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In the Physics Today article by Avron et.al. "A Topological Look at the Quantum Hall Effect" Physics Today (2003) it is suggested that to observe ordinary Hall effect, planar geometry is preferred to bar geometry as below. I am trying to understanding the reason behind this. Can someone help me? Any reference would be helpful too.

hasty experiment . . . though without success.”Hall made a fresh start and designed a different experiment, aimed at measuring, instead, the magneto- resistance—that is, the change of the electrical resistance due to the magnetic field. As we now know, that is a much harder experiment, and it too failed. Maxwell appeared to be safe. Hall then decided to repeat Rowland’s experiment.Following his mentor’s suggestion, Hall replaced the original metal conducting bar with a thin gold leaf, to compensate for the weakness of the available magnetic field.

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  • $\begingroup$ The Hall effect can be observed only in even spatial dimensions. Refer to the PRB by Qi, Hughes, and Zhang with the title: "Topological field theories of time reversal invariant insulators" $\endgroup$
    – NanoPhys
    Commented May 19, 2013 at 21:08
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    $\begingroup$ @NanoPhys: The question was about the ordinary Hall effect not the quantum Hall effect. Unless I am grossly mistaken, the ordinary Hall effect should be observable in any dimension in metals (not insulators like the QHE). $\endgroup$
    – BebopButUnsteady
    Commented Jun 26, 2013 at 19:31
  • $\begingroup$ Oops! I was a little hasty while reading the question. Sorry, my bad! Thanks @BebopButUnsteady $\endgroup$
    – NanoPhys
    Commented Jun 26, 2013 at 22:19

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Probably this is a simple geometric effect. The voltage is proportional to the width times the transverse electric field. The electric field is proportional to the current density. The current density is equal to current over (thickness times width). So when all is said and done the Hall voltage is inversely proportional to the thickness for a fixed current. Presumably the maximum current Hall could achieve was fixed, so by reducing the thickness he could increase the effect.

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