Mutual inductance between an infinite solenoid and a surrounding loop—A paradox resolved

Abstract

Students may calculate the mutual inductance between an infinite solenoid and a surrounding circular loop using an incorrect method that yields the correct answer, causing frustration and confusion. A physical explanation for the agreement of the two methods is provided that is based on the translational symmetry of the solenoid. As a consequence, the conclusion generalizes to infinite uniform solenoids of arbitrary cross section.