I did not posted this therefore I never mentioned any dimensions of anything. The author was. If he wants to make the magnet "float" it needs to be about the same diameter to avoid spinning. By the way I wasn't answering to your post. I think I know now why Grumpy is in your name. Maybe a similar word beginning with J will describe you be better.
It would be awesome if this magnet had an led on it too.
Mike,This member is "brainstorming" in another post regarding specific gravity. He is insistent if not self-indulging at the same time. I am not certain he will understand the magnetic force on a magnetic dipole depends not on magnetic induction, but the gradient of it, which is lacking in the center of the solenoid. Varying current is not going to vary this gradient so much. If you are close to the solenoid opening, then you do have this gradient. You can shoot something with a solenoid but the op wants some control.
This does sound like a high energy project b/c I want the magnet to float.