The voltage changes perpendicular to the current when magnetic field is applied.
Figure 1.
Hall effect experimental diagram
. Source. The Hall effect refers to the produced voltage , AKA on this setup.
An intuitive video is:
The key formula for it is:
where:
Applications:
  • the direction of the effect proves that electric currents in common electrical conductors are made up of negative charged particles
  • measure magnetic fields, TODO vs other methods
Other more precise non-classical versions:
In some contexts, we want to observe what happens for a given fixed magnetic field strength on a specific plate (thus and are also fixed).
In those cases, it can be useful to talk about the "Hall resistance" defined as:
So note that it is not a "regular resistance", it just has the same dimensions, and is more usefully understood as a proportionality constant for the voltage given an input current:
This notion can be useful because everything else being equal, if we increase the current , then also increases proportionally, making this a way to talk about the voltage in a current independent manner.
And this is particularly the case for the quantum Hall effect, where is constant for wide ranges of applied magnetic field and TODO presumably the height can be made to a single molecular layer with chemical vapor deposition of the like, and if therefore fixed.

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