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In eddy current non-destructive testing, using ferrite cores with different shapes produce interesting and very important predictions on locating underneath cracks, corrosions and flaws in conductive layers. This paper describes a method of calculating magnetic vector potential for an E-cored eddy current probe above a layered half space. The coil impedance variation with frequency and eddy currents are determined. The results of the calculations are in very good agreement with results from COMSOL.