Impedance of a Coil at an Arbitrary Position and Orientation Inside a Conductive Borehole or Tube

The impedance and electromagnetic field of a circularly cylindrical coil at an arbitrary position and orientation inside a cylindrical conductor, such as a borehole or tube, has been evaluated using analytical expressions. Previously, such expressions were available for two specific cases: one where the axis of the coil is parallel to the axis of the conductor and the other where the axes of the coil and conductor are perpendicular. In this paper, we consider the general case accounting for an arbitrary coil position and orientation. The analytical solution is made possible by successive transformations of the expressions for the coil field between spherical and cylindrical coordinate systems. The extended model is valuable for simulating eddy current inspections of boreholes and tubes with internal probes accounting for lateral movement and tilt.