Quantum Hall Effect and Hall Voltage

[Salamon]

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?