In the Hall Effect current is passed through a wide strip of metal in a perpendicular magnetic field. Since (some of) the negative charges in the metal move but the positive ones stay put, the magnetic field will cause a potential difference between the two sides of the strip:

Source www.nde-ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Measuring.htm

How can this potential difference be measured? Can we simply connect a thin wire transversally between the two sides of the strip and see a current flow through it?

If no, then what prevents the current from flowing?

If yes, then aren't we getting something for nothing here? Our thin wire has some resistance -- where does the energy lost as heat in the wire come from? Does the total resistance of the primary circuit increase because we connect a wire between the two sides? Increased DC resistance because we add more conducting material to the system seems to be counterintuitive.

Image Source: https://www.nde-ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Measuring.htm, via Jahan Claes.

  • $\begingroup$ I'm not sure the current title capture the subtlety of what is being asked here, but I haven't a better suggestion just now. $\endgroup$ – dmckee Jul 9 '16 at 18:43
  • $\begingroup$ @dmckee: Hmm, I've attempted to improve it. $\endgroup$ – Henning Makholm Jul 9 '16 at 18:50
  • $\begingroup$ I think that's better. And in that form it seems like the answer should be trivially "yes", which leads us right to your questions of energy and resistance. $\endgroup$ – dmckee Jul 9 '16 at 18:54
  • $\begingroup$ "Does the total resistance of the primary circuit increase because we connect a wire between the two sides?" I don't follow. Assuming an ideal voltage source, an increase in the primary circuit resistance would reduce the power delivered by the voltage source, not increase it. $\endgroup$ – Alfred Centauri Jul 11 '16 at 13:44
  • $\begingroup$ @AlfredCentauri: Consider an ideal current source instead, then. (The Hall effect is current-dependent, after all, so it makes sense to keep that constant). In order to deliver the additional energy to heat up the transverse wire, the voltage would need to increase for the same current; thus increased resistance. $\endgroup$ – Henning Makholm Jul 11 '16 at 13:46

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