"Fractional Quantum Hall Effect" sounds intimidating,
but the basic ideas can be easily explained.
First of all, "Hall effect" refers to a phenomenon
(first reported by Hall in his Ph.D. thesis of 1880 and named thus)
observed in a conducting material carrying an electrical current in
the presence of a magnetic field.
Let us examine electrical conduction for the moment,
and include the effect of a magnetic field later.
An analogy is the flow of water down a slope.
The greater the height of the slope, the faster will be the flow,
which, on the other hand, is limited by scattering (splashing)
in the sloping channel - symbolised by stones in the schematic
diagram below, where a pump return the water to the high place,
to complete the circuit.
Likewise, in electrical conduction, the current (flow of water)
is proportional to the voltage (height of slope), but inversely
proportional to the resistance of the conductor (scattering of water).
Therefore, we can determine the unknown resistance R of a material by
measuring voltage V and corresponding current I:
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