Abstract
This paper considers the solution of the skin-effect or Helmholtz equation, ∇2ψ=k2ψ, for the two-dimensional flow of a uniform alternating current perturbed by a plane crack of uniform depth. Herek is the ratio of crack depthd to skin depth δ. When the skin depth is large compared with the crack depth andkf 0, the quasi-static approach to this problem ignores the terms on the right-hand side and constructs solutions from Laplace's equation which are essentially dc solutions and are correct to orderk. In this paper we consider behavior near the limit when the skin depth is large and give solutions which are correct to orderk2. In an example we relate the results to the interpretation of readings from an ac potential difference instrument applied to the measurement of surface-breaking cracks.
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