Crossed Fields: The Hall Effect — Question 5

Question 5

Field reversal removes an even voltage offset from a Hall reading

At fixed positive current, a strip gives measured transverse voltages +.820 mV at +B and -.580 mV at -B. Model the measurement as $V_{\mathrm{meas}}(B)=V_0+V_H(B)$, with an unchanged offset V0 and odd Hall response.

1. Extract the true Hall voltage at +B and the offset.

2. If the +B reading alone were used to infer density, find the inferred-to-true density ratio in a one-carrier model.

Question 5 - Solution

Field reversal removes an even voltage offset from a Hall reading

(a) Method and calculation

$$V_H(+B)=\frac{V_{\mathrm{meas}}(+B)-V_{\mathrm{meas}}(-B)}2=.700\,\mathrm{mV}.$$$$V_0=\frac{V_{\mathrm{meas}}(+B)+V_{\mathrm{meas}}(-B)}2=.120\,\mathrm{mV}.$$

(b) Interpretation and further calculation

$$n\propto1/|V_H|.$$$$\frac{n_{\mathrm{naive}}}{n_{\mathrm{true}}}=\frac{.700}{.820}=\frac{35}{41}\simeq.8537.$$

Physical check

Field reversal removes the assumed even offset; it does not automatically remove a contribution that is odd in B.