Why change in magnetic flux produces a current?
This is very interesting question though very basic. Suppose there is a conductor which is left open, therefore an emf will be induced in that conductor but current won’t flow if the magnetic field through the conductor changes.
The electrons in a conductor remains always in random motion with some velocity say V. If it is kept under changing magnetic filed then it B (Magnetic filed) will exert a force F=qVBsinØ where Ø is angle between the velocity and magnetic field. Thus electron will move toward a particular direction decided by the cross product of Velocity vector and Magnetic Field vector. As the electrons get accumulated, a potential will be developed and hence an EMF but as the magnetic field is changing thereby EMF will also change. This is the reason, changing EMF is developed by changing magnetic field or flux.