Question

will you measure the magnetic field when the cap is fully charged? or would you measure mag field as a function of time as the cap charges/discharges?

Answer 1

The reason for the introduction of the 'displacement current' was exactly to solve cases like that of a capacitor. A magnetic field cannot have discontinuities, unlike the electric field (there are electric charges, but there are not magnetic monopoles, at least as far as we know in the Universe in its current state). There cannot be a magnetic field outside the capacitor and nothing inside