In one of his lectures, Professor Walter Lewin is ammending Ampère's Law to include displacement current (i.e. It not only depends on the current that penetrates the loop, but also on the changing electric field.)
For this he has a capacitor inbetween a wire with a current, and he shows that the magnetic field B on a point above the wire is the same whether he chooses an open surface that goes inbetween the capacitor or a flat, circular surface that stays around the wire.
He says that, for a given point P above the wire (for which he chooses a circular, flat Amperian loop around the wire first, with radius coinciding with distance to P) the magnetic field B does not take into account the displacement current, because the Electric Flux is zero!
How can the Electric Flux be zero through that closed loop? There is an Electric Field inside the conducting wire going through the loop!
2 or 3 people asked him in the comments and he said he couldn't give any more clarity.
https://youtu.be/3sP9kh4xtKo it's between 10:20 and 11:00
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