Abstract
The paper provides a closed-form expression (the General Formula) for the electric field in a Hall plate. The parameters entering in this formula are the images of the contacts extremities in the conformal map into the upper half-plane (canonical domain) and also a number of real unknown constants equal to the number of contacts. The paper gives also formulas for computing the voltages and currents at contacts of the Hall plate. Since the unknown constants are connected in a linear manner with the terminal voltages and the currents, the General Formula can be used for modeling a large variety of Hall devices. Finally, the explicit calculations require the quadrature of some analytic functions having integrable singularities.
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Dorel Homentcovschi was retired from Binghamton University, USA.
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Homentcovschi, D., Bercia, R. Analytical solution for the electric field in Hall plates. Z. Angew. Math. Phys. 69, 97 (2018). https://doi.org/10.1007/s00033-018-0989-7
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DOI: https://doi.org/10.1007/s00033-018-0989-7
Keywords
- Complex variable method
- Boundary-value problem in the complex half-plane
- Closed-form solution
- Hall plates