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For thin cracks, in eddy current testing (ECT), the field‐flaw interaction is equivalent to a current dipole layer on its surface. The dipole density is the solution of an integral equation with a hyperstrong kernel. The variation of coil impedance and eddy current distribution is directly obtained from this density by a surface integration. There is a numerical difficulty to evaluate accurately integrals for the current density near the crack. In fact, due to the singular kernel of a dyadic Green function, the integration is quasi‐singular. A specific regularisation algorithm is developed to overcome this problem and applied to represent eddy current distribution between two cracks.

The classical ϕ‐a formulations for numerical dosimetry of currents induced by extremely low frequency magnetic fields requires that the source field is provided through a vector potential. The purpose of this paper is to present a new formulation t‐b which directly takes the flux density as source term.

This formulation is implemented through finite element and validated by comparison with analytical solutions. The results obtained by both formulations are compared in the case of an anatomical computational phantom exposed to a vertical uniform field.

A good agreement between the t‐b formulation and both numerical and analytical computations was found.

This new formulation seems to be more accurate than the ϕ‐a formulation, and is more suited for situations where the magnetic field is known from experimental measurements, as there is no need for a magnetic vector potential.