Abstract
We have applied Maxwell's equations to study the physics of quantum Hall's effect. The electromagnetic properties of this system are obtained. The Hall's voltage, VH = 2πħ2ns/em, where ns is the electron number density, for a 2-dimensional system, and h = 2πħ is the Planck's constant, is found to coincide with the voltage drop across the quantum capacitor. Consideration of the cyclotronic motion of electrons is found to give rise to Hall's resistance. Ohmic resistances in the horizontal and vertical directions have been found to exist before equilibrium state is reached. At a fundamental level, the Hall's effect is found to be equivalent to a resonant LCR circuit with LH = 2π m/e2ns and CH = me2/2πħ2ns satisfying the resonance condition with resonant frequency equal to the inverse of the scattering (relaxation) time, τs. The Hall's resistance is found to be . The Hall's resistance may be connected with the impedance that the electron wave experiences when it propagates in the 2-dimensional gas.
Published Version
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