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There is a good
reason for this; nothing necessarily flows when a magnetic field changes
in a region of space. It is true that a time-changing magnetic flux
mathematically acts as a source for a non-longitudinal (non-irrotational,
maybe rotational?) electric field (EMF), but that doesn't give us license
to call it a current. Since we do not regard a time-changing magnetic
flux as the flow of some kind of magnetic displacement current, then
neither should we regard a time-changing electric flux as the flow of some
kind of electric displacement current, even though it mathematically
acts as a source for a non-longitudinal magnetic field.