omissions

Current is measured at rest and induced voltage with an open circuit during a different stroke. Their product represents virtual power. The force-mode mechanical power and velocity-mode electrical load power are each zero. Coil radius is fifty-five millimetres with one hundred sixty ideal turns. Millimetre geometry is shown with exaggerated winding and beam thickness. The rear half of the yoke is exposed as a cutaway. The optical path ends on the actual moving reflector and returns to the collector front; only its velocity projection is modelled, not interference fringes. A smooth divergence-free field supplies force and emf through one flux function; this is not a material magnet or finite-element field design. Current heating, finite winding area, self-inductance, turnaround acceleration, vibration and detailed hysteresis dynamics are omitted.

Physics tutorial

## Move the coil, then support the mass

**Background** A circular coil sits in a radial field. Circumferential current produces vertical force; vertical motion changes the linked magnetic flux and induces voltage.

**Why it matters** Measuring field strength and wire length separately is difficult. Their common geometric factor can instead be determined by motion.

Start with the essentials

- **Focus question**: When do both modes share the same magnetic factor?
- **One-sentence intuition**: Elimination requires matching working geometry and magnetic state, or an independently checked measured correction.

### Core mathematical model

#### Null weighing

$$
mg=\mathcal G_w I
$$

Positive current produces upward support. The factor belongs to the weighing position and magnetic state. Mechanical power is zero at rest.

#### Open-circuit velocity measurement

$$
U=\mathcal G_v(z)v
$$

Upward velocity and its induced emf polarity are positive. The optical projection is converted into vertical velocity using external angle metrology.

#### Equal factors give virtual power

$$
mgv=UI\quad(\mathcal G_w=\mathcal G_v)
$$

Current and voltage come from separate modes. Their product expresses virtual power rather than simultaneous conversion of gravitational power into electrical power.

#### Measured correction within the scan

$$
\widehat m=\frac{I}{g}\operatorname{interp}_{z_w}\!\left(\frac{U(z)}{v(z)}\right)
$$

Only retained voltage, position and velocity enter interpolation. A weighing position outside the map or a failed independent mass check withholds the supported mass.

### Common difficulties

#### Can the factor always cancel?

**Typical misconception** Using the same symbol in two equations guarantees cancellation.

**Better mental model** Both factors must describe the same geometry and magnetic state. Otherwise independent observations must establish their relationship.

#### Is power flowing simultaneously?

**Typical misconception** During weighing, gravitational mechanical power becomes electrical power.

**Better mental model** The coil is stationary during weighing and open circuit during velocity measurement. The current and voltage are multiplied after the separate measurements.

### Run the experiment

1. 01

   #### Follow the same coil

   Switch between Velocity and Weighing.

   **What to observe:** Velocity mode parks the mass and opens the circuit. Weighing returns the mass to the pan and holds the coil at null.

2. 02

   #### Drag the coil

   Hold the copper coil, drag vertically and save a two-mode measurement.

   **What to observe:** The current mode’s working position changes continuously. The next acquisition retains the changed map and weighing observations.

3. 03

   #### Separate the working positions

   Choose Different positions sample different fields.

   **What to observe:** Using the scan center directly biases mass. Measured interpolation works when the weighing position lies inside the scan.

4. 04

   #### Tilt the optical axis

   Choose A tilted optical axis.

   **What to observe:** The beam still lands on the moving reflector. External angle calibration converts the measured optical projection into vertical velocity.

5. 05

   #### Change magnetic history

   Choose Current changes the magnetic state.

   **What to observe:** The raw curves and current remain available. The independent known-mass check fails and the supported mass is withheld.

Physical conclusion

At the weighing position, divide induced voltage by vertical velocity, multiply by weighing current and divide by local gravity.

## Related experiments and articles

How physics instruments measure · Reading path

### How physics instruments measure

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why a Kibble balance needs two experiments**](https://sandboxphysics.com/stories/instruments/kibble-balance/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)