I was just in a conversation with someone regarding the magnetic field resulting outside of a solid cylinder, with a current moving down the center of the cylinder, and then the resulting magnetic field after removing the current. Now I haven't thought about magnetic fields/magnets for a while and felt a little rusty talking about them, and so I was hoping to get some clarification on this if I'm not thinking correctly about it. To this point, my analysis is mostly just qualitative. Imagine we have a solid cylinder that could be magnetized, and we were able to run a wire down the center insulated from the rest of the cylinder, running current through the wire. My understanding is that the resulting magnetic field outside the cylinder would be zero, with current running through the wire. But when the current is turned off, a nonzero magnetic field is produced outside the cylinder opposite in direction to the field produced by the current. I have attached two pictures depicting these two cases (excuse my poor drawing ). I have drawn a cross section of the cylinder. The red 'x' in the center represents the current running into the board. The blue arrows represent the magnetic field due to the current, and the dipoles lining themselves with the magnetic field. The black circle is the edge of the cylinder, and the green arrows represent the magnetic field outside the cylinder, due to the dipoles when there is no current. So I am imagining the dipoles within the cylinder are lining up with the magnetic field produced by the wire, and so inside we have the magnetic field due to the current plus the field due to the dipoles. The dipoles we would have at the edge of the cylinder seems to produce a net current at the edge in the opposite direction to the current in the wire, and therefore we have a magnetic field in the opposite direction outside the cylinder, producing a total magnetic field of zero outside the cylinder (I understand I haven't actually shown that quantitatively here, but it's my guess at the moment). I imagine that if we now turned the current off at the center of the cylinder, the dipoles would remain in their state like any other magnet, and so we would now have a magnetic field outside the cylinder in the direction I indicated in green. I'm not sure to what degree this would also depend on what type of magnetic material we were using. The person I was talking to claimed that with a current at the center, there would be a magnetic field outside the cylinder, but if we turned off the current there would not be a magnetic field inside or outside the cylinder. They did not give much of an argument for this and so I wasn't convinced, but now I'm curious if I'm thinking correctly about this, because I wouldn't be surprised if I'm missing something. I also wouldn't be surprised if this can't be answered qualitatively. Thanks!