Point Source and Sink in a Parallelepiped


THE potential distribution in a parallelepiped arising from a point source and sink is of practical importance in the measurement of the thickness of plates and tubes1,2, and the electrical conductivity of semiconductors3. A common practical arrangement employs four collinear equi-spaced contacts: current I is passed between the outer pair, and the potential difference V between the inner pair is measured. If the contacts are aligned centrally parallel to the longest side 2α of a rectangular block of material, its width being 2β and its thickness γ in units of the electrode spacing, the conductivity is given by the triple series:

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  1. 1

    Thornton, B. M., and Thornton, W. M., Proc. Inst. Mech. Eng., 140, 349 (1938).

  2. 2

    Warren, A. G., J. Inst. Elect. Eng., 84, 91 (1939).

  3. 3

    Valdes, L. B., Proc. Inst. Rad. Eng., 42, 420 (1954).

  4. 4

    Van der Hoff, B. M. E., and Benson, G. C., Can. J. Phys., 31, 1087 (1953).

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SIM, A., LEWIN, L. Point Source and Sink in a Parallelepiped. Nature 174, 1155 (1954). https://doi.org/10.1038/1741155a0

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