Analytical solutions to pulsed eddy current field excited by a differently oriented probe coil outside a conducting ferromagnetic pipe

Using the second-order vector potential and Lorentz reciprocity theorem, the non-axisymmetric eddy current field induced by a probe coil outside a conducting ferromagnetic pipe is obtained analytically, where the probe coil is differently oriented: its axis being along the pipe radial direction, parallel to the pipe axis, along the pipe circumferential direction. Then, the time-domain expressions of induced voltage and eddy current density in the pipe are obtained through the Laplace inverse transformation, by calculating the residues of poles. Furthermore, the diffusion process of pulsed eddy current in the pipe, and the detection sensitivity of the time-domain induced voltage signal to the wall thickness are studied. Finally, the analytical solutions are verified through the experimental results of a steel pipe. It is found that when the probe coil is positioned such that its axis is perpendicular to the pipe axis, the strongest and the most sensitive induction voltage signal for detecting the wall thickness of a ferromagnetic pipe is obtained.