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.

► A general method for acquiring analytical solutions for the eddy current field excited by a probe coil outside a metal pipe is presented.
► Closed-form expression for inner source coefficient Cs of a solenoid coil is deduced in the cylindrical coordinate system.
► We get expression for impedance change of an excitation coil.
► We get expression for induced electric tension in a pick-up solenoid coil.