Can Induced EMF Be Greater Than Actual EMF and Create Opposing Currents?

[judas_priest]

If the induced emf = -d(phi)/dt that is the rate at which the flux through a body is increasing, can the induced current ever be more than the actual current so as to oppose the field created?
Because the rate at which the flux through a body is increasing can be greater than the flux it already holds (what i mean to say is d(phi)/dt > phi). So is it possible that the induced emf be more than the actual emf creating the current?

 

[judas_priest]

Also, do Induced emf actually create current flowing in the opposite direction of the current that is causing the magnetic field? (Not the the induced magnetic field)