The Hall coefficient RH of a sample can be determined from the measured Hall voltage \(V_H=\frac{1}{d} R_H B I+R I \text {, }\)where d is the thickness of the sample, B is the applied magnetic field. I is the current passing through the sample and R is an unwanted offset resistance. A lock-in detection technique is used by keeping I constant with the applied magnetic field being modulated as B = B0sinΩt, where B0 is the amplitude of the magnetic field and Ω is frequency of the reference signal. The measured VH is
1
\(B_0\left(\frac{R_H I}{d}\right)\)
2
\(\frac{B_0}{\sqrt{2}}\left(\frac{R_H I}{d}\right)\)
3
\(\frac{I}{\sqrt{2}}\left(\frac{R_H B_0}{d}+R\right)\)
4
\(I\left(\frac{R_H B_0}{d}+R\right)\)