Journal of Applied Mathematics and Physics

Volume 7, Issue 10 (October 2019)

ISSN Print: 2327-4352   ISSN Online: 2327-4379

Google-based Impact Factor: 1.00  Citations  

The Classical Hall Effect in Multiply-Connected Plane Regions Part II: Spiral Current Streamlines

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DOI: 10.4236/jamp.2019.710153    674 Downloads   1,763 Views  Citations
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ABSTRACT

Multiply-connected Hall plates show different phenomena than singly connected Hall plates. In part I (published in Journal of Applied Physics and Mathematics), we discussed topologies where a stream function can be defined, with special reference to Hall/Anti-Hall bar configurations. In part II, we focus on topologies where no conventional stream function can be defined, like Corbino disks. If current is injected and extracted at different boundaries of a multiply-connected conductive region, the current density shows spiral streamlines at strong magnetic field. Spiral streamlines also appear in simply-connected Hall plates when current contacts are located in their interior instead of their boundary, particularly if the contacts are very small. Spiral streamlines and circulating current are studied for two complementary planar device geometries: either all boundaries are conducting or all boundaries are insulating. The latter case means point current contacts and it can be treated similarly to singly connected Hall plates with peripheral contacts through the definition of a so-called loop stream function. This function also establishes a relation between Hall plates with complementary boundary conditions. The theory is explained by examples.

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Ausserlechner, U. (2019) The Classical Hall Effect in Multiply-Connected Plane Regions Part II: Spiral Current Streamlines. Journal of Applied Mathematics and Physics, 7, 2231-2264. doi: 10.4236/jamp.2019.710153.

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