The changing magnetic field in the coil due to the change in current induces a current in the metal ring. 

Lenz’s Law states that the magnetic field in the ring opposes the magnetic field of the coil and forces the ring to fly away.

Lenz's law, physical law, discovered by the German scientist H. F. E. Lenz in 1834, that states that the electromotive force (emf) induced in a conductor moving perpendicular to a magnetic field tends to oppose that motion. When an electric motor is in operation, the armature is turning in a magnetic field, and an emf is thus induced in it. Lenz's law requires that this emf, called back emf or counter emf, oppose the motion of the armature and also the original emf, causing the motor to operate. As a result, the speed of the motor changes in such a way that the energy supplied by the original voltage source less the energy required to overcome the back emf is always exactly equal to the sum of the energy used to drive the mechanism to which the motor is attached and the energy lost as heat within the motor. Lenz's law may thus be seen as a consequence of the law of conservation of energy.

"An induced current is always in such a direction as to oppose the motion or change causing it"

Faraday's law of induction indicates that the induced Electromotive force (emf) and the change in flux have opposite signs, and it also gives the direction of the induced (emf) and current resulting from electromagnetic induction.