how does displacement current produces magnetic field and induced emf produces electric current???

displacement current  is defined in terms of the rate of change of electric displacement field.Displacement current has the units of electric current density and it has an associated magnetic field just as actual currents do. It is not an electric current due to  moving charges, but a time-varying electric field.

In materials, there is also a contribution from the slight motion of charges bound in atoms, dielectric polarization.