Analytical solution for the eddy current field due to an air-cored eccentric curved rectangular probe coil on the outside of a metal pipe

The analytical solution for the eddy current field due to an eccentric curved rectangular coil on the outside of a nonferromagnetic metal pipe is obtained in this paper. The model of eddy current field is established by a second order vector potential(SOVP) formalism, and the closed-form expressions of second order potential functions which contain the undetermined eccentric coil coefficient are achieved. In order to calculate the undetermined eccentric coil coefficient, the concentric coil coefficient is deduced through Biot-Savart law and the inverse distance in terms of modified Bessel functions at first. Then, the eccentric coil coefficient can be accessed based on the addition theorem of modified Bessel function. Using the SOVPs' closed-form expressions, induced voltage in an eccentric curved rectangular pick-up coil is computed. Experiments show that the theoretical expressions are in good agreement with the experimental measurements.