dear student
A constant magnetic field does not affect a stationary charge unlike an electric field. For a magnetic field to exert a force on a charge, the charge must have to be moving relative to the field. Hence constant flux means constant field through a constant area and therefore the charges in the loop are unaffected. When you changes the flux, you are changing the field or the area. In either case the relative velocity of the charges is non-zero, thus they affected by change in flux.