I 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 'Angular Momentum Vector and Its Magnitude'

For the quantum state ##|l,m\rangle= |2,0\rangle## the z-component of angular momentum is zero and ##|L^2|=6 \hbar^2##. According to uncertainty it is impossible to determine the values of ##L_x, L_y, L_z## simultaneously. However, we know that ##L_x## and ## L_y##, like ##L_z##, get the values ##(-2,-1,0,1,2) \hbar##. In other words, for the state ##|2,0\rangle## we have ##\vec{L}=(L_x, L_y,0)## with ##L_x## and ## L_y## one of the values ##(-2,-1,0,1,2) \hbar##. But none of these...
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