What is the differential inductance of CAT-5 twisted pair? I.e., the voltage across the pair, measured at one end, when fed differentially, with net current along the cable = 0?

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What figure did you have in mind?
In particular are you talking about the difference in inductance between the two conductors, or are you talking about the small signal inductance in the differential calculus sense?
What does your transmission line model of CAT-5 cable suggest?