Motion of a magnet inside a solenoid

Question

I have a homework problem where a bar magnet is placed halfway inside a horizontal solenoid. A cut away shows that the magnet's north pole points to the left of the page and the south pole is outside the solenoid. The coils of the solenoid point into the page on the top, and come out of the page from the bottom. The problem asks how the magnet will move when the power is turned on and current flows through the solenoid.

Using the right hand rule with my thumb pointing along the wire, I have found that the field due to the solenoid points to the left (the arrow in red), so the magnet will be pulled in that direction. I am unsure whether the magnet will shoot out the end of the solenoid, or if it will sit in the middle. I understand the magnetic field drops off outside the solenoid, so there would be no force moving it, but I am inclined to think the magnet's momentum could keep it moving, and it will leave the solenoid. A lab partner told me I could think of the ends of the solenoid as magnetic poles, so the magnet would reach equilibrium in the middle. Could someone tell me what will happen to the magnet and why?

BooleanDesigns · Answer

The magnet will most likely come flying out. Without some more sophisticated information, it is impossible to do the calculations to confirm this, but my logic here is as follows:

The north pole of the solenoid is in the direction of your arrow, and so the magnet will want to move to the right. This is mostly because the north pole inside of the magnet wishes to approach the south pole of the dipole. At this point, we're both on the same page, the only question is equilibrium or no equilibrium? My intuition is that it will fly out because the field on the inside of a solenoid is very strong in comparison to the outside, several hundred times even. As such, there will be a very large initial impulse to move the north pole of the magnet to the south pole of the solenoid; however, once the north pole has passed, the magnetic field would have to do an equal amount of work on the magnet to bring it back to rest. Because the field is so much weaker on the outside, this chance of the field doing so much work before the magnet gets too far away seems very low...

Motion of a magnet inside a solenoid

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