---
title: "How current leaves a voltage across a thin sheet"
description: "A magnetic field pushes moving charge sideways. Follow probe geometry and reversal symmetry to see how a Hall voltage is separated from ordinary pickup."
canonical_url: "https://sandboxphysics.com/stories/instruments/four-probe-hall/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/instruments/four-probe-hall/"
last_modified: "2026-11-11"
---

[How physics instruments measure](https://sandboxphysics.com/stories/instruments/)

Inside the instrument

# How current leaves a voltage across a thin sheet

Pass a current through a thin sheet and a magnetic field through its face. Charge collects at the sides, creating a transverse voltage. A slightly misplaced probe can also pick up the ordinary voltage drop along the current. Reversing the field makes these contributions follow different patterns.

Sandbox Physics · 2026-11-11

## Moving charge accumulates at an edge

Picture a thin conducting strip carrying current from left to right. A perpendicular magnetic field pushes its moving charge sideways. Charge accumulating at an edge builds an electric field of its own. In steady state, the electric and magnetic forces balance across the strip, leaving a Hall voltage between its sides.

Conventional current follows the direction positive charge would travel. Electrons are negative and drift the other way. With a fixed current, field and voltmeter convention, electron-like and hole-like ordinary Hall responses can have opposite signs. A hole is a missing electron in a crystal whose motion behaves as a positive charge.

Sources: [1]

## A misplaced probe adds an ordinary voltage drop

A resistive sheet already has a potential gradient along the current. Two probes at the same longitudinal position compare its sides. Move one probe forward and the meter also spans part of that longitudinal drop. This contribution can exceed the small sideways voltage of interest.

Keep the current fixed and reverse only the magnetic field. An ordinary Hall contribution reverses sign. Longitudinal pickup from the same probe positions usually keeps its sign. Half the difference between the readings removes that field-even contribution.

A meter offset or a temperature difference introduces further voltages. Reversing current adds another symmetry test. Counterbalanced repeated sequences and actual timestamps help separate a slow drift. Waiting until the field has settled gives the comparison a definite physical meaning.

Sources: [2] [3]

## The red lead fixes what a positive reading means

Face the sheet with current entering on the left and leaving on the right. Let positive field point toward you. A red lead below and a black lead above read bottom potential minus top potential. Swapping them changes the displayed sign, even though the carriers are unchanged. Every material interpretation needs this wiring convention.

Sources: [3]

## Four contacts also determine resistivity

Four small contacts around a uniform sheet can alternate their jobs: two supply current and two sense voltage. Two adjacent configurations yield transfer resistances belonging to those connections. The van der Pauw relation combines them into a sheet resistance belonging to the film. It applies to rectangular, circular and other hole-free shapes under its small-perimeter-contact and uniform-thickness assumptions.

Separate current and voltage connections also reduce the influence of the contacts themselves. Current-carrying leads and interfaces have extra voltage drops. A high-input-resistance voltmeter takes very little current through its probes, so their reading mainly compares the two sheet potentials. The contacts can exchange jobs while preserving this separation.

Sheet resistance is useful for a film. An independent thickness measurement converts it into bulk resistivity. The voltmeter, current readback and field probe each need their own references as well. A further known value withheld from the calibration fit tests whether the scale works at another point.

Sources: [4] [1]

## One slope can combine several populations

For a simple single-carrier model, the Hall coefficient is related to carrier density by $R_{\mathrm H}=1/(nq)$. Here $q$ is the signed carrier charge. This interpretation also takes the Hall factor to be one. More carriers then need a smaller average drift to carry the same current, changing the Hall voltage.

Electrons and holes can conduct together. Their populations and mobilities both matter: a smaller but more mobile population can dominate the Hall sign. Different mixtures can even share the same low-field slope. Curvature over a wider field range, temperature dependence and additional measurements help distinguish them. A signed transport response becomes a carrier count only with the material assumptions attached.

Sources: [3]

## [Move a contact and compare four reversals](https://sandboxphysics.com/labs/four-probe-hall/)

Displace the lower contact, then compare field reversal with the two-carrier response.

A finite rectangular sheet with point-like perimeter contacts supplies potential, current and independently calibrated conditional Hall inference.

## Sources and further reading

1. [NIST — The Hall Effect](https://www.nist.gov/pml/nanoscale-device-characterization-division/popular-links/hall-effect/hall-effect)

   Read the Lorentz-force and van der Pauw sections: transverse charge, rectangular four-perimeter-contact plate, sheet/bulk quantities and practical assumptions. This is archived informational guidance, not a current certification service.

2. [Lake Shore — Hall Measurements with MeasureLINK-MCS Software, Rev 3.0 (2020)](https://test.lakeshore.com/docs/default-source/default-document-library/hall-measurements-with-measurelink-mcs-software.pdf?sfvrsn=d569e01b_6)

   Read pages5–11 on geometry/thickness, contact I–V, DC field reversal, current/SNR and settling after the field controller reports settled. Other pages are not claimed read.

3. [Lake Shore — Model 7600 manual, Rev 1.5 (2012), Appendix A](https://www.lakeshore.com/docs/default-source/software/manuals/hall-system-manual/7600_1-5.pdf)

   Read printed A1–A6 and A12–A14 (PDF97–102,108–110): Hall factor, four-contact conventions, reversal parity, multicarrier and finite-contact limitations.

4. [L. J. van der Pauw (1958) — A method of measuring specific resistivity and Hall effect of discs of arbitrary shape](https://aki.issp.u-tokyo.ac.jp/okano/WalWiki/etc/VDP_PRR_13_1.pdf)

   Visually read scanned printed pages3,4,6,8 for the exponential relation, reciprocity/current-stream argument and contact-error examples; no full-paper reproduction claim.

[How a vernier reads between millimetres](https://sandboxphysics.com/stories/instruments/length-metrology/) [Air helps hold up the object on a balance](https://sandboxphysics.com/stories/instruments/precision-balance/) [How Cavendish Measured the Attraction Between Spheres](https://sandboxphysics.com/stories/instruments/cavendish-balance/) [Which pressure does a liquid column measure?](https://sandboxphysics.com/stories/instruments/manometer/) [The cup absorbs heat too](https://sandboxphysics.com/stories/instruments/calorimeter/) [Rotational rheometers need both torque and speed](https://sandboxphysics.com/stories/instruments/rotational-rheometer/) [Why the air beyond a pipe changes its resonance](https://sandboxphysics.com/stories/instruments/resonance-tube/) [How a seismometer reads the ground through motion inside its case](https://sandboxphysics.com/stories/instruments/seismometer/) [Why does a meter change the circuit?](https://sandboxphysics.com/stories/instruments/electrical-meters/) [How a null detector reveals a resistance](https://sandboxphysics.com/stories/instruments/resistance-bridges/) [Why a capacitor can behave like an inductor](https://sandboxphysics.com/stories/instruments/lcr-impedance/) [Where does the slow wave on an oscilloscope come from?](https://sandboxphysics.com/stories/instruments/digital-oscilloscope/) [How a lock-in amplifier finds a signal buried in noise](https://sandboxphysics.com/stories/instruments/lock-in-amplifier/) [Where a small peak in a spectrum can come from](https://sandboxphysics.com/stories/instruments/spectrum-analyzer/) [How a network analyzer separates the cable from the device](https://sandboxphysics.com/stories/instruments/vector-network-analyzer/) [When a slower quartz crystal can measure added mass](https://sandboxphysics.com/stories/instruments/quartz-microbalance/) [How an echelle spectrograph gives overlapping colors a second direction](https://sandboxphysics.com/stories/instruments/echelle-spectrograph/) [How total brightness reveals many infrared colors](https://sandboxphysics.com/stories/instruments/ftir-spectrometer/) [Measuring a Solution’s Concentration with Light](https://sandboxphysics.com/stories/instruments/uv-vis-spectrophotometer/) [How an ellipsometer reads thin-film thickness from reflected light](https://sandboxphysics.com/stories/instruments/spectroscopic-ellipsometer/) [How a polarimeter reveals mixed polarization](https://sandboxphysics.com/stories/instruments/mueller-polarimeter/) [How individual photons reveal a fluorescence lifetime](https://sandboxphysics.com/stories/instruments/tcspc-fluorescence-lifetime/) [Brillouin Microscopy Listens to Sound with Light](https://sandboxphysics.com/stories/instruments/brillouin-microscope/) [How a white sphere compares a lamp’s total output](https://sandboxphysics.com/stories/instruments/integrating-sphere-radiometer/) [How powder rings reveal atomic spacing](https://sandboxphysics.com/stories/instruments/powder-xray-diffractometer/) [How Small-Angle X-ray Scattering Reads a Particle Halo](https://sandboxphysics.com/stories/instruments/small-angle-xray-scattering/) [Why X-ray fluorescence depends on sample thickness](https://sandboxphysics.com/stories/instruments/xray-fluorescence-spectrometer/) [Why an AFM makes a bump look wider](https://sandboxphysics.com/stories/instruments/atomic-force-microscope/) [How a small indentation separates hardness from elasticity](https://sandboxphysics.com/stories/instruments/nanoindenter/) [How Differential Scanning Calorimetry Reads a Melting Peak](https://sandboxphysics.com/stories/instruments/differential-scanning-calorimeter/) [How thermogravimetry separates mass loss from the gas around it](https://sandboxphysics.com/stories/instruments/thermogravimetric-analyzer/) [How a diamond anvil cell reads pressure in ruby light](https://sandboxphysics.com/stories/instruments/diamond-anvil-cell/) [How diamond fluorescence reveals a magnetic-field direction](https://sandboxphysics.com/stories/instruments/nv-center-magnetometer/) [Reading a magnetic field in the rhythm of atoms](https://sandboxphysics.com/stories/instruments/optically-pumped-magnetometer/) [Keeping a laser in time with atoms](https://sandboxphysics.com/stories/instruments/optical-lattice-clock/) [Why a Kibble balance needs two experiments](https://sandboxphysics.com/stories/instruments/kibble-balance/) [How a dilution refrigerator keeps carrying heat away](https://sandboxphysics.com/stories/instruments/dilution-refrigerator/) [Why a bigger vacuum pump may barely help the sample](https://sandboxphysics.com/stories/instruments/ultra-high-vacuum-system/) [How microwaves read a superconducting qubit](https://sandboxphysics.com/stories/instruments/superconducting-qubit-readout/) [How an ion flight becomes a mass spectrum](https://sandboxphysics.com/stories/instruments/time-of-flight-mass-spectrometer/) [How four straight rods select ion mass](https://sandboxphysics.com/stories/instruments/quadrupole-mass-filter/)