Coil and resistor induction paradox

In my article Faraday’s Law Paradox, I have explained that in a magnetically induced coil the line integral of electric field is paradoxically zero in contraction with Faraday’s law. This paradox has aroused a long discussion which also reveals that the air gap between the coil’s terminals confused the understanding of the paradox. The closed coil below makes this paradox sharper. I will give my solution to this paradox.

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