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A mathematical analysis of the magnetic field produced by flaws in two-dimensional current-carrying conductors

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Abstract

We examine the magnetic field produced by small flaws in a two-dimensional, conducting plate carrying an otherwise-uniform current. We use a conjugate function approach to calculate the current and voltage distributions about the circular and elliptical flaws in the conducting plate, and examine the dependence of the normal component of the magnetic field upon distance, hole size, elliptical eccentricity, and elliptical orientation. We show that when the field is calculated, far from the hole, the field falls off as 1/z 3, wherez is the distance above the plate, and as 1/r 2, wherer is the distance from the center of the hole to the observation point. We also show that for circular and elliptical flaws, the normal component of the magnetic field in the far-field region is linearly related to the area of the flaw.

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Authors and Affiliations

  1. Electromagnetics Laboratory, Department of Physics and Astronomy, Vanderbilt University, Station B, Box 1807, 37235, Nashville, Tennessee

    Nestor G. Sepulveda, Daniel J. Staton & John P. Wikswo Jr.

Authors
  1. Nestor G. Sepulveda
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  2. Daniel J. Staton
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  3. John P. Wikswo Jr.
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Sepulveda, N.G., Staton, D.J. & Wikswo, J.P. A mathematical analysis of the magnetic field produced by flaws in two-dimensional current-carrying conductors. J Nondestruct Eval 11, 89–101 (1992). https://doi.org/10.1007/BF00568292

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  • DOI: https://doi.org/10.1007/BF00568292

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