Source: High school physics (Chinese)
Problem Sets:
Problem
A bar magnet is pushed into a closed solenoid from its right end and pulled out from its left end, so the magnet moves steadily to the left all the way through the coil.
Yes. The induced current reverses direction once: it flows one way while the magnet is entering (approaching) and the opposite way while the magnet is leaving (receding), the reversal occurring as the magnet passes through the middle of the solenoid.
The induced current depends on whether the flux through the coil is increasing or decreasing (Lenz's law). While the magnet approaches and enters, the flux through the coil increases, and the induced current flows in one direction (the near end of the coil takes the same polarity as the approaching pole, repelling it). After the magnet passes the middle and recedes out the far end, the flux decreases, so the induced current reverses (the near end now attracts the receding magnet). The rate of change of flux thus changes sign as the magnet passes through.