On the surface of a magnetar, what would pull harder on a 10 kg piece of iron, the gravity or the magnetic field?
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2 Answers
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Iron is nothing special to a magnetar: iron's magnetization saturates at about 2 tesla. Magnetar fields are 10^9-10^11 tesla. So, gravity wins.
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$\begingroup$ Note that the largest confirmed magnetic field on a neutron star is at the low end of your range, at 1.6 GT. See the link in this chat transcript. $\endgroup$– rob ♦Commented Jul 19, 2022 at 22:13
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2$\begingroup$ Does this mean that beyond a certain strength, a magnetic field's pull on iron does not increase? $\endgroup$ Commented Jul 19, 2022 at 22:45
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13$\begingroup$ @A.JPerez Basically yes. There's still a bit a paramagnetic attraction. But by 0.05 GT, iron atoms don't even exist: energy associated with the cyclotron motion of electrons exceeds the K shell binding energy. $\endgroup$ Commented Jul 19, 2022 at 22:59
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2$\begingroup$ @JohnDoty can you explain this a bit more or throw a link to an article about this? I'm super curious. $\endgroup$– Jarob22Commented Jul 20, 2022 at 12:20
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2$\begingroup$ @Jarob22 I don't have a good reference. This is stuff we discussed back in the 70's when we were trying to puzzle out what accretion-powered pulsars and low mass x-ray binaries were. $\endgroup$ Commented Jul 20, 2022 at 15:28
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Ferromagnitism
Below saturation, the pull is ~B dB/dx. Beyond saturation, it is ~dB/dx and can be made arbitrarily high with a strong enough gradient. An order of magnitude gradient is 1GT/10km = 10^5T/m. So a pull on the order of 10^5-10^6 stronger than a Neodymium magnet. We have about 2*10^11g of gravity so gravity wins.
Superconductors and Paramagnetism
They also suffer a saturation effect. Superconductors can only carry a certain density of current and paramagnetic materials saturate much like ferromagnetic materials. Paramagnetism aligns dipoles and saturates once there are no more dipoles to align.
Diamagnetism
This is much weaker but also doesn't saturate. It is about 10^4 times weaker at best and thus would equal ferromagnetism around 10^4 or 10^5 T. At 10^10 T it would be around (10^10T*10^5T/m)/(10^4) = 10^11 times stronger than a Neodymium magnet. This is just enough to beat gravity. However, "doesn't saturate" is not true at such extreme fields, see below.
Edit: Argument that diamagnetism is limited: Diamagnetism costs energy. Free electrons and nuclei are not diamagnetic. If this energy cost exceeded the binding energy of all the electrons to the iron nucleus the atom would fly apart. This limits the total diamagnetic energy to below ~100keV/atom. I do not expect the atoms to actually ionize in the field, instead the electrons would find a non-diamagnetic configuration, but the 100keV limit still applies. Gravity is far stronger at ~10GeV per iron atom.
Materials, what materials?
Magnetic fields this strong severely distort the shape of the atoms due to Lorentz force affecting the electron shells. Laboratory-generated fields top out around 1000 Tesla and only for under a millisecond. Whatever the case gravity still wins. After all, the crust doesn't lift off the surface!
answered Jul 20, 2022 at 18:08
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$\begingroup$ at some point, wouldn't the distortions that lead to diamagnetism simply cause the atoms to ionize rather than continue to provide an effect? $\endgroup$ Commented Jul 20, 2022 at 18:30
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$\begingroup$ @JerrySchirmer: They would still be attracted to the nucleus so why would they ionize? $\endgroup$ Commented Jul 20, 2022 at 18:33
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$\begingroup$ Does the magnetic pull and the gravitational pull add together to increase the overall pull on the 10 kg iron mass? If yes, what would be the total weight of the iron? $\endgroup$ Commented Jul 20, 2022 at 18:46
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1$\begingroup$ @A.JPerez: The total weight is almost unchanged since any ferromagnetism is outweighed by gravity. But I don't think it's iron anymore. $\endgroup$ Commented Jul 20, 2022 at 21:51