The flux Φ Φ through the surface delimited by a coil turn exists independently of the presence of the coil. Furthermore, in a thought experiment with a coil of N turns, where each turn forms a loop with exactly the same boundary, each turn will "link" the "same" (identically, not merely the same quantity) flux Φ Φ , all for a total flux linkage of λ λ = N Φ Φ . The distinction relies heavily on intuition, and the term "flux linkage" is used mainly in engineering disciplines. Theoretically, the case of a multi-turn induction coil is explained and treated perfectly rigorously with Riemann surfaces : what is called "flux linkage" in engineering is simply the flux passing through the Riemann surface bounded by the coil's turns, hence no particularly useful distinction between flux and "linkage".