Electromagnetic interaction between a conducting cylinder and a solenoid in relative motion

An analysis is presented for the mutual impedance between two solenoids that are coaxial with a conducting cylinder in relative motion. The formulation is based on the first‐order Lorentz transformation and the results obtained are sufficiently general to encompass any such situation that could arise in nondestructive‐testing schemes. A numerical example, relevant to steel‐wire ropes of 2‐cm radius used in mine hoists, indicates that even with relative velocities as high as 10 m/s, the mutual impedance at 10 Hz differs little from that calculated for zero velocity. However, the nonreciprocal effects could be significant for higher velocities and/or for more highly conducting and larger ropes.