Undergrad Quantum Hall Effect and Hall Voltage

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The Quantum Hall Effect describes the relationship between transverse and longitudinal resistance in a magnetic field. Hall resistance is defined as the ratio of Hall voltage to current, Rhall = Vhall/I, which can be confusing since current is not a vector. The Hall resistance represents the opposition to charge flow across the conductor due to the magnetic field, distinct from longitudinal resistance. The discussion highlights a common misunderstanding of how Hall voltage relates to traditional concepts of resistance. Clarifying these concepts can enhance understanding of the Quantum Hall Effect and its implications.
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I understand that the Quantum Hall Effect explains how both the transverse and longitudinal resistance vary with magnetic field strength.

I don’t get why the hall resistance is equal to the hall voltage over the current .


I know current isn’t a vector quantity but isn’t the hall resistance an opposition to the charge flow that goes across the conductor due to the magnetic field?

I have read that Ohm’s Law has nothing to do with Hall Voltage but I can’t understand why Rhall=Vhall/I

I would only think the longitudinal resistance would be an opposition to the current I.

What is wrong with the way I am visualizing this?
 

Thread 'One does not “prove” the basic principles of Quantum Mechanics'

I am slowly going through the book 'What Is a Quantum Field Theory?' by Michel Talagrand. I came across the following quote: One does not" prove” the basic principles of Quantum Mechanics. The ultimate test for a model is the agreement of its predictions with experiments. Although it may seem trite, it does fit in with my modelling view of QM. The more I think about it, the more I believe it could be saying something quite profound. For example, precisely what is the justification of...
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