  We revisit the various approximations employed to study the long-term
evolution of the magnetic field in neutron star cores and discuss their
limitations and possible improvements. A recent controversy on the correct form
of the induction equation and the relevant evolution timescale in
superconducting neutron star cores is addressed and clarified. We show that
this ambiguity in the estimation of timescales arises as a consequence of
nominally large terms that appear in the induction equation, but which are, in
fact, mostly irrotational. This subtlety leads to a discrepancy by many orders
of magnitude when velocity fields are absent or ignored. Even when internal
velocity fields are accounted for, only the solenoidal part of the electric
field contributes to the induction equation, which can be substantially smaller
than the irrotational part. We also argue that stationary velocity fields must
be incorporated in the slow evolution of the magnetic field as the next level
of approximation.
