Crossed Fields: The Hall Effect — Question 8

Question 8

Four current-field reversals isolate the Hall term from two independent pickup terms

Let s and b be signs of applied current and magnetic field. Model four readings as $V(s,b)=V_0+sA+bC+sbH$, where H is the desired Hall voltage at positive current and field. Measured values in mV are V(+,+)=1.30, V(+,-)=-.70, V(-,+)=-.30 and V(-,-)=.50.

1. Construct a signed combination that isolates H and evaluate it.

2. Find V0, A and C and verify one reading from the reconstructed model.

Question 8 - Solution

Four current-field reversals isolate the Hall term from two independent pickup terms

(a) Method and calculation

$$H=\tfrac14[V_{++}-V_{+-}-V_{-+}+V_{--}].$$$$H=\tfrac14[1.30+.70+.30+.50]=.700\,\mathrm{mV}.$$

(b) Interpretation and further calculation

$$V_0=.200\,\mathrm{mV},\quad A=.100\,\mathrm{mV},\quad C=.300\,\mathrm{mV}.$$$$V_{++}=V_0+A+C+H=.200+.100+.300+.700=1.30\,\mathrm{mV}.$$

Physical check

The Hall term is odd under either reversal and even under reversing both; the algebra projects out exactly that symmetry.