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If you have a solenoid placed like this:

Solenoid

and you drop a magnet inside the coil will the change in acceleration of the bar of magnet inside the solenoid coil over change in time be 0? i.e. will the acceleration be slightly less than gravity but stay constant throughout?

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Magnetic dipoles (like the atomic dipoles inside a magnet) are subject to a net force if placed in a non-uniform magnetic field (like the field emerging from the north pole of another magnet or a current carrying solenoid). The segments of a magnetized bar which is in the vicinity of the end of a current carrying solenoid will feel this force. Segment inside the solenoid where the field is nearly uniform will not. If the south pole of a magnet is entering the north pole of a solenoid it will be pulled in. If the north pole of a magnet is trying to leave the south pole of the solenoid, it will be pulled back. The acceleration will change as the bar is falling through. If the solenoid is shorted instead of being powered, The induced current will oppose the change in the existing flux, and the induced force will oppose the entry or the exit of the magnet.

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