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The total voltage around the loop is unchanged. The local
voltage-drops are re-arranged: a little more voltage-drop
here and a little less there.
This is easily visualized by considering a C-shaped conductor
in a changing magnetic field. Choose a loop that follows the
shape of the C, inside the material except where it has to cross
the gap. There will be no field in the bulk of the conductor.
There will be a concentrated field in the gap.