Confusion about inner inductance of transmission line

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Jackson Lee
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I was reading textbook and felt confused about this-- when trying to deal with inner inductance of transmission line, only the fraction (x/r)^2 of total current, which interlock with magnetic lines should be considered. However, isn't the inductance or even flux linkage an intermediate term(correct me if I am wrong) to electromagnetic induction? If it so, why not we directly deal with flux instead of flux linkage, because as Faraday's law, the change rate of magnetic flux equals emf?
 
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And I really really really want to know the emf is the rate of change of magnetic flux or flux linkage?
 

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