Physics 152 Winter 1999
1) Describing the classical Hall Effect was a terse but good method for introducing the Quantum Hall effect. Although no difficulties arose, the coordinate system defined in figure (1) is not a right-handed system. The explanation of the quantum Hall effect was good and had the necessary figures and equation to support the description. Perhaps enumerating the equations would make referring to them easier. All aspects of the behavior of the Hall voltage vs. magnetic field were discussed. The paper concluded in a great discussion of the usefulness of the QHE as a means for calculating the fine structure constant.
Question: The voltage V in figure (2) appears to have a distinct relation to the Hall voltage VH. That is, V appears to roughly be the slope of the Hall voltage VH. What is the exact mathematical relation?
1)
The longitudinal voltage, V, isn't the slope of the Vh vs B plot but it
is directly proportional to the slope. For the classic Hall effect, the
relationship is as follows:
Vh = (Ly*mobility/Lx)*V*B
You can see that the slope involves the voltage V and someother values
that are all constant such as the mobility and the length and width of
th sample.