Consider a metal ring kept on top of a fixed solenoid (say on a carboard) The centre of the ring coincides with the axis of the solenoid. If the current is suddenly switched on then

Explanation

When the current is switched on, magnetic flux is linked through the ring. Thus, increases in flux takes place, According to Lenz's law, this increse in flux will be opposed and it can happen in the ring moves away from the solenoid.
This happen because the flux increases will cause a counter clockwise current (as seen from the top in the ring in figure .)i.e., opposite direction to that in the solenoid.
This makes the same sense of flow of current in the ring (when viewed form the bottom of the ring ) and solenoid forming same magnetic pole infront of each other. Hence, they will repel each other and the ring will move upward.