IN40 · Separate a sideways voltage

Four-probe Hall measurement

How can reversing a magnet expose a misplaced voltage contact? Ordinary contact misalignment picks up a voltage that keeps its sign when only the magnetic field reverses. The Hall contribution changes sign. Reversing both current and field separates these patterns, with extra checks for drift and heating.

Move a contact on a rectangular conducting sheet. Follow its potential and current, then reverse current and field to separate geometric pickup from a Hall response.

Reverse the field, keep the contacts

Sheet resistance

1000\,\Omega

Bulk resistivity

0.01\,\Omega\,\mathrm m

Signed Hall coefficient

-0.001\,\mathrm{m^3/C}

One-carrier interpretation

\text{electron-like}

Current amplitude

100

Field amplitude

0.5

Contact two displacement

0

Sheet thickness

10

Drag gold contact two, or use arrow keys. Markers follow conventional current at a schematic speed.

Geometry, calibration and interpretation

Finite rectangular van der Pauw sheet; four ideal point-like ohmic perimeter contacts. Clamps and thickness are enlarged. Potential excludes singular source points. Finite/inset pads need another boundary solver.

Signed voltage is red lead two minus black lead four for current one to three. Positive field points toward the front face. Independent voltage, current, field and thickness references include distinct heldouts.

The ordinary Hall interpretation assumes a uniform isothermal sheet. Odd-current odd-field thermal signals can survive reversal. Density requires one carrier and Hall factor one; several populations may share the same slope.

Model assumptions

A homogeneous, isotropic, isothermal rectangular thin sheet has four ideal point-like ohmic perimeter contacts. A finite-rectangle Neumann Green solution supplies the zero-field potential and conserved sheet current; its stream function supplies the Hall potential. Contact shapes and thickness are enlarged. Source-point potentials are singular and excluded from drawing; finite pads, contact resistance, total contact power, thermal gradients and anisotropic transport are not solved. Voltage contacts draw no current. Independent voltage, current, magnetic-field and thickness standards include distinct heldouts. Inference reads saved channel voltages and actual times, with current/field reversal, drift and even-field nuisance terms. Large/inset/overlapping contacts and nonuniform sheets are unsupported. Reversal cannot exclude every odd-current odd-field thermal contribution. Hall density and carrier labels are conditional on ordinary one-carrier transport with Hall factor one; multiband data can give the same low-field slope. A nonlinear two-band example and absent-field example retain raw readings and supported resistance while withholding a linear Hall result. Synthetic Gaussian channel noise and settling times are teaching choices, not instrument specifications or traceable certification.

Voltages retained through reversal

Import

Measurement shown below

Cyan: positive current. Gold: negative current. Points are calibrated retained observations.

Raw channels, actual times and independent standards

Each window retains eight synchronous voltage/current/field channel readings and actual timestamps. CSV preserves all raw readings and reference metadata; JSON also labels a separate generating reference.

Scroll the table sideways, or focus it and use the arrow keys, to read every channel.

Selected run, final eight windows; readback channels are volts
End / s	Wiring	Voltage / V	Current ADC / V	Field ADC / V

Start with the essentials

Focus question: Which changes in the same voltmeter readings separate misalignment from Hall response?
One-sentence intuition: Ordinary geometric pickup reverses with current; a Hall contribution reverses with either current or magnetic field.

Core mathematical model

Red lead minus black lead

V_{24}=\phi_2-\phi_4,\qquad V_{24}^{\mathrm H}=R_{\mathrm H}IB/t

Current enters left contact one and leaves right contact three. Positive field points toward the viewer. Red contact two is below black contact four; swapping leads reverses the reading.

Four perimeter contacts determine sheet resistance

e^{-\pi R_A/R_s}+e^{-\pi R_B/R_s}=1,\qquad\rho=R_s t

Adjacent source and voltage configurations determine two transfer resistances. The van der Pauw relation assumes a homogeneous, thin, hole-free plate and small ohmic perimeter contacts. Bulk resistivity also requires independent thickness.

Common difficulties

A transverse reading

Typical misconceptionA voltmeter across the sheet measures only Hall voltage.

Better mental modelMisalignment adds longitudinal pickup, and temperature gradients add thermoelectric voltage. Reversal, reciprocity and thermal conditions constrain the interpretation.

Carrier population

Typical misconceptionOne Hall slope always counts the real carriers.

Better mental modelDifferent carrier populations and mobilities can produce the same low-field slope. Density conversion is conditional on one carrier and Hall factor one.

Run the experiment

01
Check polarity
Choose the electron-like preset and inspect the contact view.
What to observe: The bottom red lead reads a negative Hall contribution relative to the upper black lead. Field reversal changes that contribution’s sign.
02
Displace a contact
Hold gold contact two and drag along the edge.
What to observe: Its physical position and geometric pickup change together. The extracted Hall slope stays stable under the supported conditions.
03
Let the meter drift
Choose the drifting-voltmeter preset.
What to observe: The fit uses saved actual times to separate a linear drift from reversal dependence.
04
Test the interpretation
Compare the two-carrier and no-field presets.
What to observe: Unsupported linear Hall conclusions disappear while raw voltages and sheet resistance remain available.
05
Replay an older run
Keep a run, move a contact, then select the older run and export.
What to observe: Its readings and calibration remain unchanged through current controls, recalibration and reset.

Four-probe Hall measurement

Voltages retained through reversal

Reverse current and field separately

Core mathematical model

Red lead minus black lead

Four perimeter contacts determine sheet resistance

Common difficulties

A transverse reading

Carrier population

Run the experiment

Check polarity

Displace a contact

Let the meter drift

Test the interpretation

Replay an older run

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