Two coils are wound around the same cylindrical form. When the current in the first coil is decreasing at a rate of $-0\mathrm{.}240$ A$/$sA$/$s$,$ the induced emf in the second coil has a magnitude of $1\mathrm{.}65103$ VV$.$ What is the mutual inductance of the pair of coils? If the second coil has $20$ turns, what is the flux through each turn when the current in the first coil equals $1\mathrm{.}15$ AA$?$ If the current in the second coil increases at a rate of $0\mathrm{.}355$ A$/$sA$/$s$,$ what is the magnitude of the induced emf in the first coil?