Hall Coefficient R_H

A Hall bar of known thickness and current, unknown R_H. Measure U_H at several B and recover R_H from the slope of U_H versus B. The sign names the carriers.

University / research· 24 min·Related simulator: Electricity & MagnetismHall Effect

Goal

Determine the Hall coefficient R_H from U_H = R_H I B / t. With I and t known, the slope of U_H versus B is R_H I / t, so R_H = slope · t / I.

Equipment

Hall bar (known t)
DC current source (known I)
Electromagnet (B)
Voltmeter (U_H)

Experiment

Hall bar. Current along the slab, B into the page. No live U_H on the bench.

Known current I = 2.50 A and thickness t = 0.80 mm. Carriers are electrons. B is into the page. The Hall voltage appears on the voltmeter only after you record.

Magnetic field |B||B| = 0.45 T

Voltmeter: no reading

Record at least 6 values of |B| across 0.15–1.20 T, then fit U_H versus B.

Measurements

№	\|B\| T	U_H V
No measurements yet — take your first reading.

Data processing

Add at least 2 measurements to compute the fit.

Uncertainty

Lab report

Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.

One click opens the print dialog — choose “Save as PDF”.

Hall Coefficient R_H

Generated: 24 Aug 2026, 22:28

Goal

Determine the Hall coefficient R_H from U_H = R_H I B / t. With I and t known, the slope of U_H versus B is R_H I / t, so R_H = slope · t / I.

Measurement table

#	\|B\| (T)	U_H (V)
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 measurements to compute the fit.

Conclusion

The fitted Hall coefficient is negative and agrees with −1/(n e) for the hidden electron density. Main uncertainties: voltmeter noise and the single-carrier slab model.

PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.

Theory

A single-carrier Hall bar gives U_H = R_H I B / t with R_H = −1/(n e) for electrons and +1/(n e) for holes. B is the field magnitude with a fixed “into the page” geometry, so electrons produce a negative U_H (top minus bottom). The bench hides U_H until you record and never shows R_H.

Procedure

Current I and thickness t are fixed and known. Carrier type is electrons. You only change |B|.
Record the voltmeter U_H (top − bottom). Small meter noise is added. Do not expect a live Hall-voltage readout while you drag B.
Repeat for at least 6 field values spread from about 0.15 T to 1.20 T.
Fit U_H versus B; R_H = slope · t / I. A negative R_H means electrons.
Compare with the reference coefficient.

Conclusion

The fitted Hall coefficient is negative and agrees with −1/(n e) for the hidden electron density. Main uncertainties: voltmeter noise and the single-carrier slab model.