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Physics/Magnetic repulsion and field strength decrease

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Hello Steve,

I have a question that is probably very basic, but I don"t seem to be able to find an answer online for my specific question, and I am wondering if you could help me understand something related to magnetic attraction and repulsion.

I was playing around with some disc magnets and a (ferrous) metal screw the other day and noticed that when a magnet attracted the screw, the screw became magnetized itself and attracted another magnet. The distance between the two magnets was too far for them to attract each other, but the presence of the screw extended the magnetic field (I do not know if "extended" is the right word to use). In this scenario, the magnets' poles were arranged so that they would have attracted each other had they been close enough, but when I turned one of the magnets around so that they would repel each other, and then tried the same thing with the screw in the middle, there was no repulsion - both magnets were simply attracted to the screw. I then tried the same thing with a much smaller piece of ferrous metal (a scissor blade) and the magnets repelled each other.
Can you tell me what is going on here?
Is it fair to say that the attraction of the magnets to the ferrous metal competes with the repulsion of the magnets against each other? In the case of the larger ferrous object (the screw), the repulsion is weak due to the larger distance between the magnets, so the attraction of the magnets to the metal is much stronger than the extent to which they repel each other. Is my thinking correct here?
I have assumed the ferrous metal object cannot "transfer" repulsion in the same way it transfers attraction. If this correct, would the repelling field of the magnets decrease with distance at the same rate as they would in free space? Even though there is ferrous metal in contact with the magnets, should I still use the formula 1/r3 to calculate the magnets' field decrease with distance?

Sorry if this is very basic stuff - not quite alternative theories of physics! I have another, more complex, and I hope more interesting, question to ask, but I need to confirm my understanding first.

Thanks for reading my question and best regards,
Eddie

Answer
I don't usually do a cut-and-paste breakdown, but that's a lot of questions, so let's get started:

"Is it fair to say that the attraction of the magnets to the ferrous metal competes with the repulsion of the magnets against each other?"

That's kind of it, in sweeping terms.  In more detail, the spins in the metal you put between the magnets will realign, generating its own internal field structure.  The actual field structure can become quite complex, but the fields from the ends of the screw will reduce the repulsive forces on the magnets themselves.  It will result in stress within the screw itself, however, but that's something you can't directly observe.


Next:
"In the case of the larger ferrous object (the screw), the repulsion is weak due to the larger distance between the magnets, so the attraction of the magnets to the metal is much stronger than the extent to which they repel each other. Is my thinking correct here?"

Yes, the parts of the screw which are closer to a particular magnet will be attracted to it.  Due to the strong distance dependence, especially.  You might find things to be very different if you put the ferrous metal directly on one of the magnets, which could dominate the magnetization of the metal.  That would effectively bring the pole it is attached to closer to the other magnet and increase the repulsion instead of decreasing it when it is in the middle.

Next:
"I have assumed the ferrous metal object cannot "transfer" repulsion in the same way it transfers attraction. If this correct, would the repelling field of the magnets decrease with distance at the same rate as they would in free space? Even though there is ferrous metal in contact with the magnets, should I still use the formula 1/r3 to calculate the magnets' field decrease with distance?"

See the previous question's answer, actually.  The fields of the magnets are unchanged.  What's happening is that you're superimposing a field due to a magnetized ferrous metal.  Because of the complex geometry now involved, simple rules about distance are not terribly useful.  Hope this helped.

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Dr. Stephen O. Nelson

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I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

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I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

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Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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