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The Quarterly Journal of Mechanics and Applied Mathematics 1951 4(1):23-28; doi:10.1093/qjmam/4.1.23
© 1951 by Oxford University Press
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THE RESISTANCE OF A RECTANGULAR METAL PLATE WITH AN INTERNAL ELECTRODE

S. D. DAYMOND

( Mathematical Institute, The University Liverpool )

A steady current enters a rectangular metal sheet through a small circular internal electrode and flows out through an electrode which coincides with the rectangular boundary. The problem of finding the effective resistance is essentially that of determining a harmonic function {Phi} which is constant over each electrode. The appropriate complex potential function is expressible in Jacobean elliptic functions; the {delta}-functions, however, are found to be more suitable for the numerical work involved, and are used below. Altogether there are four parameters (two of these are coordinates of position of the inner electrode); numerical values of the resistance are found, therefore, only for certain special but representative values of these parameters. A brief discussion of the numerical results occurs at the end.


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