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# A significant amount of work concerns models of coils

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A significant amount of work concerns models of coils that have shapes other than the classical cylindrical coil or positions that destroy the axisymmetry. A problem of great interest is the evaluation of the three-dimensional electromagnetic field for a coil with an arbitrary shape and orientation above a conducting half space. 70 Electromagnetic Testing F IGURE 5. Plate separation in system of two plates: (a) setup; (b) transient electric potential. Depicted signal is coil voltage subtracted from response of same coil due to conducting half space. Percentage of parameter variation is in terms of thickness of one slab. (a) Coil Reference sample Plate separation Transient electric potential (V) 20 15 10 5 0 –5 0 100 200 300 400 500 Time (μs) Coil Test sample (b) Legend = 50 percent = 37.5 percent = 25 percent = 12.5 percent = 0 percent F IGURE 6. Bottom plate metal loss above system of two plates: (a) setup; (b) transient electric potential. Depicted signal is coil voltage subtracted from response of same coil due to conducting half space. Percentage of parameter variation is in terms of thickness of one slab. (a) Coil Reference sample Bottom plate metal loss Transient electric potential (V) 25 20 15 10 5 0 –5 0 100 200 300 400 500 Time (μs) Coil Test sample (b) Legend = 50 percent = 37.5 percent = 25 percent = 12.5 percent = 0 percent

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Weaver 32 presented a general theory of electromagnetic induction in a conducting half space by an external magnetic source using the electric and magnetic hertz vectors whereas Hannakam 33 provided solutions for a filamentary coil using the similar second order vector potential formulation. Based on the latter formulation, Kriezis 34 evaluated the eddy current density induced in a conducting half space by a filamentary coil whose axis is parallel to the surface. Other researchers like Beissner 35 and Bowler 36 have favored Green’s dyadic functions in solving the problem. Bowler was able to present analytical expressions for the eddy current density of a vertically oriented cylindrical coil over a conducting half space, thus extending the results of Kriezis to an eddy current probe coil of finite cross section. Beissner 37 and Tsaknakis 38 presented formulas for the eddy current distribution from cylindrically symmetric sources inclined at an arbitrary angle with respect to the surface normal. The general solution for a nonsymmetric source is in the form of a two-dimensional fourier integral. Numerical computations for the nonsymmetric case are therefore more demanding than those needed to evaluate fields from Dodd and Deeds formulas, where the integrals are one-dimensional. A semianalytical model was also presented by Juillard 39 for the same problem where the coil is divided in a number of elements called point current sources. The problem is solved for each point current source and superposition is applied to compute the electromagnetic field from the whole coil. Another technique for computing the magnetic field, based on the fourier transform, was presented by Panas 40 and Sadeghi, 41 who solved the problem of an elliptical coil and a
• Fall '19
• Wind, The Land, Magnetic Field, Dodd, Modeling of Electromagnetic Testing

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