Analytical solutions to eddy current field excited by a probe coil near a conductive pipe

Eddy current field excited by a probe coil near a conductive pipe is studied analytically by means of a second-order vector potential formalism in this paper. Closed-form expressions of the second-order vector potentials are deduced directly in the cylindrical coordinate system by using the Biot-Savart law and the reciprocal of distance described by the modified Bessel functions and exponential functions. Both the impedance change of an excitation coil and the induced voltage in a pick-up solenoid coil are obtained. The theoretical results are in excellent agreement with the experimental results, which verifies the analytical solutions.